Yang Shi | Research

Module 01 / Card 01

This card is organized as two mechanism branches. The first branch builds the collision-kernel logic for acoustic, hydrodynamic, Brownian, and turbulent agglomeration, explaining why droplets collide and grow under acoustic waves and turbulent flow. The second branch extends the same microphysical perspective to isotope exchange between micro-droplet groups and environmental vapor, showing how acoustic forcing can alter hydrogen and oxygen isotope signatures in collected water.

The acoustic agglomeration model defines collision frequency through an aggregation kernel. Orthokinetic agglomeration describes particle collisions caused by differential oscillatory motion in the sound field, while hydrodynamic agglomeration accounts for wake/refill interaction between droplets. Brownian and turbulent agglomeration further represent thermal diffusion and vortex-driven particle collision in real fluid media.

The figures first define the orthokinetic collision picture and then translate it into a frequency-response rule, showing how droplet-pair interactions vary across fog, cloud, rain, child droplets, and condensation nuclei.

Fig. 1. Schematic diagram of the orthokinetic agglomeration process.

Influence of acoustic frequency on orthokinetic acoustic agglomeration kernel function — Fig. 2. Influence of acoustic frequency on the kernel function of orthokinetic acoustic agglomeration: (a) interactions between fog, cloud, and rain droplets; (b) interactions between child droplets and condensation nuclei.

1. Droplet agglomeration induced by acoustic waves

1.1. Orthokinetic agglomeration

The propagation of sound waves instigates vibration of the ambient air. In a polydisperse aerosol, droplets of different sizes respond with different inertia and phase lags, producing relative displacement inside the agglomeration volume. The collision probability between particle groups is quantified by the kernel function.

Equation 1 collision kernel extracted from source PDF

(1)

Equation 2 agglomeration volume extracted from source PDF

(2)

Kernel function of orthokinetic agglomeration

(3)

1.2. Hydrodynamic agglomeration

Hydrodynamic agglomeration supplements the orthokinetic mechanism by considering flow disturbance, wake capture, and rapid refill around moving droplets. The hydrodynamic interaction kernel links acoustic velocity, particle diameter, relaxation response, and particle-pair geometry.

Aggregation kernel function of hydrodynamic interaction

(4)

2. Droplet agglomeration induced by turbulent flows

Under high-energy turbulent flow, particle migration is no longer controlled only by acoustic relative displacement. Brownian diffusion and turbulent collision should be considered together to represent droplet agglomeration in a real fluid environment.

2.1. Brownian agglomeration

Brownian agglomeration describes collision and coalescence caused by irregular thermal motion of particles suspended in a fluid. It becomes important for small particles and condensation nuclei, where diffusion can maintain particle encounters even without strong acoustic relative motion.

Equation 5 Brownian agglomeration kernel extracted from source PDF

(5)

Equation 6 Stokes-Einstein diffusion coefficient extracted from source PDF

(6)

2.2. Turbulent agglomeration

Turbulent agglomeration represents collision driven by eddies and pulsations across different scales. Particles smaller than the Kolmogorov microscale are mainly controlled by viscous-layer collision, while larger particles are influenced by inertial-layer mechanisms.

Equation 7 turbulent agglomeration kernel extracted from source PDF

(7)

Equation 8 Kolmogorov microscale extracted from source PDF

(8)

The isotope-exchange branch describes dynamic molecular exchange between micro-droplet groups and environmental water vapor. Light molecules tend to remain in the vapor phase, while heavier isotope molecules are preferentially retained by droplets; acoustic forcing accelerates exchange and increases the heavy-isotope content of accumulated water.

The isotope figures connect mechanism and evidence: the process diagram defines the exchange pathway between micro-droplet groups and ambient vapor, while the isotope-relationship plot compares accumulated water with source precipitation under different experimental conditions.

Micro-droplet vapor isotope-exchange model processes between micro-droplet groups and environmental water vapor — Fig. 3. Schematic diagram of isotope exchange processes between the micro-droplet groups and environment water vapor.

Hydrogen and oxygen isotope relationship of accumulated water with precipitation source under different conditions — Fig. 4. Hydrogen and oxygen isotopes relationship of accumulated water with precipitation source under different conditions.

3. Droplet-environment isotope exchange theory

The governing equations assume that water molecules in micro-droplets and environmental vapor are composed of H₂O, HDO, and H₂¹⁸O. The exchange is treated as equivalent to molecular exchange, with unchanged chamber temperature and saturated water content during the process.

The isotope-exchange governing equations are grouped below, following the same compact formula style used in the field-observation card.

(16)

(17)

Key Findings

Section | Acoustic and turbulent agglomeration mechanisms

Orthokinetic agglomeration explains how different droplet sizes oscillate with different phase lags, creating relative motion and collision opportunity under sound waves.
The frequency-response curves show an effective low-frequency window for fog, cloud, rain-droplet, child-droplet, and condensation-nucleus interactions.
Hydrodynamic interaction adds wake/refill effects to the acoustic collision kernel and helps describe droplet capture around moving particles.
Brownian and turbulent agglomeration extend the model from ideal acoustic oscillation toward realistic atmospheric multiphase environments.

Section | Micro-droplet isotope exchange theory

Micro-droplet isotope exchange is modeled as dynamic molecular exchange between droplets and environmental vapor containing H₂O, HDO, and H₂¹⁸O.
Light molecules are more active in the vapor phase, whereas heavy isotope molecules are preferentially retained by droplets during exchange.
The governing equations connect isotope ratio, isotope composition, molecular mass loss, ventilation coefficient, and hydrogen/oxygen isotope enrichment rates.
The accumulated-water isotope plots support acoustic-wave influence on hydrogen and oxygen isotope relationships under different source-water conditions.

Source: [1] Shi, Y., Wei, J., Bai, W., Zhao, Z., Ayantobo, O.O., & Wang, G. (2023). Theoretical analysis of acoustic and turbulent agglomeration of droplet aerosols. Advanced Powder Technology, 34, 104145. https://doi.org/10.1016/j.apt.2023.104145; [2] Bai, W., Wei, J., Li, Q., Shi, Y., Ni, S., & Lei, F. A study on the collision and deposition of droplets and its hydrogen and oxygen isotopes characteristics under the action of sound waves. Journal of Applied Acoustics, 2021, 40(01), 103-112. (In Chinese)

Module 01 / Card 02

This card translates the mechanism card into laboratory evidence through two connected experimental branches. The first branch establishes a controlled chamber system for micro-droplet generation, acoustic forcing, monitoring, and isotope sampling. The second branch uses large factorial tests to identify critical SPL thresholds and the droplet-size sensitivity range, turning the experimental response into design parameters for later field operation.

Controlled chamber experiments compare acoustic operation with natural sedimentation, linking the experimental device, micro-droplet generation, acoustic forcing, laser monitoring, environmental vapor sampling, and isotope analysis into one repeatable laboratory workflow.

The device figure introduces the experimental boundary conditions for the paper: water supply, micro-droplet generation, acoustic forcing, laser sizing, humidity-temperature monitoring, vapor sampling, isotope analysis, and final water collection are integrated in one chamber workflow.

Figure 1. Schematic and site photograph of the experimental device: 1-water tank; 2-water pump; 3-micro-droplets sample collection bottle; 4-nozzle; 5-acoustic generator; 6-air chamber; 7-laser-emitting end; 8-laser-receiving end; 9-data analysis computer; 10-temperature and humidity sensors; 11-environmental water vapor sampling port; 12-water vapor isotope analyser; and 13-beaker. The micro-droplets generation device included 1, 2, and 4; acoustic generator included 5 and 9; monitoring devices included 7-12; and water sample collection included 3 and 13.

The droplet-size figure provides the response variable for the chamber experiment. D90 and the size spectrum show whether acoustic forcing shifts the micro-droplet population toward larger droplets compared with natural sedimentation.

Variations in D90 and micro-droplet size spectrum — Figure 2. (a) Variations in D90 and (b) micro-droplets size spectrum and its cumulative frequency.

Experimental process and conditions

The threshold test alternates natural settlement and acoustic-intervention runs. Frequency is scanned from 30 to 280 Hz at 10 Hz intervals, and SPL is adjusted from 70 to 130 dB at 5 dB intervals. Each scenario includes three control or replicate experiments; sample collection lasts more than 180 s after instrument calibration, with room temperature held near 20°C. The complete test matrix contains 840 groups and more than 300,000 droplet samples.

Experimental data processing

For a fixed frequency, the critical SPL is identified when the average droplet size increases by more than 0.1 μm. SPL₀ is accepted as the critical value when SPL₁ = SPL₀ + 5 dB produces a larger size increment and stable agglomeration. A one-way ANOVA at the 0.05 level is then used to identify the DSSR, namely the droplet-size range with a significant acoustic response.

The threshold figures turn repeated experiments into operational design parameters. The critical-SPL plot identifies the sound-pressure level range where droplet growth becomes statistically effective at each acoustic frequency, while the DSSR-width plot shows how broad the sensitive droplet-size range is under different frequencies.

Figure 3. The Critical SPL threshold identifications at different acoustic frequencies. The shaded area represents the effective SPL range for acoustic interference.

Figure 4. Width of DSSR with respect to different acoustic frequency.

Key Findings

Section | Microphysical Chamber Experiment

Acoustic operation produces a positive trigger effect on D90 and droplet growth.
Isotope and size-spectrum diagnostics give complementary evidence for acoustic intervention.

Section | Critical SPL Threshold Identification

Droplet response depends on sound distribution, concentration, frequency, and entrainment.
Critical SPL threshold identification and response time provide practical design thresholds for acoustic devices.

Source: [1] Bai, W., Wei, J., Shi, Y., Zhao, Z., & Li, Q. (2021). Microphysical characteristics and environmental isotope effects of the micro-droplet groups under the action of acoustic waves. Atmosphere, 12, 1488. https://doi.org/10.3390/atmos12111488; [2] Bai, W., Wei, J., Yang, H., He, J., Shi, Y., & Li, Q. Experimental and theoretical analysis of hydrogen and oxygen isotope effects of droplet group under the action of low-frequency acoustic waves. Journal of Basic Science and Engineering, 2022, 30(06), 1357-1365. (In Chinese); [3] Bai, W., Shi, Y., Zhao, Z., & Wei, J. (2022). Investigation of critical response characteristics of micro-droplets under the action of low-frequency acoustic waves. Frontiers in Environmental Science, 10, 972648.

Module 01 / Card 05

This card focuses on the summer field-operation paper. It follows a complete evidence chain from field-site geography and instrument deployment, to acoustic test procedure and radar scanning, to precipitation-sequence processing and radar-reflectivity response, showing how laboratory acoustic mechanisms are evaluated under real plateau precipitation conditions.

The deployment section establishes the field basis for summer acoustic precipitation tests in the source region of the Yellow River. It links the study-area terrain, acoustic and radar equipment, operation procedure, radar scan strategy, and precipitation-sequence processing into one repeatable field-evaluation workflow.

The study-area figure establishes the terrain and location context for summer acoustic tests, which is essential because topography controls water-vapor transport, cloud development, and radar observation geometry in the SRYR.

Fig. 1. Geographical location of the acoustic study area. The 3 arc sec SRTM DEM (v1) covering the SRYR was used.

