A method for simulating nearshore wave-current-sediment coupling considering nonlinear effects of wave breaking

Abstract

The application discloses a kind of nearshore wave-flow field-sediment coupling simulation method considering wave breaking nonlinear effect, belong to nearshore hydrodynamics field, including: input WRF high-resolution wind field, tidal boundary condition and water depth information, initialize wave, flow field, sediment module;Using improved wave breaking energy dissipation formula to calculate local wave breaking dissipation energy, obtain wave energy density spectrum and breaking probability;Under the calculation of nearshore flow field in the nonlinear correction of radiation stress, update hydrodynamic boundary condition;Using coupling diffusion coefficient to calculate sediment suspension and deposition, update sediment concentration distribution;Through cyclic iteration, make wave, flow field, sediment mutually coupled, realize nearshore wave-flow field-sediment simulation under extreme conditions such as typhoon, storm surge and strong wind wave.The method of the application can improve the prediction accuracy of wave height, flow velocity and sediment concentration under strong wind wave conditions in the nearshore, and be used for typhoon storm surge forecasting, harbor siltation evaluation and nearshore ecological environment management.

Description

Technical Field

[0001] This invention relates to the fields of marine meteorological numerical simulation and nearshore hydrodynamics, and particularly to a nearshore wave-flow-sediment coupling simulation method that considers the nonlinear effects of wave breaking. Background Technology

[0002] In nearshore areas, the frequent occurrence of extreme weather events such as typhoons, storm surges, and strong winds and waves poses severe challenges to disaster prevention and mitigation, port operations, and ecological protection in coastal regions. The traditional COAWST model's multiphysics coupling simulation results of air-sea, wave, current field, and sediment transport are insufficient to meet the high accuracy and reliability requirements of real-world simulations.

[0003] If the energy dissipation after wave breakup is underestimated, the calculated wave height of nearshore waves will be lower than expected, which will affect the design of coastal protection projects. At the same time, it will also lead to errors in the calculation of tidal currents and sediment transport in nearshore waters. In the event of typhoons or storm surges, this error will be amplified or even directly affect disaster prevention and mitigation decisions and engineering safety assessments.

[0004] Simple processing of wave-current interactions weakens the ability to simulate nonlinear wave-flow field coupling mechanisms. Furthermore, the velocity field distribution characteristics and swell features under the superposition of nearshore residual current structure, tidal current, and waves cannot be accurately predicted, leading to difficulties in optimizing harbor and waterway safety and harbor dredging construction schemes. This further complicates coastal ecological maintenance and hydrodynamic management.

[0005] Existing sediment transport models are not accurate enough in predicting suspended sediment and deposition processes under strong wind and wave conditions, making it difficult to meet the practical needs of port siltation prediction, estuary sediment management, and the restoration of nearshore ecosystems such as mangroves and salt marshes. Deviations in sediment transport can further affect the accuracy of coupled wave-flow-sediment simulations, creating a series of cascading errors and limiting the engineering application value of numerical simulations.

[0006] Based on the above analysis, there is an urgent need to establish a new numerical simulation method for wave-flow-sediment coupling, which can achieve higher accuracy in numerical simulation under strong wind and wave conditions nearshore, while improving the accuracy of wave breaking and dissipation, nonlinear wave-current coupling, and sediment transport. Enhancing the numerical simulation capabilities of the COAWST model can also provide technical support and guarantees for coastal disaster prevention and mitigation, port siltation management, and nearshore ecological environmental protection, and is of great significance for improving the engineering application value of tides and waves in marine engineering. Summary of the Invention

[0007] To address the shortcomings of existing COAWST multiphysics coupling models in the application of nearshore strong wind and wave conditions, this invention proposes a nearshore wave-flow-sediment coupling simulation method that considers the nonlinear effect of wave breaking, in order to improve the accuracy and stability of numerical simulation of waves, flow fields and sediment transport under nearshore strong wind and wave conditions.

[0008] This invention adopts the following technical solution: a nearshore wave-flow-sediment coupling simulation method considering the nonlinear effect of wave breaking, comprising the following steps:

[0009] Step 1: Input WRF high-resolution wind field data, tidal boundary conditions and water depth data, perform joint filtering processing of wind field and tidal data, initialize the initial conditions of wave module, initial conditions of flow field module, initial concentration of sediment module, and local parameters.

[0010] Step 2: Perform wave simulation using the improved wave breaking energy dissipation formula to calculate the local wave breaking energy dissipation. Meanwhile, considering the effects of wave height, water depth ratio and wave steepness on energy dissipation, the wave energy density spectrum and breakage probability are calculated.

[0011] Step 3, Flow Field Calculation Stage, in the radiation stress The nearshore flow field is calculated under nonlinear correction, the hydrodynamic boundary conditions are updated, the nonlinear coupling effect of wave-flow field is enhanced, and the characteristics of nearshore residual flow and backflow vortex power are reproduced.

[0012] Step 4: In the sediment transport calculation stage, the coupling diffusion coefficient is used. Calculate sediment suspension and deposition, update sediment concentration distribution, and perform dynamic coupling among wave, flow field, and sediment.

[0013] Step 5: Perform iterative updates , and This allows for the coupling of waves, flow fields, and sediment until the simulation time step ends or the calculation converges, enabling nearshore wave-flow-sediment simulation under extreme conditions such as typhoons, storm surges, and strong winds and waves.