The device photograph figure documents the field implementation of the acoustic-interference system and the monitoring network, including the speaker, KaKu weather radar, Ka cloud radar, and disdrometer.

Fig. 2. Photograph of acoustic and monitoring devices: bird view of field site (a), fluidic air-modulated speaker (b), KaKu weather radar (c), Ka cloud radar (d), and disdrometer (e).

The procedure figure explains how acoustic tests and radar observation are synchronized. It connects the intervention timeline with radar scanning so that cloud and precipitation changes can be attributed more carefully.

Fig. 3. Procedure for acoustic precipitation tests and radar operation principle.

The sequence-processing figure defines how natural, operation, restoration, and comparison samples are separated. This step is the methodological bridge between raw rainfall records and effect evaluation.

Fig. 4. Data processing method of a precipitation sequence.

The evidence section moves from macro-scale radar and rain-gauge responses to microphysical DSD structure. It combines Ka-band reflectivity evolution, vertical DSD concentration changes, and spatial rain-rate redistribution to evaluate whether acoustic operation modifies cloud-water gathering, raindrop spectra, and near-field precipitation patterns.

The Ka-band reflectivity figure gives the main radar evidence for the summer case, showing how cloud and weather radar echoes evolve around the acoustic operation window.

Fig. 5. Temporal evolution of Z measured by cloud and weather radars in Ka band for PPI mode with pitch angle of 21.8°. The dashed window indicates the angle interval and the radar azimuth angle in RHI mode.

The vertical DSD-profile figure extends the radar-reflectivity evidence to microphysical structure. During acoustic operation, the overall zenith distribution of raindrop concentration is not strongly changed, but concentration shifts appear for specific particle-size ranges and height layers. The spectra show increases for small droplets and larger drops in selected periods, decreases for medium-size droplets at higher altitudes, and a broad reduction across the vertical section near the end of the rainfall process.

Fig. 6. Temporal evolution of vertical DSD profile for stratiform precipitation. (a) t = 0-20 min, (b) t = 20-40 min, (c) t = 40-60 min, and (d) t = 60-80 min.

The spatial rain-rate maps divide the 120 min operation rainfall sequence into six 20 min windows. Before acoustic operation, average rain rates within 5 km of the operation center are relatively similar except for a western measurement point. After the acoustic device is turned on, higher rain rates appear around selected stations and become more concentrated near the operation center, especially shortly after activation and again after shutdown, suggesting liquid-water gathering above the operation zone.

Spatial distribution of average rain rate during operation cases — Fig. 7. Spatial distribution of the average rain rate during operation cases: (a) t₁ = 0-20 min, (b) t₂ = 20-40 min, (c) t₃ = 40-60 min, (d) t₄ = 60-80 min, (e) t₅ = 80-100 min, and (f) t₆ = 100-120 min.

Key Findings

Section | Field Rainfall-Enhancement Operation Deployment

Cloud-radar and weather-radar consistency checks support multi-sensor evaluation.
The tests provide a bridge from laboratory droplet agglomeration to plateau-scale precipitation intervention.

Section | Macro- and Micro-Scale Evidence Evaluation

Radar reflectivity, liquid water content, and rain rate are sensitive to acoustic application, especially in stratiform clouds.
Vertical DSD and spatial rain-rate diagnostics add microphysical and near-field evidence for acoustic operation effects.

Source: [1] Shi, Y., Wei, J., Qiao, Z., Shen, W., Yin, J., Hou, M., Ayantobo, O.O., & Wang, G. (2022). Investigation of strong acoustic interference on clouds and precipitation in the source region of the Yellow River using KaKu radar. Atmospheric Research, 267, 105992; [2] Shi, Y., Wei, J., Li, Q., Yang, H., Qiao, Z., Ren, Y., et al. (2021). Investigation of vertical microphysical characteristics of precipitation under the action of low-frequency acoustic waves. Atmospheric Research, 249, 105283; [3] Pan, P., Shi, Y., Zhao, Z., Wang, J., Cao, J., Bai, W., Xie, H., & Wei, J. Microphysical characteristics of precipitation under the intervention of acoustic over an inland arid region. Arid Land Geography, 2021, 44(04), 906-913. (In Chinese)

Module 02 / Card 01

The research integrates river ecological replenishment in North China with hydrodynamic routing and water-balance analysis, focusing on how reservoir releases reconnect dry or seasonal channels, expand wetted area, and improve ecological and groundwater recharge effects under limited water supply.

This section extracts the laws and operating modes of river ecological replenishment from hydrodynamic and water-balance perspectives. It connects first-arrival prediction, streamflow routing and collection-rate analysis, lake-river recovery, wetted-area estimation, seepage loss, and groundwater conservation into an effect-assessment framework.

Mainstream arrival timePredict when the replenishment wave reaches key downstream control sections.

Flow process and collection rateAnalyze streamflow routing, water-loss ratio, and the effective received-water process.

River-lake recoveryEstimate water-surface expansion and restoration response during ecological replenishment.

Water balance and rechargeQuantify storage change, evaporation, seepage loss, and groundwater conservation.

The overview figure links the Yongding River and Chaobai River replenishment areas with a hydrodynamic-routing and water-balance concept model. Muskingum routing, received flow, seepage, groundwater-level response, and impermeable-layer controls are combined into one operational logic.

Fig. 1. Hydrodynamic and water-balance framework for ecological river replenishment, linking mainstream arrival-time prediction, flow-process and collection-rate analysis, river-lake recovery and water-surface area estimation, and groundwater conservation.

Water-balance calculation and water-surface area estimation are summarized as:

W_inflow - W_outflow = ΔW + W_loss(1)

W_total = ∑_i=1^n-1[S_i + S_i+1 + (S_iS_i+1)^0.5]L_i / 3(2)

W_evap = A × (E - P)(3)

W_seep = W_loss - W_evap(4)

S_total = (B_i + B_i+1)L_i / 2(5)

The replenishment-pattern summary figure organizes ecological river replenishment into hydrodynamic target constraints, multi-objective water-balance constraints, and basin-scale safety protection. It further extracts operating modes under different constraints, including outlet flow, along-route loss, evaporation, seepage, and flow-travel time.

Ecological river replenishment characteristics and pattern summary — Fig. 2. Summary of ecological river replenishment characteristics and patterns under hydrodynamic constraints, multi-objective water-balance constraints, and basin-scale safety protection.

This section compares ecological replenishment effects and optimized operating modes in the Chaobai River and Yongding River. The analysis links evolution time, water-collection rate, water-surface control, seepage loss, initial channel condition, and release-volume constraints to support river-specific replenishment-mode selection.

Chaobai River. The result figure compares evolution time, water-collection rate, water-surface area, and seepage-loss rate under dry-channel, wet low-water-level, and wet high-water-level initial states. Larger replenishment volumes accelerate mainstream evolution, increase outlet collection, expand wetted area, and reduce seepage loss.

Fig. 3. Chaobai River ecological replenishment responses under different channel conditions: evolution time, outlet water-collection rate, water-surface area, and seepage-loss rate versus upstream replenishment volume.

The Chaobai target-constraint figure translates replenishment into hydrodynamic and multi-objective water-balance decisions. Sustained-flow replenishment is preferred over square-wave or triangular-wave releases, and suitable replenishment ranges balance outlet delivery, groundwater recharge, and channel storage.

Fig. 4. Chaobai River hydrodynamic and multi-objective water-balance target constraints for ecological replenishment, comparing water-surface area, water-collection rate, seepage-loss rate, replenishment volume, initial water-deficit depth, and flow time.

Yongding River. The result figure summarizes the same four replenishment responses. Under the same release volume, dry-channel routing has the shortest evolution time but smaller water-surface area and generally higher seepage loss than wet-channel states.

Fig. 5. Yongding River ecological replenishment responses under different channel conditions: evolution time, outlet water-collection rate, water-surface area, and seepage-loss rate versus upstream replenishment volume.

The Yongding target-constraint figure summarizes hydrodynamic and multi-objective water-balance controls for ecological replenishment, defining preferred release ranges for dry and wet initial channel states.

Fig. 6. Yongding River hydrodynamic and multi-objective water-balance target constraints for ecological replenishment, comparing water-surface area, water-collection rate, seepage-loss rate, replenishment volume, initial water-deficit depth, and flow time.

Key Findings

Section | Effect Assessment and Measurement Framework

Stable releases can reconnect channels, but optimal flow depends on first-connection time, seepage, and water-loss ratio.
Hydrodynamic target constraints and multi-objective water-balance constraints jointly define robust ecological replenishment modes.

Section | Ecological-Replenishment Effect Assessment and Optimization

A large-initial-flow then smaller-maintenance-flow strategy can improve full-line connection, groundwater recharge, and channel-storage allocation.
Yongding River and Chaobai River replenishment require different preferred release ranges under dry-channel and wet-channel initial states.

Source: [1] Xu, J., Wu, Y., Qiu, W., Li, S., Wang, M., Shi, Y., & Wei, J. Ecological water replenishment and discharge mode in Beijing section of the Yongding River. South-to-North Water Transfers and Water Science & Technology, 2023, 21(4), 669-678. (In Chinese) https://doi.org/10.13476/j.cnki.nsbdqk.2023.0066; [2] Wu, Y., Xu, J., Qiu, W., Wang, M., Li, S., Shi, Y., & Wei, J. A study on ecological water replenishment scheduling scheme of Chaobai River in Beijing section. Water Resources and Hydropower Engineering, 2023, 54(9), 180-189. (In Chinese)

Module 02 / Card 02

SWAT-MODFLOW is used to resolve runoff generation and conversion fluxes in the Yongding River basin, a sensitive system with mountain runoff, strong alluvial-fan infiltration, plain discharge, recent ecological replenishment, and pronounced extreme-precipitation response.

The model selects the Yongding River basin to represent the full cycle from mountain runoff generation to alluvial-fan infiltration and plain runoff discharge. The daily simulation is calibrated from 2020-01-01 to 2024-02-29 and validated from 2024-03-01 to 2025-02-28. The model reproduces seasonal groundwater fluctuation and rainfall-recharge peak-valley response, with full-period R² > 0.7, NSE between 0.623 and 0.777, and PBIAS from -2.62% to 1.51%.

The model-input figure defines the SWAT-MODFLOW spatial basis, including soil type, land use, DEM, aquifer thickness, hydraulic conductivity, and specific yield. Together these layers determine runoff generation, infiltration capacity, and groundwater response across the basin.

Fig. 1. SWAT-MODFLOW model inputs for the Yongding River basin: soil type, land use, DEM, aquifer thickness, hydraulic conductivity, and specific yield.

The stratigraphic section explains the physical basis of surface-water and groundwater exchange along the alluvial-proluvial fan. River infiltration and lateral recharge dominate the upper fan, precipitation and evapotranspiration affect the middle fan, and vertical infiltration, lateral discharge, and groundwater extraction become important downstream. This hydrogeological structure controls how river replenishment is stored, transferred, and released through aquifers and aquitards.

Stratigraphic section of river-aquifer exchange along the alluvial-proluvial fan — Fig. 2. Stratigraphic section of surface-water and groundwater exchange along the upper, middle, and lower alluvial-proluvial fan, showing river infiltration, lateral recharge, vertical infiltration, lateral discharge, and groundwater extraction.