[0014] Preferably, in step 1, the system is initialized before the simulation is conducted by providing the system with a high-resolution wind field (including horizontal wind speed) given by WRF. and vertical wind shear information ), tidal boundary conditions and water depth data .

[0015] Subsequently, the wind field and tidal data were processed by joint filtering, and low-pass filtering was used to remove short-term noise while retaining the tidal cycle and storm surge characteristics on long-term time scales.

[0016] A low-pass filter is represented as:

[0017] ;

[0018] in, , These represent the output time and the input time, respectively. Represents the time series of original wind speeds or tides; This represents the low-pass filter kernel function with the cutoff frequency; This represents the new signal obtained after filtering the original signal.

[0019] This operation effectively removes high-frequency short-time noise from the original signal while preserving the main tidal cycle and storm surge scale variations.

[0020] The initial conditions for the wave module are:

[0021] ;

[0022] ;

[0023] in, Significant wave height field; The initial distribution function represents the two-dimensional directional spectrum; These represent the angular frequency and direction of propagation of the wave, respectively. It is a two-dimensional directional spectrum; It represents the wave height at the initial spatial location.

[0024] The flow field module is initialized as follows:

[0025] ;

[0026] ;

[0027] in, It is obtained by synthesizing large-scale tidal circulation and local wind-generated flow, and is used to represent the velocity fields in the U and V directions at the initial moment; This represents the horizontal velocity component.

[0028] The initial concentration formula for the sediment module is:

[0029] .

[0030] The empirical formula used in the formula is:

[0031] ;

[0032] in, This indicates a reference concentration; This indicates the characteristic thickness of the sedimentary layer; The vertical coordinates represent the height calculated upwards from the riverbed or seabed.

[0033] Furthermore, in order to reflect the east-west characteristics of the shallow water area, local parameters are calculated, including:

[0034] Water depth gradient:

[0035] ;

[0036] Low coefficient of friction:

[0037] ;

[0038] in, , representing the von Kármán constant; Indicates the roughness length.

[0039] Local wave steepness:

[0040] ;

[0041] in, Used to represent local wave height, Used to represent wavelength, determined by the dispersion relation:

[0042] ;

[0043] ;

[0044] in, This represents the wave frequency. The wave number is represented. Indicates the depth of water.

[0045] These local parameters will serve as input conditions for subsequent breakup energy consumption and coupling diffusion coefficients, providing a physical basis for maintaining consistency among the wave-flow-sediment modules in subsequent coupled calculations, thereby ensuring the stability and convergence speed of the numerical simulation results.

[0046] Preferably, in step 2, the wave simulation adopts an improved wave breaking energy dissipation formula, while considering the influence of wave height to water depth ratio, wave steepness and breaking probability on wave energy dissipation, so that the calculation of wave breaking energy is more in line with the physical characteristics of complex conditions in nearshore shallow water areas, thereby improving the wave height prediction accuracy under nearshore shallow water and strong wind and wave conditions.

[0047] The improved formula for local wave breaking dissipation is expressed as follows:

[0048] ;

[0049] in, This indicates the energy dissipated by local wave breaking. ; This represents an empirical adjustment coefficient used to control the dissipation magnitude, which can be flexibly adjusted according to specific conditions such as the sea area and storm. The wave height / depth ratio and wave steepness index are derived from historical observation data. Indicates instantaneous wave height , Indicates local water depth , Indicates wavelength ; This represents the probability of breakage (values ​​0–1), indicating the likelihood of breakage occurring. Indicates water density ; Represents gravitational acceleration; Indicates wave frequency .

[0050] The wavelengths involved in the formula The beam is obtained by solving the dispersion relation:

[0051] ;

[0052] ;

[0053] in, Angular frequency , For wave number.

[0054] Breakage probability Expressed in the form of a smooth threshold function, with wave steepness Core control factor:

[0055] ;

[0056] in, Indicates the critical wave steepness; As an adjustment parameter, when the wave steepness approaches the critical value, the probability of breakage increases sharply, which is consistent with the actual measurement pattern.

[0057] To incorporate the terrain effect, in the adjustment coefficient Add a water depth gradient coupling term, the expression of which is:

[0058] ;

[0059] Wherein, in the expression The benchmark adjustment coefficient; Indicates reference depth; Indicates empirical parameters; This represents the water depth gradient magnitude; this formula can adaptively enhance breakup dissipation in shallow water areas and regions with drastic water depth changes.

[0060] Within the framework of the frequency-direction spectrum, the total fragmentation energy dissipation is obtained by spectral integration:

[0061] ;

[0062] After spectral discretization, frequency bands are used. and direction The grid representation is as follows:

[0063] ;

[0064] in, and It represents the discrete interval of frequency and direction; This represents the fragmentation and dissipation term.

[0065] Furthermore, in the numerical calculation process, a second- or third-order finite volume scheme is used to integrate the spectral equations to ensure energy conservation and reduce numerical dissipation.

[0066] As a preferred option, the discrete update equation is expressed as:

[0067] ;

[0068] in, For spectral component energy; This represents the input of wind energy and the contribution of nonlinear interactions; Represents the fragmentation dissipation term; Indicates the time step.

[0069] Through the above improvements, this invention not only introduces the coupling of wave height / depth ratio and wave steepness into the dissipation term, but also achieves adaptive correction to complex inshore topography through water depth gradient adjustment. At the same time, it uses probability functions to simulate the uncertainty of wave breaking, and ensures energy conservation in spectral integrals and numerical discretization, thereby improving the physical rationality and numerical stability of wave breaking energy in the calculation process.

[0070] Preferably, in step 3, after the wave calculation is completed, the nearshore flow field is updated using the coupling effect of radiation stress.

[0071] The traditional definition of the radiation stress tensor is:

[0072] ;

[0073] ;

[0074] ;

[0075] In the formula, Represents the directional spectrum; Indicates wave number; This indicates the local water depth.

[0076] Based on this, a nonlinear correction term is introduced, and the improved radiation stress formula is:

[0077] ;

[0078] in, This represents the nonlinearly corrected radiation stress tensor (Pa). This represents the traditional linear radiation stress value (Pa); This represents a nonlinear correction coefficient, used to enhance the wave-flow field coupling effect; Represents the velocity component (m / s); This represents the ratio of wave height to water depth, indicating the nonlinear effect in shallow water.

[0079] Based on nonlinear radiation stress correction, the nearshore residual current structure and the dynamic characteristics of tidal-surge-wave interaction can be reproduced, and the surge acceleration zone, backflow vortex, and nearshore velocity distribution anomalies under extreme conditions such as typhoons and storm surges can be accurately obtained.

[0080] The flow field calculation uses the finite volume method to discretize the momentum equation and utilizes the third-order Runge-Kutta time integral, which ensures the stability of the numerical calculation even under strong wind and wave conditions.

[0081] Furthermore, an adaptive CFL conditional control algorithm is used to ensure computational stability. Under conditions of high winds and waves, the time step corresponding to the local flow velocity and wave height is adaptively adjusted. To avoid numerical oscillations and divergence, the time step is calculated using the following formula:

[0082] ;

[0083] In the formula, The CFL coefficient is 0.2-0.5. This represents the horizontal velocity component; For shallow water wave speed, They are respectively the distance from the walking distance. This is the improved coupling diffusion coefficient.

[0084] Preferably, in step 4, the sediment transport equation is calculated using the energy dissipation coupled diffusion coefficient formula, specifically as follows:

[0085] ;

[0086] in, Indicates sediment concentration (kg / m³); The improved coupling diffusion coefficient (m² / s) is calculated using the following formula:

[0087] ;

[0088] in, Represents the baseline diffusion coefficient (m² / s); This represents the coupling coefficient, which reflects the enhancing effect of fracturing energy on sediment diffusion; This indicates the sediment settling velocity (m / s). This indicates the source and sink of sediment, taking into account the effects of river-estuary sediment transport, anthropogenic sediment discharge, erosion and sedimentation, etc.

[0089] This method directly converts wave breaking energy into energy that affects the coupling diffusion coefficient, realizing a dynamic correlation between it and suspended sediment concentration and local wave state. Under conditions such as typhoons and high winds and waves, it can significantly improve the prediction accuracy of sediment suspension and deposition, and improve the simulation accuracy of port siltation and nearshore ecological sediment transport.

[0090] Preferably, in step 5, the wave, flow field, and sediment modules are iteratively coupled after each time step completes the calculation: the wave module is updated. Flow field module update Sediment module update and This process iterates until the simulation time step ends or the numerical results converge.

[0091] Compared with the prior art, the present invention, employing the above technical solution, has the following technical effects:

[0092] 1. This invention introduces an improved two-factor formula based on wave height / depth ratio and wave steepness, which better simulates the wave breaking process under shallow water and strong wind / wave conditions, improving the accuracy of wave height, wave energy spectrum, and nearshore circulation. This improvement is of great significance for coastal protection engineering design, marine operation safety, and typhoon / storm surge forecasting. By incorporating nonlinear radiation stress correction in the wave-current coupling process, the simulation effect of the wave-flow field is improved, resulting in a more realistic reproduction of nearshore residual current structure, tidal wave velocity distribution, and swell characteristics. Compared with traditional linear or semi-empirical processing methods, it can better reproduce nonlinear dynamic processes, enhancing the reliability and scientific rigor of nearshore hydrodynamic simulation.

[0093] 2. This invention proposes a method for coupling energy dissipation and diffusion coefficient, which uses the improved calculated value of crushing energy dissipation to replace the calculated value of sediment diffusion, greatly improving the prediction accuracy of suspended sediment concentration and sedimentation amount; by improving the iterative coupling process and time step control, the stability and calculation speed of the simulation under extreme wind and wave conditions are optimized.

[0094] 3. The method of this invention couples the wave-flow field-sediment process throughout the entire process, and can achieve high-precision and stable nearshore wave-flow field-sediment simulation under extreme conditions such as typhoons, storm surges and strong winds and waves. This improves simulation efficiency and engineering operability, and can provide technical support for coastal disaster prevention and mitigation, port construction and ecological conservation. Attached Figure Description

[0095] Figure 1 This is a flowchart of the nearshore wave-flow field-sediment coupling simulation method of the present invention;

[0096] Figure 2 This is a flowchart of the improved wave breaking dissipation calculation method of the present invention;

[0097] Figure 3 This is a schematic diagram of the nonlinear radiation stress correction and a sediment coupling logic diagram of the present invention;

[0098] Figure 4 This is a schematic diagram of the dynamic distribution of sediment in the embodiment;

[0099] Figure 5 This is a flowchart of the coupling iteration in the embodiment;

[0100] Figure 6 This is a comparison chart of application examples. Detailed Implementation

[0101] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of the application will be further described in detail below with reference to the accompanying drawings. The described embodiments are only a part of the embodiments involved in this invention. All non-innovative embodiments based on these embodiments by other researchers in the art are within the protection scope of this invention. Furthermore, the step numbers in the embodiments of this invention are only set for ease of explanation and do not limit the order of the steps. The execution order of each step in the embodiments can be adaptively adjusted according to the understanding of those skilled in the art.