The groundwater-validation figure combines spatial groundwater-elevation patterns with station-scale simulated and observed groundwater-level series. It shows that the calibrated model captures both spatial gradients and temporal fluctuations during calibration and validation periods.

Groundwater elevation and station-scale validation of SWAT-MODFLOW — Fig. 3. Groundwater elevation distribution and station-scale validation of simulated and observed groundwater levels during calibration and validation.

The monthly water-balance figure identifies the dominant runoff and exchange components. LATQ dominates normal runoff components, meaning precipitation infiltration preferentially converts into lateral flow. During the July 2023 extreme flood period, SWGW becomes the dominant source, indicating strong vertical infiltration through Quaternary sand-pebble-gravel layers.

Fig. 4. Monthly water balance and runoff-generation components in the Yongding River basin, highlighting LATQ dominance under normal conditions and SWGW dominance during the July 2023 flood period.

The groundwater-rise validation figure compares simulated and observed groundwater rise across monitoring stations. It confirms that the model can reproduce recharge-driven water-level recovery and supports diagnosing how ecological replenishment and extreme rainfall alter groundwater storage.

Fig. 5. Station-scale groundwater-level rise validation, including monitoring wells, simulated and observed groundwater rise, and predicted-versus-actual comparisons.

Seasonally, GWSTOR follows a summer-storage and winter-depletion pattern. SWGW increases as temperature, precipitation, and vegetation transpiration rise, reaching a peak exchange rate during the main flood season in August.

Key Findings

Section | SWAT-MODFLOW Runoff Generation and River-Aquifer Conversion Fluxes

SWAT-MODFLOW resolves runoff generation, river leakage, aquifer recovery, and conversion fluxes in the Yongding River basin.
The daily model reproduces seasonal groundwater fluctuations and rainfall-recharge peak-valley responses during calibration and validation.
LATQ dominates normal runoff components, indicating that precipitation infiltration preferentially converts into lateral flow.
During the July 2023 extreme flood period, SWGW becomes dominant, implying strong vertical infiltration through Quaternary sand-pebble-gravel layers.
GWSTOR shows summer storage and winter depletion, while SWGW peaks in August as precipitation, temperature, and vegetation transpiration increase.

Source: [1] Xu, J. Groundwater Renewal and Process Responses in the Beijing Plain under a Changing Environment. PhD dissertation, Tsinghua University, 2026. (In Chinese); [2] Supplied English SWAT-MODFLOW runoff-generation and river-aquifer conversion-flux figures.

Module 02 / Card 03

The work links macro-scale rainfall redistribution under Tibetan Plateau warming with microphysical raindrop-size distribution and radar QPE relations, forming a multi-scale view of plateau precipitation and atmospheric-water resources.

The macro branch evaluates Tibetan Plateau rainfall and temperature redistribution under CMIP6 future scenarios. It links terrain-controlled river systems with spatial changes in mean daily rainfall and surface air temperature, then diagnoses how warming reshapes rain-frequency distributions across light, moderate, and heavy rain-rate bins.

The plateau map establishes the orographic and river-system background for interpreting future rainfall redistribution across the Tibetan Plateau.

Geographical map of Tibetan Plateau elevation and major rivers — Fig. 1. Geographical map of the TP region showing the elevation and major rivers.

The CMIP6 change maps compare future rainfall and temperature signals across scenarios and models, revealing where warming and precipitation redistribution reinforce or diverge across the plateau.

Spatial pattern of rainfall and temperature changes under SSP scenarios in CMIP6 models — Fig. 2. Spatial pattern of absolute changes (%) in mean daily rainfall (a-f) and temperature (g-l) in BCC-CSM2-MR and FGOALS-g3 CMIP6 models between 2021-2060 and 1981-2020 under SSP126, SSP245, and SSP585 scenarios in the TP region.

The rain-frequency figure moves from maps to distributional change, showing how warming shifts the occurrence of different rain-rate classes across future decades.

Future decadal changes in rain frequency distribution normalized by surface air temperature — Fig. 3. Climatologies of future decadal changes in rain frequency distribution (%/K) normalized by mean surface air temperature as a function of rain-rates under (i) SSP126, (ii) SSP245, and (iii) SSP585 scenarios from (a) BCC-CSM2-MR and (b) FGOALS-g3 CMIP6 models between 2021 and 2060 in the TP region. Delta rf1, Delta rf2, and Delta rf3 denote rain-frequency changes between 2021-2030 and 2031-2040, 2031-2040 and 2041-2050, and 2041-2050 and 2051-2060, respectively.

The microphysical branch uses disdrometer-based drop-size-distribution diagnostics to separate convective and stratiform rainfall over Dari and Delingha, compare log10Nw-D0/Dm regimes, and connect mass-weighted mean diameter with multi-frequency radar attenuation and dual-frequency-ratio relations.

The log10Nw-D0 scatter figure separates convective and stratiform rainfall microphysics, giving a reference for how plateau rainfall differs between sites and regimes.

Fig. 4. Scatter diagram of log10Nw versus D0 for convective and stratiform rainfall over (a) Dari and (b) Delingha. The mean values of log10Nw versus D0 are plotted as error bars with +/-1 x standard deviation. The dashed line splitting the two rainfall types was given by Bringi et al. (2003): log10Nw = -1.6D0 + 6.3.

The log10Nw-Dm frequency plot adds occurrence probability to the microphysical classification, comparing plateau rainfall against maritime and continental convective regimes.

Fig. 5. Scatterplots of log10Nw against Dm color-coded by normalized occurrence frequency. The two rectangles represent the maritime and continental convective regimes; the red dashed line splitting the two rainfall types was given by Bringi et al. (2003). The mean values of log10Nw versus Dm are plotted with +/-1 x standard deviation as error bars.

The radar-relation figure links drop-size parameters to Ka/Ku retrieval variables, providing empirical constraints for attenuation, reflectivity, and dual-frequency-ratio-based rainfall estimation.

Scatterplots of Dm against attenuation to reflectivity ratio and dual-frequency ratio — Fig. 6. Scatterplots of Dm-k/Ze and Dm-DFR at Dari and Delingha. Ze (mm6 m-3) is the effective radar reflectivity factor, k is the specific attenuation (dB km-1), and k/Ze is the attenuation-to-reflectivity ratio; DFR (dB) is the dual-frequency ratio, equal to 10log10(Ze-Ka/Ze-Ku). The black lines represent fitted curves constraining the shape parameter mu = 3.

Key Findings

Section | Macro-Scale Precipitation Redistribution over the Tibetan Plateau

Rainfall changes affect plateau eco-hydrological processes and water-resource regimes.
Plateau precipitation should be diagnosed across both spatial-climatological and cloud-microphysical scales.

Section | Microphysical Rainfall Structure and Radar QPE Relations

Rain spectra become wider and flatter as rain rate increases, especially for convective rainfall.
Macro rainfall redistribution and microphysical DSD jointly constrain water-resource and precipitation-intervention analysis.

Source: [1] Climatological changes in rainfall distributions at different rain-rates under Qinghai-Tibet Plateau warming during 1981-2060. https://doi.org/10.1007/s00704-023-04383-7; [2] Li, Q., Wei, J., Yin, J., Qiao, Z., Cao, J., & Shi, Y. (2022). Microphysical characteristics of raindrop size distribution and implications for radar rainfall estimation over the northeastern Tibetan Plateau. Journal of Geophysical Research: Atmospheres, 127, e2021JD035575.

Module 02 / Card 04

The research connects two lake-focused technologies: catchment classification for Tibetan Plateau closed lakes and Hydroformer-based monthly lake-level reconstruction. The first branch explains why closed lakes with similar climate forcing can show dissimilar area changes through catchment descriptors, while the second branch reconstructs lake-level dynamics from incomplete observations using frequency-domain attention and causality-aware multi-attention learning.

The branch classifies 322 naturally closed lake catchments larger than 1 km² on the Tibetan Plateau from 1981 to 2020. It uses hierarchical minimum-variance clustering and six representative topography and land-surface descriptors, then links the resulting classes to hydro-meteorological and geographical-environmental attributes to explain why lake area changes are spatially coherent but temporally diverse.

The hydrogeological map defines the closed-lake catchment inventory and the regional analysis unit. Because closed lakes have no surface-water outlet, their area changes provide a sensitive signal of climate, glacier meltwater, groundwater contribution, evaporation, and catchment storage processes. The numbered representative lakes help anchor the classification across arid, semi-arid, plateau, mountain, and glacier-influenced settings.

Hydrogeological map of Tibetan Plateau closed lake catchments — Fig. 1. Hydrogeological map of the TP showing the 322 closed lake catchments. (1-Dachaidan Lake; 2-Bajiu Co; 3-Chen Co; 4-Yamzhog Yumco; 5-Zonag Lake; 6-Keqikekumukule Lake; 7-Kumukuli Lake; 8-Kunggyu Co; 9-Langa Co; 10-Ngangla Ringco; 11-Unnamed Lake (35.22°N, 83.68°E); 12-Como Chamling; 13-Daggyai Co; 14-Gyesar Co; 15-Paiku Co; 16-Gaotai Lake; 17-Jiangcuo Lake; 18-Nara Yumco).

The flowchart organizes the analysis into three steps: classify closed lake catchments using stable physical descriptors, characterize each class with hydro-meteorological and geographical variables, and interpret hydrological behavior through lake-area changes. This design avoids treating all Tibetan Plateau lakes as one uniform group and instead asks whether similar catchments share similar response mechanisms.

Flowchart for classifying and analyzing closed lake catchments — Fig. 2. Schematic diagram of the proposed flowchart for the classification, characterization, and analysis of hydrological behavior in closed lake catchments on the TP.

The descriptor figure explains why topography and land-surface attributes are suitable for catchment grouping. Catchment area, elevation, slope, vegetation cover, and geographic position influence runoff generation, evaporation, snow and glacier contribution, soil-water retention, and the pathway by which climate signals are converted into lake-area expansion or shrinkage.

Topography and land surface descriptors for catchment classification — Fig. 3. Topography and land surface descriptors used for catchment classification and their role in the catchment.

The classification map shows that the resulting five clusters are geographically coherent and have distinct hydro-meteorological characteristics. Red circles mark glacier-meltwater-recharged catchments, helping separate lake expansion driven by precipitation from expansion supported by cryospheric melt, permafrost degradation, groundwater or geothermal contribution, and other local water sources.

Fig. 4. Closed-lake catchment classification between 1981 and 2020. Note: the red circles indicate catchment recharged by glacial meltwater.

Hydroformer is a frequency-domain enhanced multi-attention Transformer for monthly lake-level reconstruction under limited and incomplete observations. It uses meteorological reanalysis variables and lake-level records, decomposes each time series into seasonal and trend components, and learns both temporal dependence and cross-variable causal structure. Tests across 50 lakes show robust performance for reconstruction periods from one-half to three times the training-test length, including cases with substantial missing data.

The architecture figure shows how raw lake-level and catchment meteorological series are first decomposed into seasonal and trend components. These components are then separately learned by Hydroformer through embedding, encoding, and decoding, allowing the model to handle nonstationary lake-level change instead of forcing one network to learn trend, seasonality, and residual variation at the same time.