[0102] In one embodiment of the present invention, a nearshore wave-flow-sediment coupling simulation method considering wave breaking nonlinear effects is provided, such as... Figure 1 As shown, the steps are as follows:

[0103] Step 1: Initialization phase. Obtain WRF high-resolution wind field data, tidal boundary conditions and water depth data, and set the initial state of waves, flow field and sediment as the basis for subsequent coupled calculations.

[0104] Step 101: The wind field data consists of horizontal wind speed components given at different time steps, respectively. and The unit is meters per second.

[0105] The tidal boundary conditions give the amplitude of the main tidal components. ,frequency With phase The time series function used to determine the tidal level at the boundary:

[0106] .

[0107] Step 102: Water depth information is distributed in two-dimensional space. The input is in the form of , used to define the bottom boundary conditions of the ROMS and SWAN modules.

[0108] To avoid numerical instability caused by abrupt topographic changes, the water depth field is smoothed, and the updated formula is as follows:

[0109] ;

[0110] in, Indicates the depth of water; This represents the smoothing coefficient, with a value ranging from 0.1 to 0.3. This represents the difference between the average water depth of adjacent grid points and the water depth of the current grid point.

[0111] Step 103: After receiving external data, spatial and temporal interpolation needs to be performed on the received data to ensure that it is consistent with the time-varying COAWST mode grid and time step.

[0112] In this embodiment, spatial interpolation uses bilinear interpolation, and temporal interpolation uses linear interpolation. The specific formulas are as follows:

[0113] ;

[0114] in, and Representing adjacent time points The physical quantity value.

[0115] Step 104: During the wave field initialization process, if observation data exists, directly assign it as the initial significant wave height. Conversely, if there is no observational data, an empirical spectral function is used for setting.

[0116] Significant wave height With the zeroth moment of the wave energy spectrum The relationship between the two is as follows:

[0117] ;

[0118] ;

[0119] in, Represents the spectrum of a wave; It represents the frequency of the wave.

[0120] Step 105: During flow field initialization, a tidal driving component can be added to the driving component of the boundary to determine the initial velocity distribution of the inner domain under the drive of the wind field. If necessary, the flow field can also be adjusted by using the geostrophic balance approximation method.

[0121] Initialization of the sedimentation site includes setting the suspended sediment concentration. and sediment settling velocity For fine particles, calculations can be performed using Stokes' law:

[0122] ;

[0123] In the formula, Indicates the density of sediment particles; Indicates the density of water; Indicates particle diameter; This indicates hydrodynamic viscosity.

[0124] The above steps demonstrate how to properly set up the three initial fields: wave, flow field, and sediment. By generating a standard input file, we can effectively ensure the reliability and stability of the simulation results when performing coupled wave-flow-sediment simulations using the COAWST model.

[0125] Step 2: Wave simulation stage, such as Figure 2 As shown, the calculation path of joint control of (H / h) and (H / L) is presented. The modified wave breaking energy dissipation formula is used to consider the influence of wave height to water depth ratio and wave steepness on energy dissipation, and wave energy and breaking probability are calculated respectively.

[0126] A significant improvement in this embodiment is the addition of an improved wave breaking energy dissipation formula. That is, taking into account both wave height and water depth ratio. and wave steepness The influence of three factors on wave breaking energy dissipation effectively avoids the phenomenon of insufficient wave breaking energy dissipation in shallow water and high wind and wave conditions, which is present in the traditional Battjes & Janssen model.

[0127] Step 201: Use the wave height obtained from the initialization data. Wave frequency and water depth The wavelength was calculated using the dispersion relation. With wavenumber This allows us to determine the basic parameters of the waves:

[0128] ;

[0129] ;

[0130] ;

[0131] in, This represents the angular frequency; this calculation is used to determine the propagation characteristics of waves in shallow, medium, and deep water conditions.

[0132] Step 202: In traditional models, energy dissipation from breakup typically depends only on... This approach fails to accurately reflect the effect of wave steepness. This embodiment improves upon it, and the improved local wave breaking dissipation formula is expressed as follows:

[0133] ;

[0134] in, This indicates the energy dissipated by local wave breaking. ; This represents an empirical adjustment coefficient used to control the dissipation magnitude, which can be flexibly adjusted according to specific conditions such as the sea area and storm. The wave height / depth ratio and wave steepness index are derived from historical observation data. Indicates instantaneous wave height , Indicates local water depth , Indicates wavelength , This represents the probability of breakage (values ​​0–1), indicating the likelihood of breakage occurring. Indicates water density ; Represents gravitational acceleration; Indicates wave frequency .

[0135] Specifically, this embodiment introduces This feature can increase the dissipation of shortwave breaking energy during strong typhoons, thereby improving the accuracy of nearshore wave height forecasts.

[0136] Step 203: Add a breakup probability correction term to the energy dissipation formula to prevent all wave energy from entering the breakup process simultaneously, as shown below:

[0137] ;

[0138] in, Used to represent critical wave steepness; This is then used as an adjustment parameter. When the wave steepness approaches the critical value, the probability of breakage increases sharply, which is consistent with the actual measurement pattern.

[0139] Step 204: Update the wave energy balance equation and spectrum. In the SWAN wave module, the wave energy density spectrum... Satisfies the wave energy balance equation:

[0140] ;

[0141] in, Represents the group velocity vector; Represents the energy spectrum; Indicates wind energy input item; Represents nonlinear interaction terms; This represents the improved energy dissipation term for breakage.

[0142] At regular time steps, the frequency-direction spectrum distribution is updated using the method described above, and the significant wave height is calculated based on this spectrum distribution. Mean wave direction Key parameters, etc.

[0143] Step 205: Stabilize and iterate the numerical values. To prevent excessive fragment energy dissipation from causing spectral collapse, set adaptive stability control coefficients. Its function is as follows:

[0144] ;

[0145] in, To limit the proportion of spectral energy dissipation (usually taken as 0.3–0.5), the energy dissipation in each time step cannot exceed a certain proportion of the total energy, thereby maintaining the stability of the spectral values.

[0146] Step 206: The system outputs new wave field information, including: significant wave height. Wave direction distribution Energy spectrum The radiation stress input conditions and sediment transport module directly participate in the subsequent flow field calculation.

[0147] Step 3: Flow field calculation stage, such as Figure 3 As shown, nonlinear corrections are used to update the radiation stress in the nearshore flow field. The nearshore flow field was updated, and the hydrodynamic boundary conditions were adjusted to reflect the wave-flow field interaction.

[0148] Step 301: Based on the flow field calculations, the two-dimensional momentum equation under the shallow water governing equations is obtained, which can be expressed as:

[0149] ;

[0150] ;

[0151] in, Indicates the horizontal velocity component; Represents the Coriolis parameter; Indicates the height of the free surface; Indicates the density of water; Indicates water depth; This represents the corrected radiation stress components; It represents external forces such as friction and wind stress.

[0152] Step 302: To enhance the coupling effect between waves and the flow field, especially the nonlinear effect in shallow water, this embodiment introduces a nonlinear correction term related to the velocity component in the wave-flow coincidence process.

[0153] The traditional definition of the radiation stress tensor is:

[0154] ;

[0155] ;

[0156] ;

[0157] in, Represents the directional spectrum; Indicates wave number; This indicates the local water depth.

[0158] Corrected radiation stress As the driving force in the momentum equation:

[0159] ;

[0160] in, This represents traditional linear radiation stress; Indicates the correction factor; Represents the velocity component (m / s) in the wave-current recombination process. This represents the wave height-to-depth ratio, reflecting nonlinear effects in shallow water. This correction allows for more accurate capture of surge acceleration and backflow structures under extreme conditions.

[0161] Step 303: The hydrodynamic boundary conditions of the model are jointly determined by external forcing (such as tides and wind fields) and internal wave drive. At the open boundary, the water level conditions can be given by tidal forecasts and storm surges. The flow field in the inner domain of the model is continuously driven by the radiation stress gradient term modified by this invention, based on the external forcing, thereby realizing the dynamic simulation of wave-induced flows such as nearshore circulation and residual current.

[0162] Step 304: Spatial discretization of the momentum equation is performed using the finite volume method, and the flow velocity and water level are iteratively updated using an explicit or semi-implicit time-progression method.

[0163] Preferably, in this embodiment, the momentum equation is spatially discretized using the finite volume method, and the flux at the unit interface is approximately represented as follows:

[0164] ;

[0165] In the formula, Indicates characteristic wave velocity; This represents the flux function.

[0166] The time progression uses a third-order Runge-Kutta format, and the update steps are as follows:

[0167] ;

[0168] ;

[0169] ;

[0170] In the formula, Represents the discrete spatial operator. Indicates the current time step The variable value at time, , This represents the values ​​of the first and second intermediate steps in the calculation.

[0171] To ensure the numerical stability of the entire coupled mode under extreme wind and wave conditions, the time step is... The selection of the value must follow a unified and comprehensive control condition, which simultaneously considers the limitations of advection flow, shallow water wave propagation, and vertical sediment diffusion. The calculation formula is as follows:

[0172] ;

[0173] In the formula, The CFL coefficient is 0.2-0.5. This represents the horizontal velocity component; For shallow water wave speed, These represent the spatial distance step lengths. This comprehensive control condition effectively avoids numerical oscillations and divergence.

[0174] Step 305: Obtain improved flow field results, including: water level distribution. Horizontal flow velocity , And the radiation stress-driven circulation structure after nonlinear correction, which will be used as the hydrodynamic input conditions in the next stage of sediment transport calculation.

[0175] Step 4: Sediment transport calculation stage, such as Figure 4 As shown, the coupling diffusion coefficient is used. This process is used to calculate sediment suspension and deposition, and to update the sediment concentration field, achieving dynamic coupling between waves, flow field, and sediment.