Fig. 5. Hydroformer architecture. (a) After being processed by a time series decomposition block (Decomposition), the raw time series are individually fed into the Hydroformer for learning; (b) The Hydroformer model's internal processing workflow includes three key stages: Embedding, Encoding, and Decoding.

The multi-attention figure is the core mechanism of Hydroformer. The Frequency-Enhanced Attention (FEA) block transforms sequences into the frequency domain so that low-frequency long-term trends and high-frequency short-term fluctuations can be learned efficiently. The Causality-based Cross-dimensional Attention (CCA) block then constrains information exchange among meteorological variables, helping identify which factors directly or indirectly affect lake-level variation.

Hydroformer multi-attention mechanism — Fig. 6. Multi-Attention Mechanism. (a) FEA block; (b) CCA block.

The comparison figure benchmarks Hydroformer against commonly used ML models, deep-learning models, and advanced Transformer variants. The source study reports that Hydroformer improves MSE and MAE by more than 20% against advanced AI-based models and generalizes across lakes with very different sizes, making it suitable for long-term monthly lake-level reconstruction where remote-sensing records are short or discontinuous.

Hydroformer comparison with supervised methods — Fig. 7. Comparison with Supervised Methods. (a) Frequently used ML models and DL model; (b) advanced Transformer-based models.

Key Findings

Section | Closed-Lake Catchment Classification and Hydrological Behavior

Closed lakes on the Tibetan Plateau have changed significantly over four decades, but catchment-scale responses are not uniform; classification is needed to separate terrain, climate, glacier, vegetation, and groundwater controls.
Hierarchical minimum-variance clustering groups 322 closed lake catchments into geographically coherent clusters with distinct hydro-meteorological characteristics.
Lake-area expansion can be driven by precipitation variability, glacier and snowmelt supply, permafrost or active-layer change, groundwater or geothermal contribution, and land-surface conditions depending on catchment class.

Section | Hydroformer Lake-Level Reconstruction and Forecasting

Hydroformer improves monthly lake-level reconstruction by separating seasonal and trend structures before applying frequency-enhanced and causality-based attention.
The FEA block captures long-term and short-term lake-level signals in the frequency domain, while CCA improves interpretability by representing cross-variable meteorological influence pathways.
Hydroformer supports long-term lake-level reconstruction under short or incomplete records, strengthening diagnosis of plateau water storage and hydrological balance.

Source: [1] Hou, M., Wei, J., Shi, Y., et al. (2024). Closed-lake catchment classification and hydrological behavior analysis on the Tibetan Plateau. Catena, 242, 108090; [2] Hou, M., Wei, J., Shi, Y., et al. (2024). Hydroformer: Frequency domain enhanced multi-attention Transformer for monthly lake level reconstruction with low data input requirements. Water Resources Research, 60.

Module 02 / Card 05

The work presents an integrated diagnostic framework for regional water balance in the potential source area of the Western Route of the South-to-North Water Transfer Project, linking natural water budget, socio-economic demand, ecological flow, and social-ecological competition into a unified balance and coupling-coordination assessment.

The method diagnoses regional water balance from four complementary views: natural water budget balance, socio-economic supply-demand balance, in-channel ecological water balance, and competition between socio-economic and ecological water use. Positive indicators represent surplus or sufficient water availability, while the social-ecological competition term is treated as a negative deviation indicator.

The framework figure defines regional water balance as the intersection of basin water balance, human-nature balance, and regional supply-demand balance. It clarifies how natural water-budget balance, socio-economic supply-demand balance, in-channel ecological water balance, and social-ecological competition jointly form an integrated water-resource, socio-economic, and ecological system balance.

Fig. 1. Integrated diagnostic framework for regional water balance.

The methodology figure translates the conceptual balance framework into four diagnostic dimensions. Each dimension is expressed as a balance element, converted into a connotation variable ΔS, and then integrated into harmony degree V_HAR, coupling degree V_COU, and coupling-coordination degree V_TOT.

Fig. 2. Dimensions, elements, and process of water balance diagnostic methodology.

The coupling-trajectory figure shows how total coupling and subsystem coupling relationships evolve through time. The colored background separates coupled imbalance, over-developed coupling, and healthy coupling, while the curves compare total coupling with pairwise links among water-resource, socio-economic, and ecological systems.

Fig. 3. Evolution process of coupling coordination degree in water source regions. (S1, S2, and S3 denote water resources, socioeconomic, and ecological systems, respectively).

The overall balance degree is obtained by weighted summation and imbalance transformation. Here, ω_i and f_i denote the calculation weight and transformation mode for each diagnostic perspective.

V_HAR = Σ_i=1ⁿω_iV_i = Σ_i=1ⁿω_if_i(ΔS_i-non) (18)

V_COU = { [Π_i=1ⁿf_i(ΔS_i)] / [(1 / n)Σ_i=1ⁿf_i(ΔS_i)]ⁿ }^1/n (19)

V_TOT = √(V_HARV_COU) (20)

For positive indicators, loose and tight balance thresholds are adaptively defined around the background mean and standard deviation: loose balance falls within V_μ ± σ, while tight balance extends to V_μ ± 3σ. The negative social-ecological competition indicator keeps fixed thresholds: imbalance [0.6, 1], tight balance [0.2, 0.6], loose balance [0.05, 0.2], and balance [0, 0.05].

Key Findings

Section | Water-balance diagnosis and coupling coordination

The framework converts natural budget, socio-economic demand, ecological flow, and social-ecological competition into one regional water-balance diagnostic structure.
Adaptive loose/tight balance thresholds use the local background mean and standard deviation, allowing the judgment criteria to reflect basin-specific water-resource conditions.
V_HAR measures the harmony of system states, V_COU measures interaction and dependency among water-resource, socio-economic, and ecological subsystems, and V_TOT integrates both.
The coupling-coordination trajectory supports comparison of whether water use, ecological protection, and economic development are moving toward a more coordinated state.
The diagnostic result can identify when water-supply and ecological-use conflicts move beyond natural adjustment and may require management intervention.
The method provides a policy-oriented basis for source-area management and inter-basin transfer planning.

Source: [1] Zhang, Y., Wei, J., Shi, Y., & Hou, M. Comprehensive diagnostic framework and application of water balance in the water source area of the Western Route of the South-to-North Water Diversion Project. Journal of Changjiang River Scientific Research Institute, 2025, 1, 1-13.

Module 02 / Card 06

The work investigates spatio-temporal hydrological-cycle characteristics in the upper reaches of the Yangtze River (URYR) from 1980 to 2030, combining multi-source remote sensing, water-budget diagnosis, and attention-enhanced machine learning to forecast exploitable water resources (EWR) and interpret dominant hydro-climatic and human-regulation drivers.

The LSTM-AT branch connects basin-scale hydrological-cycle diagnosis with annual EWR prediction. It first characterizes precipitation, evapotranspiration, runoff, and terrestrial water storage across strongly heterogeneous sub-basins, then uses lagged hydro-meteorological variables, human-activity indicators, historical EWR, VMD decomposition, and attention weighting to preserve temporal causality and improve interpretability.

The study-area figure anchors the prediction task in a physically complex water tower region. The URYR covers about one million square kilometers, spans large elevation gradients, and is divided into major sub-basins such as the Jinsha, Min-Tuo, Jialing, Wu, and main-stem Yangtze sections, where terrain, monsoon climate, and river-network structure jointly control water availability.

Study area of the upper Yangtze River region — Fig. 1. Study area of the URYR, illustrating sub-basin delineation, topography (DEM), hydrographic network, and administrative boundaries.

The LSTM-AT framework figure translates hydrological memory into a forecasting architecture. Multi-year input sequences combine current and lagged hydro-meteorological factors, human surface-water use, reservoir storage, and historical EWR; attention weights then identify informative time steps and drivers before the final annual EWR prediction is produced.

Framework of the LSTM-AT model for EWR forecasting — Fig. 2. The framework of the LSTM-AT model for EWR forecasting.

The EWR evolution figure evaluates temporal robustness using expanding split experiments S1-S4. It shows that the model captures interdecadal EWR tendencies and relative variability, while major drought, flood, and Super El Nino years expose the remaining difficulty of representing abrupt hydrological extremes with limited annual samples.

Fig. 3. Interannual evolution of EWR and model split experiments (S1–S4) with major flood, drought, and Super El Niño events highlighted.

Key Findings

Section | LSTM-AT forecasting of exploitable water resources

The URYR shows strong spatial heterogeneity: precipitation ranges from roughly 230 mm in the arid northwest to more than 1600 mm in the humid southeast, while evapotranspiration varies from below 100 mm at high elevations to more than 800 mm in low-lying regions.
Runoff and terrestrial water storage follow comparable spatial gradients, and runoff is strongly controlled by precipitation, especially in the Min-Tuo River basin.
Over 1980-2015, precipitation generally increases and drives higher evapotranspiration, while runoff decline in the upper Jinsha River reflects combined climate-change and human-activity effects.
The LSTM-AT model integrates hydro-meteorological drivers, human regulation variables, historical EWR, VMD decomposition, and attention weights to forecast annual EWR while preserving temporal causality.
Split experiments S1-S4 show that the framework is not dependent on one train-test partition and can reproduce interdecadal EWR tendencies, although exceptionally wet and dry years remain harder to match in amplitude.
Predictions indicate a dynamically stable regional water balance, while EWR in the upper Jinsha River shows a fluctuating upward trend of about 2.13 +/- 0.87 mm/yr, highlighting the need to distinguish renewable EWR from storage-consuming water availability.

Source: [1] Shi, Y., Zhang, Y., Hou, M., & Wei, J. (2026). Spatio-temporal hydrological cycle characteristics in the upper reaches of the Yangtze River: A multi-source remote sensing and machine learning perspective. Journal of Hydrology: Regional Studies, 64, 103142.

Module 03 / Card 01

This U-WSR theory and measurement framework organizes urban water resources system resilience from two linked layers: a conceptual model that couples ecosystem, engineering system, and socio-economic system, and a measurement framework that builds, screens, weights, validates, and integrates resilience indicators. The assessment connects water resources, water ecology, water environment, and water disasters with survival, sustainability, comfort, and safety dimensions.

The conceptual model defines the objects and functions of an urban water resources system through ecological, engineering, and socio-economic subsystems. The measurement framework then translates this conceptual structure into an indicator workflow, including data accessibility, authenticity, relevance screening, redundancy reduction, weight calculation, reality validation, comprehensiveness checking, and integrated application.

The conceptual model clarifies the resilience objects and functions of the urban water resources system before indicators are selected.

Conceptual model of urban water resources system resilience — Fig. 1. Conceptual model linking systems and components, behaviors and functions, core water-resilience dimensions, and the wheel model of urban water resources system resilience indicators.

The measurement framework follows a closed-loop workflow: establish the theoretical structure, propose candidate indicators, verify data accessibility and authenticity, screen relevance, remove redundant indicators, calculate weights, and validate the result through reality checking and comprehensiveness review. The PSR diagnostic logic supports the workflow by connecting external pressure, system state, and management response, so the final indicator set can be used for diagnosis, comparison, planning, and feedback-driven improvement.

The measurement framework converts the conceptual model into an operational indicator workflow for screening, weighting, validation, and integrated resilience assessment.

Measurement framework for urban water resources system resilience — Fig. 2. Measurement framework for constructing, screening, weighting, validating, and integrating U-WSR indicators, with the PSR model as a supporting diagnostic logic.

Key Findings

Section | U-WSR Theory and Measurement Framework

Urban water resources system resilience can be interpreted through four core dimensions: water-resource security, water-ecology sustainability, water-environment livability, and water-disaster safety.
The conceptual model links ecosystem, engineering system, and socio-economic system through water use, discharge, replenishment, regulation, treatment, and management functions.
The wheel model provides an indicator structure covering biodiversity, restorability, stability, disaster resistance and recovery, source diversity, redundancy, and inflow stability.
The measurement workflow combines conceptual framing, data screening, indicator redundancy control, weight calculation, PSR diagnosis, and application-oriented validation.

Source: [1] Urban water-system resilience measurement framework. Internal report/source material, 2026. (In Chinese)

Module 03 / Card 03

The research frames current Singapore-based resilience research for the Malacca/Singapore coastal system, focusing on sea-level rise, storm surge, compound water levels, waves, and flood-protection planning.

The Singapore branch builds a coupled WRF-ROMS-SWAN modeling chain for tropical-cyclone wind, wave, current, pressure, heat-flux, and storm-surge processes around the Malacca Strait and Singapore coastal waters. The workflow emphasizes how atmospheric forcing, ocean circulation, wave-induced roughness, vortex force, sea-surface temperature feedback, and wave-current refraction exchange information during compound coastal extremes.

The first three figures explain the coupling mechanics. They show how WRF, ROMS, and SWAN exchange atmospheric fluxes, sea-surface temperature, wind stress, wave parameters, bottom-boundary-layer information, and current-modified wave generation and propagation.

WRF ROMS SWAN atmosphere ocean wave coupling variables and flux exchange — Fig. 1. WRF-ROMS-SWAN coupling framework for atmosphere-ocean-wave flux exchange, including bulk fluxes, wave-enhanced bottom boundary layer options, vortex force, and cloud-rain-evaporation feedbacks.

SST exchange and surface flux wave roughness coupling among WRF ROMS and SWAN — Fig. 2. SST exchange among WRF, ROMS, and SWAN, together with surface-flux and wave-roughness coupling for momentum flux, sensible heat flux, latent heat flux, and WRF surface-layer schemes.

Wave generation and propagation modified by ocean currents — Fig. 3. Wave-current coupling in SWAN and ROMS: wind-wave generation is modified by ocean currents, while wave celerity, direction, refraction, and propagation are affected by current and bathymetric gradients.

The application workflow integrates historical typhoon tracks, bathymetry, climatic boundary data, wind fields, wave fields, and tide data before running coupled-model sensitivity tests. Validation compares model output with buoy observations and remote-sensing evidence, using typhoon cases to check whether the coupled system reproduces tropical-cyclone pressure fields and coastal-extreme evolution.

The validation figures connect data preparation with operational testing. The setup diagram organizes boundary forcing, model initialization, sensitivity experiments, and validation data, while the Kai-Tak case maps modeled sea-level pressure fields onto observed storm-track evolution.

Model setup data preparation running tests and validation workflow for Singapore coastal typhoon simulation — Fig. 4. Model setup and validation workflow: data preparation, model initialization, boundary and forcing-condition analysis, time-step and grid sensitivity, wind-wave-current sensitivity, buoy validation, and remote-sensing comparison.

Typhoon Kai Tak track and modeled sea level pressure validation around Singapore and the South China Sea — Fig. 5. Typhoon Kai-Tak validation example showing storm-track evolution and modeled sea-level pressure fields at selected times during the event.

Key Findings

Section | Coupled Atmosphere-Ocean-Wave Modeling for Singapore Coastal Extremes

Compound coastal hazards require joint consideration of tropical-cyclone winds, storm surge, waves, currents, sea-level rise, rainfall, and coastal exposure.
The WRF-ROMS-SWAN coupling chain links atmospheric fluxes, ocean circulation, wave growth, wave-current interaction, bottom-boundary-layer stress, and SST feedbacks in one modeling framework.

Section | Model Setup, Sensitivity Testing, and Typhoon Validation

Sensitivity testing across time step, grid size, domain region, wind forcing, wave conditions, and currents supports robust setup for Singapore and Malacca Strait coastal-extreme simulation.
Typhoon-track and sea-level-pressure validation provide the first evidence chain for applying the coupled model to coastal flood-resilience assessment and protection planning.

Source: [1] Singapore coastal flood resilience and coupled WRF-ROMS-SWAN modeling framework. Internal report/source material, 2026.

Module 04 / Card 02

The work explains how light oil and medium-viscosity oil layers fail when retained by floating booms under waves and currents, combining instability theory with experimental observations and threshold diagnosis.

Oil-water interface instability mechanism

Oil spills can seriously damage marine and coastal environments, while floating booms often lose containment efficiency under waves and currents. This theoretical study treats boom failure as an oil-water interface instability problem in a two-layer fluid. Using an eigenfunction expansion framework, it links current velocity, oil-water density ratio, slick thickness, boom draft, and wave condition to the vertical hydraulic pressure structure, showing that the pressure gradient near the oil-water interface is the dominant criterion for instability.

The mechanism figures first define the force balance and coordinate transformation used to formulate oil-water interface instability. They establish the hydraulic-pressure-gradient variables before the zoning map and validation comparison translate the theory into wave-current failure diagnosis.

Force analysis of an oil-film element — Fig. 1. Force analysis of oil film element.

S-C coordinate transformation for oil-water interface analysis — Fig. 2. Sketch of S-C coordinate transformation.

Vertical equilibrium of an infinitesimal oil-film element gives the pressure-gradient relation

dpdz = -(ρ₂ - ρ₁)g(1)

The S-C mapping converts the interface coordinate to the physical vertical coordinate as

z = h√(ζ² - 1)(2)

Using Bernoulli's equation, the front-side liquid pressure gradient in the unidirectional-flow case is

dp_cdz = -ρU²22h²z(h² - z²)²(3)

Here p_c denotes the front-liquid pressure; ρ = ρ₁ for z < h₁, and ρ = ρ₂ for z > h₁.

The zoning and gradient-comparison figures convert the theoretical pressure-gradient criterion into interpretable failure regions. The map shows where wave-current coupling promotes interface instability, and the gradient comparison checks the predicted pressure structure against experiment.

Wave-current coupling zoning map for oil-water interface instability — Fig. 3. Zoning map with the wave-current coupling case.

For combined wave-current forcing, the front pressure is decomposed into the current-induced term and the wave-potential contribution

p = ρU²2[1 - z²h² - z²] + i(ω - K₀⁽ⁿ⁾U)ρφ^(m,1), m = 1, 2(4)

Combining the interface equilibrium condition with the wave-current pressure structure gives

-(ρ₂ - ρ₁)g = -ρU²22h²z(h² - z²)² + i(ω - K₀⁽ⁿ⁾U)ρφ^(m,1)(5)

The critical pressure-gradient index and the wave-current pressure-gradient index are then expressed as

I_c = (ρ₂ - ρ₁)g hρU² = ρ₂ - ρ₁ρFr²(6)

I = z / h[1 - (z / h)²]² - i(ω - K U)φ^(m,1)U²h(7)

I describes the dimensionless hydraulic pressure-gradient distribution, I_c is the critical instability criterion of the oil-water interface, and Fr = U / √(g h).

Comparison of theoretical and experimental hydraulic pressure gradients — Fig. 4. Comparison of theoretical value and experimental value of hydraulic pressure gradient.

Oil-spill observation and slick evolution

The experimental branch focuses on moderate-viscous oil retained by floating booms under current-only and wave-current conditions. It documents the slick profile evolution, monitoring points on the boom and oil slick, the transition from stable containment to drainage and entrainment failure, and the influence of oil viscosity, spilled volume, skirt length, material stiffness, and buoyancy-weight ratio.

The experimental image sequence moves from test configuration to failure process. The setup and monitoring figures define the observation system, while the containment and slick-evolution figures show how oil deformation, drainage, entrainment, and wave-modulated emission develop under increasing hydrodynamic forcing.

Experimental setup and floating boom components for oil containment tests — Fig. 5. The schematic diagram of experimental setup and site snapshot of boom components.

Monitoring points on floating boom and ambient oil slick — Fig. 6. Positions of monitoring points on floating boom and ambient oil slick.

Fig. 7. Containment process of spilled oil with medium and low viscosity.

Slick evolving process under current alone — Fig. 8. Sketch of slick evolving process under the action of current alone: (a) U = 0.06 m/s; (b) U = 0.15 m/s; (c) U = 0.27 m/s; (d) U = 0.66 m/s.

Slick evolving process under wave-current forcing — Fig. 9. Sketch of slick evolving process under the action of waves and current. U = 0.2 m/s, H = 0.06 m, T = 1.2 s: (a) at wave crest; (b) at wave trough; (c) at emission moment.

Improved SPH simulation of spilled oil

The improved SPH simulation reconstructs spilled-oil containment in a numerical wave-current flume and uses Dynamic Boundary Particles (DBPs) to stabilize multiphase particle motion around solid boundaries. The method targets particle disorder near the intersections among oil, water, air, boom skirt, flume wall, inlet, and outlet boundaries.

Because the continuous-density method updates particle density, free-surface conditions are automatically satisfied by the mesh-free SPH formulation, so no special boundary conditions are imposed on free-surface particles. Solid boundaries are described by double rows of Dynamic Boundary Particles (DBPs) following Crespo et al. (2007) and Ren et al. (2015). The DBPs have the same physical attributes as normal fluid particles because they satisfy the mass and momentum conservation equations and the equation of state, but they do not follow the XSPH position update. Their density, pressure, and mass are filtered according to the surrounding water, oil, and mixed-phase particles, preventing boundary-particle disorder in multiphase motion around the floating boom.

The SPH figure sequence documents the full numerical evidence chain: flume construction, DBP solid-boundary treatment, velocity-profile validation, near-boom vorticity response, and modeled-measured oil slick evolution. The images show why the improved boundary treatment is needed before the model is used for containment diagnosis.

Numerical SPH wave-current flume for spilled oil simulation — Fig. 10. Sketch of numerical wave-current flume. U_x and U_y denote the horizontal and vertical component of particle velocity; θ_I and θ_O denote the inflow and outflow angles at the inlet and outlet with respect to the horizontal direction.

Dynamic Boundary Particles for flume and floating boom treatment — Fig. 11. Sketch of solid boundary treatment: DBPs in the water flume (left); DBPs of the simplified floating boom (right). Different colors distinguish particles with different masses.

Vertical profiles of mean horizontal velocity for current and wave-current validation — Fig. 12. Vertical profiles of the mean horizontal velocity: current alone (left); waves (H = 0.12 m, T = 1.4 s) following current (right).

Velocity and vorticity distributions near the floating boom under current alone — Fig. 13. Snapshots of velocity and vorticity distributions near the floating boom for current alone.

Modeled and measured oil slick under combined wave and current — Fig. 14. Snapshots of modeled and measured results of oil slick subject to the combined wave and current (H = 0.06 m, T = 1.2 s, U = 0.2 m/s): (a) boom at wave trough; (b) boom at wave crest.