[0176] Step 401, in this embodiment, the sediment transport equation is expressed using an improved diffusion coefficient that incorporates crushing energy coupling:

[0177] ;

[0178] in, The concentration of suspended sediment; Represents the velocity vector; Indicates the settling velocity; This indicates the source / sink of sediment (estuary sediment transport, anthropogenic discharge, etc.).

[0179] Furthermore, this embodiment introduces an improved coupling diffusion coefficient. This explicitly couples the enhancement of wave breaking energy to vertical mixing and horizontal diffusion:

[0180] ;

[0181] in, Indicates the basic eddy diffusion coefficient; Indicates the energy coupling coefficient; This indicates that energy is dissipated as the waves break up; Indicates the density of water; Represents wave height; Indicates the wave frequency.

[0182] Specifically, to ensure physical plausibility and avoid excessive negative or diffuse values ​​at extreme levels, in this embodiment, Restriction and normalization are applied:

[0183] ;

[0184] ;

[0185] in, Indicates the lower limit and upper limit. Indicates the local wave steepness. It is a normalization parameter used to suppress the non-physical coupling of low-energy spectral components to diffusion.

[0186] Step 402: Using the vertical profile assumption based on the Rouse distribution and coupling it with the diffusion coefficient to link the vertical structure and bed exchange:

[0187] ;

[0188] ;

[0189] in, Indicates reference height Concentration at that location, Indicates the roughness length. Denotes the Kármán constant; Indicates frictional speed; This represents the number of Rouses.

[0190] The relationship between frictional velocity and bed surface stress is as follows:

[0191] ;

[0192] ;

[0193] in, Indicates the shear stress on the bed surface. Indicates the bed friction coefficient. The near-bed velocity is indicated.

[0194] The bed erosion-deposition flux is given by the following formula:

[0195] ;

[0196] ;

[0197] in, Indicates the erosion rate, Indicates the erosion coefficient. Indicates the critical shear stress; This represents the deposition flux.

[0198] The evolution of bed height is represented by the Exner equation:

[0199] ;

[0200] in, Indicates the bed surface elevation. Indicates the porosity of the bed. This indicates the bed-borne transport flux.

[0201] Step 403: Introduce the turbulent energy production term and the breakup energy contribution and synthesis model, which allows the vertical turbulent production and diffusion of breakup energy to be directly coupled:

[0202] ;

[0203] in, This represents the turbulent energy generated during fluid shearing; This represents the efficiency coefficient for converting spectral dissipated energy into near-bed turbulent energy.

[0204] Turbulent viscosity Represented as:

[0205] ;

[0206] ;

[0207] That is, the reference diffusion coefficient It exhibits a proportional relationship with turbulent viscosity, where, Represents the standard coefficients in a turbulence model; These are empirical coefficients. Through this coupling operation, By increasing Indirect enhancement of production items This naturally enhances vertical and horizontal mixing in areas of strong fragmentation.

[0208] Step 404: In terms of numerical implementation, operator splitting is used to handle horizontal transport and vertical diffusion-settlement. Specifically, the horizontal term is discretized using an explicit higher-order upwind scheme with a finite volume method, while the vertical diffusion-settlement term is handled implicitly using finite difference to ensure stability. The discretized expression is as follows:

[0209] ;

[0210] in, This represents the horizontal and vertical difference operators; This indicates the grid points. Sediment sources / sinks at the location; This represents the vertical difference operator.

[0211] To maintain global mass conservation, the bed flux boundary condition adopts bed-water flux consistency, expressed as:

[0212] ;

[0213] in, Indicates deposition flux; Indicates the elevation of the bed surface.

[0214] The time step needs to simultaneously satisfy both the horizontal CFL condition and the vertical diffusion stability condition:

[0215] ;

[0216] .

[0217] This embodiment achieves a sediment transport coupling module that is physically consistent, numerically stable, and easy to calibrate by explicitly coupling the spectral breaking energy into the diffusion coefficient and simultaneously providing coupling relationships and constraint treatments in vertical profile, bed exchange, turbulent closure, and numerical discretization.

[0218] Step 5: In the coupling iteration phase, such as Figure 5 As shown, the wave, flow field, and sediment modules are calculated and updated through loops. and The process continues to iterate until the simulation ends and convergence is achieved, or until the computation time ends and the entire process is terminated.

[0219] Step 501: In the COAWST mode, a cyclic logic iterative method is used in the coupling process:

[0220] ;

[0221] Among them, superscript Indicates the current iteration step; This indicates improved wave breaking energy dissipation; Represents the nonlinearly corrected radiation stress; This represents the improved coupling diffusion coefficient; Indicates significant wave height; Indicates sediment concentration.

[0222] After each time step, the wave field, flow field and sediment field can continuously interact and feedback each other throughout the entire simulation period, and gradually tend to a stable state over time.

[0223] Step 502: For each iteration, the wave module first outputs the corrected breakdown energy dissipation. and significant wave height The above two parameters are used to correct the radiation stress in the flow field:

[0224] ;

[0225] The obtained radiation stress value is then used as a forced term in the momentum equation and input into the flow field module to realize the dynamic adjustment of nearshore velocity and residual flow by waves.

[0226] Step 503, the flow field module completes the adjustment of the new water level. and flow rate After calculation, the results are passed to the sediment transport module to calculate the convective transport term of sediment:

[0227] ;

[0228] Among them, the flow field shear stress determines the friction velocity. This, in turn, determines the distribution of sediment profile (Rouse number). Therefore, changes in the flow field can also affect the suspension and settling rates of sediment.