EPR-MOGA containment-loss model

The EPR-MOGA based section converts the observed oil-containment failure process into compact symbolic expressions for initial failure velocity and post-failure oil-loss rate. This separates the empirical threshold diagnosis from the image-based experimental observation, while keeping both tied to oil properties, spilled volume, boom geometry, and hydrodynamic forcing.

The initial failure velocity is estimated by combining KH instability, skirt length, spilled volume, and the tilt factor of the boom skirt

U_i = 0.369 ln(U_KH²) + 0.975D²α^1.5ln(DV) + 1.722, CoD = 0.79(8)

After containment failure starts, the oil-loss rate under current-only forcing is described by

q_E = 0.0254V²α exp(α^1.5D) + 0.0002I_U^0.5V²α^1.5 + 75286.03I_U^1.5D^1.5V exp(V^0.5α^1.5) + 0.788, CoD = 0.93(9)

Here U_i is the initial failure velocity, q_E is the oil-loss rate, U_KH is the critical KH instability velocity, D is skirt length, V is initial spilled volume, α is the ratio of drag force to counter weight, and I_U is the current-velocity increment relative to initial failure velocity.

These empirical expressions are constructed with EPR-MOGA, a nonlinear global stepwise regression method coupled with a multi-objective genetic algorithm. The model does not require the expression structure, variable exponents, or related parameters to be specified a priori; instead, they are estimated from training data and selected by balancing symbolic simplicity, physical interpretability, and fitting accuracy.

Key Findings

Section | Oil-water interface instability mechanism

Floating-boom failure is primarily interpreted as an oil-water interface instability problem under wave-current forcing.
The eigenfunction expansion analysis connects oil-water density ratio, slick thickness, boom draft, current velocity, and wave condition to the pressure-gradient criterion.
Oil-film instability is governed by the vertical hydraulic pressure profile, with the pressure gradient near the interface acting as the dominant indicator.
Wave-current coupling modifies the dimensionless hydraulic pressure gradient, so the instability threshold must be evaluated through both I and I_c.

Section | Oil-spill observation and slick evolution

Medium- and low-viscosity oils show different containment processes, with slick stretching, near-boom thickening, vortex tearing, drainage, entrainment, and periodic emission observed under increasing forcing.
Current-only tests reveal progressive slick deformation from headwave formation to vortex-area development and sheltered-area transport near the boom.
Wave-current tests show crest-trough modulation of the oil slick and periodic emission, highlighting the stronger unsteady forcing imposed by waves.

Section | Improved SPH simulation of spilled oil

DBP-based boundary treatment suppresses particle disorder near solid boundaries while retaining SPH mass, momentum, and equation-of-state consistency.
The numerical wave-current flume reproduces current circulation, wave forcing, and inlet/outlet boundary motion for spilled-oil containment simulation.
Velocity-profile validation, vorticity snapshots, and modeled-measured oil slick comparisons support the SPH model for diagnosing boom-oil-water interaction under waves and currents.

Section | EPR-MOGA containment-loss model

Initial failure velocity depends on KH instability velocity, skirt length, spilled volume, and skirt tilt factor.
Oil-loss rate increases after failure and is sensitive to oil volume, current increment, skirt length, and boom resistance.
EPR-MOGA provides symbolic regression formulae for initial failure velocity and oil-loss rate, giving compact threshold tools for emergency oil-spill response.

Source: [1] Shi, Y., Li, S., Zhang, H., Chen, H., & Zhou, R. Analysis of instability mechanism of oil-water interface of oil boom under wave-current. Journal of Tianjin University (Science and Technology), 2018, 51(07), 691-701. (In Chinese) https://doi.org/10.11784/tdxbz201707073; [2] Shi, Y., Wei, J., Li, S., Peng, S., & Zhang, B. (2020). Experimental study on containment of moderate-viscous oil by floating boom subject to waves and currents. Applied Ocean Research, 94, 102003; [3] Feng, X., & Shi, Y. Numerical study of containment of spilled medium-viscosity oil in wave-current flow. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001634.

Module 04 / Card 03

The work presents a permeable multi-tube floating breakwater and a validated SPH numerical model for wave-structure interaction, emphasizing rapid deployment, mooring response, porosity-driven dissipation, and wave-transmission reduction.

Tri-buoy floating-breakwater attenuation

The tri-buoy floating breakwater uses three cylindrical buoyant modules arranged in a triangular frame to form a rapidly deployable wave-attenuation unit. A two-dimensional SPH numerical wave tank with an active absorbing wave maker and a sponge layer is used to model wave interaction with the hinged permeable multi-tube floating structure. The motion is driven by hydrodynamic and mooring forces, while the comparison between impermeable and permeable types clarifies how porous openings reduce wave transmission through turbulent dissipation, flow exchange, and phase disturbance around the structure.

The figure sequence links structural concept, model validation, and attenuation performance. The schematic compares impermeable and permeable tri-buoy designs, the snapshot comparison checks SPH motion against laboratory photographs, and the coefficient plots quantify how wave steepness and relative water depth control transmission reduction.

Impermeable and permeable tri-buoy floating breakwater designs — Fig. 1. Schematic of tri-buoy floating breakwater: (a) impermeable type; (b) permeable type.

Numerical snapshots and laboratory photographs of tri-buoy floating breakwater motion — Fig. 2. Qualitative comparison of the numerical snapshots and laboratory photographs: (a) t = t0, (b) t = t0 + T/4, (c) t = t0 + T/2, and (d) t = t0 + 3T/4.

Transmission coefficient versus wave steepness for floating breakwater — Fig. 3. Modeled results of transmission coefficients of floating breakwater K_t versus wave steepness H/L subject to various wave conditions.

Transmission coefficient versus relative water depth for floating breakwater — Fig. 4. Modeled results of transmission coefficients of floating breakwater K_t versus relative water depth d/L subject to various wave conditions.

Key Findings

Section | Tri-buoy floating-breakwater attenuation

The three-cylinder arrangement provides a compact floating breakwater unit that can be assembled as impermeable or permeable modules for nearshore and harbor wave attenuation.
Numerical snapshots reproduce the laboratory-observed free-surface evolution and floating-body motion across one wave cycle, supporting the physical interpretation of the device response.
Transmission coefficient K_t decreases as wave steepness H/L and relative water depth d/L increase, showing that wave condition and deployment depth jointly control attenuation performance.
Permeable cylindrical modules support additional energy dissipation through flow exchange and porous interaction, improving the device concept for rapid coastal protection.

Source: [1] Cao, Y., Shi, Y., Bai, Y.C., Li, S.W., Chen, H.B., & Yang, H.L. (2018). Numerical modeling of permeable floating breakwater under the action of waves. Journal of Coastal Research, Special Issue No. 85, 1101-1105.

Module 04 / Card 04

The work develops an FD-SPH coupled solver for incompressible free-surface flows, using SPH in the near-field region where wave breaking, overtopping jets, and complex free-surface deformation occur, while the mesh-based FD model resolves the far-field wave propagation with higher efficiency.

FD-SPH coupling for wave breaking

The coupled algorithm decomposes the computational domain into a near-field SPH subdomain around the structure and a peripheral mesh-based FD subdomain. The SPH model resolves severe free-surface deformation, wave impact, breaking, and fluid-structure interaction with high fidelity; the FD model resolves the remaining wave flume on a structured Cartesian grid to reduce the computational load. The two solvers are connected by an overlapping region, which functions as a transition zone for fluid-mass transfer, free-surface movement, velocity, pressure, turbulence quantities, and boundary information.

The first three figures explain the coupled solver architecture. They move from the submerged-breakwater computational domain to the mesh-based FD cell system and then to the FD-SPH information-exchange methodology, showing why the severe free-surface zone and far-field wave-propagation zone are solved differently.

Computational domain for wave propagation over a submerged breakwater — Fig. 1. Configuration of the computational domain for wave propagation over a submerged breakwater.

Fig. 2. Two-dimensional vertical sketch of the mesh-based FD model. Five rectangular cell types are defined on the structured Cartesian grid according to fluid and solid volume fractions; scalars are located at cell centers and vectors on cell surfaces.

Coupling methodology for a structure subjected to wave load — Fig. 3. Principle of the coupling methodology for a structure subjected to wave load: computational-domain decomposition and two-way information exchange between FD grids and SPH particles.

FD to SPH. Flow information is transferred from the FD model to the SPH model by defining multiple layers of FD-forced particles in a narrow belt inside the overlapping region. Their velocity, pressure, SPS turbulence stress, and turbulent viscosity are obtained by bilinear interpolation from the structured FD grids. The FD-forced zone is kept one to two kernel radii wide so that nearby generic SPH particles retain complete kernel support.

SPH to FD. Lagrangian SPH solutions are mapped back to the internal boundary of the FD subdomain, called the SPH-forced interface, using Shepard interpolation. SPH free-surface elevations reset the VOF boundary values by comparison with vertical grid coordinates, while velocity and pressure are updated from particle quantities. Turbulence quantities use zero-gradient boundary conditions at the interface.

Open-boundary particle management. A particle generation and elimination mechanism handles fluid-mass transfer and free-surface passage across the SPH open boundary, preventing ineffective particle accumulation and maintaining particle distribution during wave propagation through the coupled domain.

The final two figures focus on how the coupled model remains stable and what it resolves. The open-boundary sketch explains particle generation and removal at the SPH boundary, while the velocity snapshots show the resulting wave-breaking evolution over the submerged breakwater.

Particle generation at open boundary of SPH subdomain — Fig. 4. Sketch of particle generation at open boundary.

Horizontal velocity component for wave breaking over a submerged breakwater — Fig. 5. Snapshots of horizontal velocity component for the evolution of wave breaking over a submerged breakwater.

Key Findings

Section | FD-SPH coupling for wave breaking

Domain decomposition assigns the severe free-surface deformation zone to SPH and the far-field wave-propagation region to a mesh-based FD solver, balancing local accuracy with global efficiency.
The overlapping region connects the two subdomains and supports two-way exchange of mass, free-surface position, velocity, pressure, and turbulence information.
FD-forced particles transmit Eulerian grid solutions into the SPH subdomain through bilinear interpolation, while the SPH-forced interface maps particle solutions back to FD boundary values through Shepard interpolation.
The open-boundary particle-generation mechanism maintains particle continuity when the free surface crosses the SPH boundary.
Horizontal-velocity snapshots show the coupled model resolving wave breaking over the submerged breakwater, including crest steepening, jet-like high-velocity zones, and downstream turbulent evolution.

Source: [1] Liu, K., Liu, Y., Li, S., Chen, H., Chen, S., Arikawa, T., & Shi, Y. (2023). Coupling SPH with a mesh-based Eulerian approach for simulation of incompressible free-surface flows. Applied Ocean Research, 138, 103673. https://doi.org/10.1016/j.apor.2023.103673.

Module 04 / Card 05

The work develops analytical and numerical estimates of dynamic forces on turbidity curtains under currents, waves, and combined wave-current flow, supporting the design of buoy diameter, curtain strength, sinker weight, and sediment-control deployment for dredging and navigation-channel protection.

Silt-curtain force-balance design

Turbidity curtains provide a deployable barrier for controlling suspended solids generated by dredging and spoil-disposal operations. When the curtain is long enough for the sinker to be supported by the seabed, the design problem becomes a coupled force-balance problem: the water-level difference across the curtain drives a current-induced tension, while waves add dynamic stretching and additional curtain force. The resulting equations connect the buoy submergence depth H, curtain angle α₀, water depth h, water-level difference Δh, buoy radius r, and total tension T.

The first two figures define the engineering mechanics of the silt curtain. The design sketch gives the buoy, curtain, sinker, water depth, water-level difference, and geometric variables, while the force sketch decomposes the loads acting on the sinker and curtain before the nonlinear design equations are applied.

Fig. 1. Sketch and main design parameters of silt curtain.

Forcing sketch of silt-resisting curtain for sinker and curtain — Fig. 2. Forcing sketch of silt-resisting curtain: sinker on the left and curtain on the right.

Eq. (1) and Eq. (2) constitute nonlinear algebraic systems for solving H and α₀ by iteration under different buoy-submergence cases.

2Tρgr sinα₀ - Δh cosα₀ - 2ΔhrH = Δh²r - Δh(1)

For H > r,

-(1 - cosβ) sinβ + [2 sinβ + cosα₀](1 - sinα₀) - (Hr - 1)sinθ + [sinθ + Hr] + (2Hr - 1 + cosα₀)sinα₀ - 2Tρgr²cosα₀ = 0(2a)

For H < r < H + Δh,

Hrcosθ + (2Hr - 1 + cosα₀)sinα₀ - Δhr(1 - cosβ) + (2Δhr + cosα₀)(1 - sinα₀) - T cosα₀ = 0(2b)

If H + Δh < r,

Hrcosθ + (cosα₀ - sinβ)(cosβ - sinα₀) + (2Hr - 1 + cosα₀)sinα₀ - 2Tρgr²cosα₀ = 0(2c)

The wave-induced tension is first evaluated from the wave impact response, then combined linearly with the current-induced force to obtain the total curtain tension.

T_w = √22σa coth(kh) sinα₀√ME(3)

T = T_c + T_w(4)

The contour map converts the analytical solution into an engineering chart for selecting minimum buoy diameter under specified water depth and cross-curtain water-level difference.

Contour map of minimum buoy diameter versus water level difference and water depth — Fig. 3. Contour map of minimum buoy diameter r versus water level difference Δh and water depth h. Unit: m.

Key Findings

Section | Silt-curtain force-balance design

The turbidity curtain is modeled as a buoy-sinker-flexible-curtain system whose force state is controlled by water-level difference, water depth, curtain geometry, and wave-current forcing.
For steady current, the curtain tension is proportional to water depth and the water-level difference between the two sides of the curtain.
The buoy submergence depth H and curtain deviation angle α₀ increase with increasing water-level difference Δh, making buoy diameter a key design variable.
Eq. (1) and Eq. (2) provide iterative nonlinear systems for H and α₀, while Eq. (3) and Eq. (4) extend the estimate to wave-induced and combined wave-current tension.
The minimum buoy diameter map translates the mechanics into a design chart for selecting buoy size under specified water depth and cross-curtain water-level difference.

Source: [1] Li, S., Ji, Z., Wu, Q., Zhang, H., & Shi, Y. (2018). Estimation of dynamical forces on turbidity curtain in combined wave-current flow. Journal of Coastal Research, Special Issue No. 85, 1181-1185.

Module 05 / Card 01

The research organizes local scour and sediment-transport mechanics from particle-resolved and continuum numerical viewpoints. CFD-DPM clarifies bed-load and suspended-load coexistence under high-flow-intensity sediment-laden conditions, while ISPH, WCSPH, CgLes, Eulerian simulation, VIV analysis, wave-current coupling, and AI prediction extend the interpretation toward pipeline-scour diagnosis.

A coupled CFD-DPM model resolves high-flow-intensity sediment transport, emphasizing the coexistence of bed load and suspended load, sediment-concentration distribution, turbulence modulation, particle collision, and the transition layer between transport modes. The turbulent flow is simulated using the CgLes CFD code, a grid-based model with a fixed Cartesian grid for spatial discretization and second-order numerical accuracy in both time and space. Sediment-particle motion and interaction are simulated using the DPM model, with two-way coupling between each particle and the fluid.

The CFD-DPM image pair connects instantaneous coherent flow structures with particle transport modes, showing how turbulent events lift sediment from bed load into suspension.

CFD-DPM instantaneous sediment particle velocity and coherent flow structures — Fig. 1. Instantaneous results of sediment-particle velocity and distribution, flow velocity, and coherent flow structures.

Distribution of bed load and suspended sediment particles under CFD-DPM simulation — Fig. 2. Distribution of bed load and suspended sediment particles. Blue marks unmoving sediment, green marks bed load, red marks suspended sediment, and dashed lines separate transport modes.

SPH-based modeling extends sediment-water simulation from particle-scale concentration diffusion to rough-bed boundary treatment. The ISPH branch solves a suspended-sediment advection-diffusion equation with hindered settling and turbulent diffusion, while the WCSPH branch uses ghost boundary particles to represent small-scale bed roughness and improve near-bed velocity and shear-stress transfer.

The SPH method grid combines schematic variables, governing transport, boundary treatment, and concentration validation to show how sediment-water exchange is represented in meshless form.

SPH schematic of non-equilibrium suspended sediment transport — Fig. 3. Non-equilibrium sediment transport, including flow velocity, eddy viscosity, and suspended-sediment concentration.

Suspended-sediment transportDCDt=∂(ω_sC)∂z+ν_s∇²C

The governing equation describes concentration change as the sum of settling-induced advective flux and turbulent diffusive flux. Hindered settling is introduced through ω_s = ω₀(1 - C)^η, where C is sediment concentration, ω_s is vertical settling velocity, and ν_s is the sediment diffusion coefficient.

SPH ghost particle bottom boundary treatment schematic — Fig. 4. Ghost boundary particles modify the bottom boundary layer and support rough-bed open-channel flow simulation.

Fig. 5. Predicted concentration profiles reproduce the non-equilibrium adjustment from near-bed concentration to far-field Rouse-type behavior.

Ghost-based rough-bed boundary

An improved boundary treatment quantitatively characterizes bed roughness based on ghost boundary particles. The velocities of GBPs are explicitly calculated using evolutionary polynomial regression with a multiobjective genetic algorithm, improving the near-bed velocity and shear-stress response.

Generalized bottom boundary condition

A generalized bottom boundary condition accounts for both deposition velocity and equilibrium concentration. It supports simulation of non-equilibrium suspended sediment transport using a generalized sediment transport equation.

Eulerian simulation links wave-current forcing, vibrating pipeline motion, and local seabed scour. The numerical framework resolves the coupled water-sediment-pipeline system under pure flow and wave-current interaction, supporting diagnosis of vibration amplitude, scour depth, and parameter sensitivity.

The vibrating-pipeline figures move from numerical-tank setup to response diagnostics, linking hydrodynamic forcing, pipeline motion, and scour depth under pure-flow and wave-current cases.

Cross-sectional view of the water tank and Eulerian numerical domain for vibrating pipeline scour — Fig. 6. Cross-sectional view of the water tank. *o_s* denotes the coordinate origin of the earth-fixed system.

Fig. 7. Vibration process of pipeline with different reduced velocities under pure flows, for cases with h = 0.35 m, U = 0.35-0.55 m/s, e/D = 0, and D = 0.10 m.

Vibration amplitude and scour depth under wave-current interaction with different KC numbers — Fig. 8. Vibration amplitude of pipeline and scour depth under wave-current interaction with different KC numbers, for cases with h = 0.35 m, U = 0.35 and 0.50 m/s, e/D = 0, D = 0.10 m, H = 0.02-0.05 m, and T = 0.6-1.5 s.

Machine-learning prediction converts high-fidelity CFD simulation outputs into a fast surrogate model for local scour depth beneath vibrating submarine pipelines. The framework combines physics-informed input features with integrated ML learners, enabling rapid screening of scour response under waves and currents while retaining the structure of the validated numerical database.

The ML figures show how CFD-generated cases are transformed into a prediction workflow and then tested through training and validation error distributions.

Flow map of the combination algorithm of the machine learning model — Fig. 9. Flow map of the combination algorithm of the ML model.

Relative errors of predicted scour depth on training and validation sets across different machine learning models — Fig. 10. Relative errors of predicted S/D on the training and validation sets across different ML models.

Key Findings

Section | CFD-DPM sediment-transport mechanics

The coupled CFD-DPM model resolves high-flow-intensity sediment transport with two-way interaction between flow turbulence and discrete sediment particles.
Bed load and suspended load coexist in a transition layer, where the two transport modes exchange particles rather than remaining sharply separated.
Particle collision strongly affects bed-load velocity, while coherent structures above the bed lift particles into suspension and reshape concentration distribution.

Section | SPH-based sediment-water simulation

SPH solves suspended-sediment concentration transport through settling-induced advection and turbulent diffusion, including hindered-settling effects under high concentration.
Generalized bottom boundary treatment links deposition velocity, equilibrium concentration, and near-bed sediment exchange.
Ghost boundary particles quantitatively characterize rough-bed boundary layers and improve near-bed velocity and shear-stress representation.

Section | Vibrating-pipeline scour response

Eulerian simulations connect pipeline vibration, wave-current forcing, local scour, and seabed morphology in a unified numerical tank.
Pipeline response and scour depth vary with reduced velocity, KC number, wave height, period, and current velocity.
The results provide a diagnostic route from hydrodynamic excitation to structural vibration and scour-risk assessment beneath submarine pipelines.

Section | Machine-learning scour-depth prediction

High-fidelity CFD simulations provide physically constrained training data for rapid prediction of local scour depth beneath vibrating pipelines.
The ML framework compares XGBoost, decision tree, SVM, MLP, and integrated MLP-XGBoost prediction across training and validation sets.
The coupled MLP-XGBoost model improves generalization and reaches approximately 90.91% prediction accuracy within a 20% error margin.

Source: [1] Zhang, B., Wu, B., Li, S., & Shi, Y. (2021). Large eddy simulation of sediment transport in high flow intensity by discrete particle method. Journal of Hydraulic Research, 59(4), 605-620; [2] Ge, S., Li, S., Liu, Y., Shi, Y., Wang, D., & Yang, T. (2026). ISPH simulation of non-equilibrium suspended sediment transport using a generalized sediment transport equation. Journal of Marine Science and Engineering, 14, 900; [3] Shi, Y., Wei, J., Li, S., Song, P., & Zhang, B. (2019). A meshless WCSPH boundary treatment for open-channel flow over small-scale rough bed. Mathematical Problems in Engineering. https://doi.org/10.1155/2019/1573049; [4] Shi, Y., Yang, H., Wei, J., Yu, H., Liu, Y., Ge, S., Bai, Z., & Li, S. (2022). Numerical study of scour below vibrating pipelines under waves and currents. Ocean Engineering, 266, 112718; [5] Shi, Y., Wei, J., Yang, H., Li, S., & Li, Y.P. (2025). Prediction of local scour beneath vibrating submarine pipelines subjected to waves and currents based on CFD and machine learning approach. Ocean Engineering. https://doi.org/10.1016/j.oceaneng.2025.123777.

Module 05 / Card 02

The work focuses on local scour around vertical piles and bridge piers, emphasizing horseshoe vortices, wake interaction, bed deformation, and hydraulic-safety diagnosis.