[0229] Step 504, Sediment Concentration Field After the update, it will have a reaction effect on the turbidity and effective water depth of the water body, thereby changing the propagation environment of waves and flow fields, that is, completing the correction of the feedback mechanism:

[0230] The impact on waves lies in the increased water density caused by high concentrations of sediment. Changes in wave velocity corrected:

[0231] ;

[0232] It alters the dispersion relation; its impact on the flow field lies in the elevation of the bed surface due to sediment deposition. Changes have occurred, and the water depth has been updated. This changes the bottom boundary conditions of the momentum equation.

[0233] Step 505: Determine coupling convergence. If each time step of the coupling iteration needs to satisfy the convergence condition, then set the following criterion:

[0234] ;

[0235] in, This represents the convergence threshold, which is usually taken as... If the conditions are met, the computation at this time step is considered converged; otherwise, the iteration continues until convergence or the maximum number of iterations is reached. .

[0236] Step 506: To avoid numerical divergence during the iteration process, this invention introduces an adaptive time step control strategy:

[0237] ;

[0238] When numerical oscillations are detected during the iteration process, the system will reduce the step size to maintain stability.

[0239] Step 507: After the coupling iteration phase is completed, the system outputs the wave field results (significant wave height). directional distribution Energy spectrum ), flow field (water level) Flow velocity distribution (circulation structure) and sediment field (three-dimensional concentration) Changes in bed surface ).

[0240] In particular, the method of this invention and the traditional COAWST and improved methods are compared in terms of wave height, flow velocity, and sediment concentration in typhoon storm surge simulation. Figure 6 As shown, the energy dissipation-sediment diffusion coupling method of this invention significantly improves performance compared to the traditional COAWST model. This method ensures that the system composed of waves, flow field, and sediment maintains energy conservation in each iteration, increasing computational convergence and accuracy. It improves simulation efficiency and engineering operability while maintaining accuracy.

[0241] These results are the final simulation results of the fully coupled model, which can be directly used in corresponding engineering applications such as typhoon storm surge simulation, port siltation prediction, and coastal protection engineering assessment.

[0242] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A nearshore wave-flow-sediment coupling simulation method considering the nonlinear effects of wave breaking, characterized in that, Includes the following steps: Step 1: Input WRF high-resolution wind field data, tidal boundary conditions and water depth information, perform joint filtering of wind field and tidal data, and initialize wave module, flow field module, sediment module and local parameters; Step 2: Perform wave simulation using the improved local wave breaking energy dissipation formula to calculate the local wave breaking energy dissipation. Meanwhile, considering the effects of wave height, water depth ratio and wave steepness on energy dissipation, the wave energy density spectrum and breakage probability are calculated. The improved formula for local wave breaking dissipation is expressed as follows: ； in, This indicates the energy dissipated by the breaking of local waves; This represents an empirical adjustment coefficient used to control the magnitude of dissipation. This indicates the wave height / depth ratio and the wave steepness index; Indicates the probability of breakage; Indicates the density of water; Represents gravitational acceleration; Indicates the wave frequency; This represents the wave height at the initial spatial location; Indicates the depth of water; Indicates wavelength; The probability of breakage Using a smooth threshold function, through wave steepness Core control factor: ； in, Indicates the critical wave steepness; To adjust the parameters; The adjustment coefficient The addition of a water depth gradient coupling term adaptively enhances breakup dissipation in shallow water areas and regions with drastic water depth changes. The expression is as follows: ； in, The benchmark adjustment coefficient; Indicates reference depth; These are empirical parameters; Indicates the magnitude of the water depth gradient; Step 3, Flow Field Calculation Stage, in the radiation stress The nearshore flow field is calculated under nonlinear correction, the hydrodynamic boundary conditions are updated, and the nonlinear coupling effect of wave-flow field is enhanced. Step 4, Sediment Transport Calculation Stage: Using the Coupling Diffusion Coefficient Calculate sediment suspension and deposition, update sediment concentration distribution, and perform dynamic coupling among wave, flow field, and sediment. Step 5, the coupling iteration phase, involves updating through iterative loops. , and This allows for the coupling of waves, flow fields, and sediment until the simulation time step ends or the calculation converges, enabling nearshore wave-flow-sediment simulation under extreme conditions such as typhoons, storm surges, and strong winds and waves.

2. The nearshore wave-flow-sediment coupling simulation method considering wave breaking nonlinear effects according to claim 1, characterized in that, In step 1, the wind field data provides the horizontal wind speed components at different time steps. and The tidal boundary conditions give the amplitude of the main tidal components. ,frequency With phase This is used to determine the tidal time series function at the boundary; the water depth information is distributed in two-dimensional space. Formal input, used to define the bottom boundary conditions of the ROMS and SWAN modules; Using wind field data, tidal boundary conditions, and water depth data provided by WRF, joint filtering of wind field and tidal data is performed. A low-pass filter is used to remove short-term noise while preserving long-term tidal cycles and storm surge characteristics. The low-pass filter is represented as follows: ； in, , These represent the output time and the input time, respectively. Represents the time series of original wind speeds or tides; The low-pass filter kernel function representing the cutoff frequency; This represents the new signal obtained after filtering the original signal.