Vertical-cylinder scour is a classic sediment-structure interaction problem in hydraulic and coastal engineering. The ISPH simulation is organized around laboratory flume validation, final scour-pit morphology, and pressure-coefficient comparison, linking hydrodynamic loading around a cylinder with the development of local bed erosion.

The flume and scour-pit figures establish the benchmark experiment and final bed response used to validate ISPH simulation around a vertical cylinder.

Laboratory flume for sediment bed scour around a vertical cylinder — Fig. 1. Laboratory flume for sediment bed scour around cylinder (unit: m).

Final sediment scouring pit around a cylinder under laboratory and numerical comparison — Fig. 2. Final sediment scouring pit for flow condition h = 0.3 m and u* = 0.0125 m/s.

The pressure-comparison pair validates the near-cylinder hydrodynamic field at the stagnation zone and upstream bed, where scour-driving forces are concentrated.

Comparison of stagnation pressure coefficient across flow depth between ISPH and documented data — Fig. 3. Stagnation pressure across the flow depth, following Roulund et al. (2005).

Comparison of bed pressure coefficient along the upstream centerline between ISPH and documented data — Fig. 4. Pressure on bed along the upstream centerline, following Roulund et al. (2005).

Key Findings

Section | Bridge-Pier and Vertical-Cylinder Scour

The laboratory flume and cylinder-scour configuration provide a controlled benchmark for testing ISPH simulation of sediment-bed deformation around vertical structures.
The final scour-pit morphology captures the asymmetric erosion pattern and near-cylinder bed response under h = 0.3 m and u* = 0.0125 m/s.
Pressure-coefficient comparisons against Roulund et al. (2005) validate the ISPH hydrodynamic field near the stagnation zone and upstream bed centerline.
The work extends sediment-water SPH modeling from horizontal pipeline scour toward vertical piles, bridge piers, and hydraulic-structure safety diagnosis.

Source: [1] Wang, D., Shao, S., Li, S., Shi, Y., Arikawa, T., & Zhang, H. (2018). 3D ISPH erosion model for flow passing a vertical cylinder. Journal of Fluids and Structures, 78, 374-399. https://doi.org/10.1016/j.jfluidstructs.2018.01.003.

Module 05 / Card 03

The research connects module 1's acoustic-agglomeration mechanism with multiphase numerical simulation, using DEM-style particle dynamics to resolve droplet motion, collision, and coalescence under acoustic forcing.

A three-dimensional CFD-DEM droplet-breakup simulation coupled model is used to resolve droplet aerosol transport, acoustic-pressure structure, acoustophoretic force, and parcel-scale collision/coalescence in an agglomeration chamber. The simulation links chamber-scale device design with droplet-size-spectrum evolution under different acoustic frequencies.

The device figure defines the agglomeration chamber, parcel variables, and coordinate system used for the CFD-DEM acoustic simulation.

Fig. 1. Schematic drawing of acoustic agglomeration device. x, dp, and Np denote the horizontal distance from the chamber inlet, parcel diameter, and parcel number, respectively. The origin is located at the centroid of the chamber inlet.

The validation pair checks the simulated chamber flow and outlet droplet distribution before acoustic-frequency effects are interpreted.

Fig. 2. Sectional velocity distribution and velocity profile along the central axis of the agglomeration chamber. u denotes flow velocity along the chamber, while x and z represent positional coordinates along and perpendicular to the chamber.

Measured and modeled droplet aerosol distribution at the chamber outlet — Fig. 3. Comparisons between measured and modeled droplet aerosol distribution at the end of the agglomeration chamber.

The frequency pair compares acoustic pressure and parcel trajectories at 18 kHz and 24 kHz, showing how frequency relocates agglomeration pathways.

Acoustic pressure isosurface and parcel trajectory at 18 kHz — Fig. 4. Acoustic pressure isosurface and parcel trajectory at f = 18 kHz.

Acoustic pressure isosurface and parcel trajectory at 24 kHz — Fig. 5. Acoustic pressure isosurface and parcel trajectory at f = 24 kHz. The wave-type and rainbow legends represent acoustic pressure in Pa and acoustophoretic force in N, respectively.

Key Findings

Section | Acoustic Droplet-Group Agglomeration Simulation

CFD-DEM droplet-breakup simulation coupling links the chamber flow field, acoustic pressure, parcel trajectory, and droplet-size distribution in one particle-resolved simulation framework.
Velocity-profile and droplet-distribution comparisons provide model validation before using the chamber simulation for acoustic-parameter interpretation.
Acoustic frequency reshapes pressure isosurfaces and acoustophoretic-force pathways, producing different parcel trajectories and agglomeration zones at 18 kHz and 24 kHz.
The simulation offers a numerical bridge from acoustic device design to atmospheric-water-resource droplet growth and aerosol removal.

Source: [1] Shi, Y., Wei, J., Qiu, J., Chu, H., Bai, W., & Wang, G. (2020). Numerical study of acoustic agglomeration process of droplet aerosol using a three-dimensional CFD-DEM droplet-breakup simulation coupled model. Powder Technology, 362, 37-53. https://doi.org/10.1016/j.powtec.2019.12.017.

Module 05 / Card 04

The work studies violent free-surface impact when a wedge enters water through air and oil layers, representing coupled air-oil-water multiphase dynamics relevant to marine hazards and offshore hydrodynamics.

The wedge-entry validation tests whether the improved multiphase SPH boundary treatment can reproduce rapid interface deformation, oil-water separation, and particle stability when a solid body crosses the air-oil and oil-water interfaces. This benchmark supports later oil-boom simulations by first validating the model against a controlled two-layer laboratory experiment.

The tank figure defines the laboratory wedge-entry benchmark used to test multiphase SPH across air, oil, and water layers.

Water tank and falling wedge laboratory snapshot — Fig. 1. Water tank and falling wedge used in the laboratory experiment: site snapshot (left); schematic view (right).

Schematic view of water tank and falling wedge — Fig. 1. Water tank and falling wedge used in the laboratory experiment: site snapshot (left); schematic view (right).

Particle snapshots of wedge entry using original and improved dynamic boundary particles — Fig. 2. Particle snapshots of wedge entry at time t = 0.15 s (black lines denote the oil-water interface): original DBPs (left); improved DBPs (right).

Comparison between experimental photos and modeled wedge-entry results across air oil and oil water interfaces — Fig. 3. Comparisons between experimental photo (left) and modeled results (right) of wedge entry across the air-oil and oil-water interfaces: (a) t1 = 0.08 s, (b) t2 = 0.16 s, (c) t3 = 0.24 s, and (d) t4 = 0.36 s.

Key Findings

Section | Air-Oil-Water Multiphase Wedge Impact

The wedge-entry experiment provides a compact benchmark for validating multiphase SPH across air-oil and oil-water interfaces.
The improved DBP treatment suppresses particle disorder near the wedge boundary and produces a cleaner interface response than the original DBP scheme.
Modeled wedge-entry sequences reproduce the observed penetration, interface depression, splash-up, and late-stage oil-water deformation.
The validated air-oil-water model supports subsequent simulations of spilled oil contained by flexible floating booms under wave-current coupling.

Source: [1] Shi, Y., Li, S., Chen, H., He, M., & Shao, S. (2018). Improved SPH simulation of spilled oil contained by flexible floating boom under wave-current coupling condition. Journal of Fluids and Structures, 76, 272-300. https://doi.org/10.1016/j.jfluidstructs.2017.09.014.

Module 06 / Card 01

Wave energy is a promising sustainable resource, yet nearshore wave-energy converters still need robust structures that can match wave-induced pressure, internal oscillation, and power take-off response. The EC-OWC concept uses a bottom-fixed semi-cylindrical elastic capsule connected to an oscillating-water-column chamber, converting traveling-wave pressure into bulge-wave motion and then into oscillatory air-water-column energy.

Integrated EC-OWC summary linking the device concept, bulge-wave mechanism, experimental setup, capsule relaxation response, and hydrodynamic-efficiency trend. The section connects the elastic capsule, wave-induced pressure, OWC chamber, and PTO response as one wave-energy conversion chain.

The EC-OWC figures follow the full conversion chain from device concept and wave-pressure forcing to experimental realization, capsule relaxation, and hydrodynamic efficiency.

Schematic diagram of wave pressure acting on an elastic capsule — Fig. 2. Schematic diagram of wave pressure and bulge-wave response.

Sketch of the EC-OWC experimental setup — Fig. 3. Sketch of the experimental setup, with the physical elastic capsule prototype shown as the auxiliary image.

Physical elastic capsule prototype in the wave flume — Fig. 3. Sketch of the experimental setup, with the physical elastic capsule prototype shown as the auxiliary image.

Relaxation of the elastic capsule in response to wave action — Fig. 4. Capsule relaxation when z/H is too small.

Hydrodynamic efficiency and amplification trend of EC-OWC — Fig. 5. Hydrodynamic efficiency and amplification.

Key Findings

Section | Elastic Capsule OWC Hydrodynamic Performance

The EC-OWC consists of a closed semi-cylindrical elastic tube fixed to the bed and connected with a modified OWC, providing a new nearshore wave-energy-converter configuration.
Wave pressure excites a free bulge wave inside the capsule; physical modeling confirms that the bulge-wave velocity follows one-dimensional longitudinal wave theory.
The PTO/air-chamber response is approximately linear under EC-OWC operation, and the ring-opening mode with an opening ratio near 0.76% can substitute the impulse turbine in model tests.
The maximum primary hydrodynamic efficiency is about 0.475; when relative water depth is about 0.07-0.09, the efficiency can reach about 0.4.
Efficiency is controlled by the matching of wave period, internal oscillation period, phase, relative hydraulic head, and capsule length. The system approaches a near-resonant state when the capsule length is close to half a wavelength.
If z/H is too small, local relaxation of the elastic capsule weakens its expansion-contraction capability and causes energy loss, explaining the low-efficiency regime shown by the relaxation photograph and efficiency curve.

Source: [1] Yu, H., Bai, Z., Shi, Y., Zhao, C., Liu, X., & Wang, Y. Hydrodynamic performance of an elastic capsule oscillating water column type WEC: An experimental study. Applied Ocean Research, 2024, 142, 103850. https://doi.org/10.1016/j.apor.2023.103850.

Physics-guided digital twins for hydrosphere applications

Atmospheric water-resource utilization: acoustic microphysics, engineered intervention, and field evaluation

Background

Main Outcomes

Acoustic and turbulent agglomeration theory for droplet aerosols

Key Findings

Linked Papers and Projects

Integrated water-resource diagnosis and regulation: replenishment, storage, balance, and forecasting

Background

Main Outcomes

Linked Papers and Projects

Climate-resilient urban and coastal water systems: assessment, warning, and compound-flood protection

Background

Main Outcomes

Linked Papers and Projects

Nearshore emergency protection and coastal defense: oil containment, wave attenuation, and sediment control

Background

Main Outcomes

Linked Papers and Projects

Multiphase hydrodynamics and local scour: sediment transport, droplet dynamics, and impact processes

Background

Main Outcomes

Linked Papers and Projects

Clean water–energy systems: wave and tidal-current energy, and hydro–wind–solar coordination

Background

Main Outcomes

Linked Papers and Projects