3. The nearshore wave-flow-sediment coupling simulation method considering wave breaking nonlinear effects according to claim 1, characterized in that, In step 1, the initial conditions for the wave module are: ； ； in, Significant wave height field; The initial distribution function represents the two-dimensional directional spectrum; These represent the angular frequency and direction of propagation of the wave, respectively. It is a two-dimensional directional spectrum; The initial conditions for the flow field module are: ； ； in, This is obtained by synthesizing large-scale tidal circulation and local wind-generated flow, used to represent the velocity fields in the U and V directions at the initial moment; Indicates the horizontal velocity component; The initial concentration of the sediment module is: ； in, The concentration of suspended sediment is expressed by the following formula: ； in, Indicates the reference concentration; Indicates the characteristic thickness of the sedimentary layer; The vertical coordinates represent the height calculated upwards from the riverbed or seabed.

4. The nearshore wave-flow-sediment coupling simulation method considering wave breaking nonlinear effects according to claim 3, characterized in that, In step 1, the local parameters include: water depth gradient : ； in, Indicates the depth of water; Low coefficient of friction : ； in, Represents the von Kármán constant; Indicates the roughness length; Local wave steepness : ； in, Represents local wave height; Wavelength is determined by the dispersion relation: ； ； in, Indicates the wave frequency; Indicates wave number.

5. The nearshore wave-flow-sediment coupling simulation method considering wave breaking nonlinear effects according to claim 4, characterized in that, In step 2, within the framework of the frequency-direction spectrum, the total fragmentation energy dissipation is obtained by spectral integration: ； After spectral discretization, frequency bands are used. i and direction j The grid representation is as follows: ； in, and It represents the discrete interval of frequency and direction; Represents the fragmentation dissipation term; Integrating the spectral equation using a second- or third-order finite volume scheme, the discrete update equation is expressed as: ； in, For spectral component energy; This represents the input of wind energy and the contribution of nonlinear interactions; Represents the fragmentation dissipation term; Indicates the time step.

6. The nearshore wave-flow-sediment coupling simulation method considering wave breaking nonlinear effects according to claim 5, characterized in that, In step 3, the nearshore flow field radiation stress is updated using nonlinear correction. The nearshore flow field is updated using the following method: Step 301: Obtain the two-dimensional momentum equation based on the shallow water control equations according to the flow field calculation; Step 302: Introduce a nonlinear correction term related to the flow velocity component, and adjust the corrected radiation stress. As the driving source in the momentum equation; Step 303: Simulate nearshore circulation and wave-induced flow dynamics: The hydrodynamic boundary conditions are determined by external forcing of tides and wind fields and internal wave drive. The water level conditions at the open boundary are given by tidal forecasts and storm surge increase methods. The inner domain flow field is continuously driven by the modified radiation stress gradient term based on external forcing. Step 304: Spatial discretization of the momentum equation is performed using the finite volume method, and the flow velocity and water level are iteratively updated using an explicit or semi-implicit time-progression method. Step 305: Obtain improved flow field results, including: water level distribution. Horizontal flow velocity and The nonlinearly corrected radiation stress-driven circulation structure serves as the hydrodynamic input condition for the sediment transport calculation stage in step 4.

7. The nearshore wave-flow-sediment coupling simulation method considering wave breaking nonlinear effects according to claim 6, characterized in that, The two-dimensional momentum equation based on the shallow water governing equations is expressed as: ； ； in, Represents the Coriolis parameter; Indicates the height of the free surface; This represents the corrected radiation stress components; Indicates the external force term; The corrected radiation stress , is represented as: ； in, This represents the radiation stress after nonlinear correction; This represents a correction factor used to enhance wave-flow field coupling. Represents the velocity component in the wave-current recombination process; This represents the wave height to water depth ratio, used to reflect nonlinear effects in shallow water.

8. The nearshore wave-flow-sediment coupling simulation method considering wave breaking nonlinear effects according to claim 7, characterized in that, The momentum equation is spatially discretized using the finite volume method, and the flux at the element interface is approximately expressed as: ； In the formula, Indicates characteristic wave velocity; Represents the flux function; The time progression uses a third-order Runge-Kutta format, and the update steps are as follows: ； ； ； In the formula, Represents the discrete spatial operator. Indicates the current time step The variable value at time, , This represents the values ​​of the first and second intermediate steps in the calculation; Adaptive adjustment of the time step corresponding to local flow velocity and wave height By employing an energy dissipation-sediment diffusion coupling strategy, the energy balance of the wave-flow-sediment system is maintained during the iteration process. The time step calculation formula is as follows: ； In the formula, Represents the CFL coefficient; Shallow water wave speed; These are the spatial distances from the walking distance; This is the improved coupling diffusion coefficient.

9. The nearshore wave-flow-sediment coupling simulation method considering wave breaking nonlinear effects according to claim 7, characterized in that, In step 4, the sediment transport equation is constructed using an improved diffusion coefficient incorporating breakup energy coupling, and the formula is as follows: ； in, Indicates sediment concentration; Indicates sediment source / sink; Indicates the sediment settling velocity; The improved coupling diffusion coefficient is calculated using the following formula: ； in, Indicates the reference diffusion coefficient; This represents the coupling coefficient, reflecting the enhancing effect of fracturing energy on sediment diffusion. Indicates the wave frequency.

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