A method considering the flow characteristics of a unidirectional vortex-driven rip flow system

Abstract

The present invention provides a method that considers the flow characteristics of a unidirectional vortex-driven rift flow system, wherein a vertical coastal structure with a strong reflection effect on waves reflects the incident irregular waves and forms a large-scale negative vortex-driven rift flow system within the first standing wave wavelength in the reflection zone upstream of the structure. The method applies a simplified model of a nonlinear gentle slope equation accelerated by GPU parallelization to simulate a unidirectional vortex-driven rift flow system near a structure. The model has both accurate dispersion and higher computational efficiency. By comparing the incident wave spectrum of irregular waves in the model with the experimental results, the ability of the model of the present invention to generate random waves is verified. Based on the numerical model, the different flow characteristics of the unidirectional vortex-driven rift flow system compared to the common counter-vortex-driven rift flow system are demonstrated, and the influence of the wave reflection coefficient of the structure on the flow characteristics of the unidirectional vortex-driven flow system is analyzed.

Description

Technical Field

[0001] The present invention belongs to the technical field of marine engineering hydrodynamics, and in particular relates to a method considering the flow characteristics of a unidirectional vortex-driven rip current system. Background Art

[0002] Rip currents are a common natural disaster on the coast. They not only cause coastal erosion and changes in the offshore ecological environment, but also pose a serious threat to the lives and safety of tourists. Previous studies have mostly considered rip current systems driven by vortex pairs (i.e., vortex pairs that appear almost symmetrically about the rip current), such as the vortex pairs that appear on both sides of a short-crest wave and the rip currents they cause between the short-crest waves (Wei Z, Dalrymple RA, Munan X, Roland G, Morteza D. Short-Crested Waves in the Surf Zone [J]. Journal of Geophysical Research: Oceans. 2017, 122: 4143–4162.) and the groove rip currents driven by vortex pairs caused by uneven wave breaking along the coast at the spacing between multi-segment submerged reefs (Chen Q, Dalrymple RA, Kirby JT, Kennedy AB, Haller M C. Boussinesq Modeling of a Rip Current System. Journal of Geophysical Research: Oceans. 1999, 104(C9): 20617–20637.). Due to the symmetry of the driving vortex, the distribution and motion patterns of these rip currents are relatively easy to predict and describe. However, the motion characteristics of rip currents driven by asymmetric, unidirectional vortices are often more difficult to consider. This is because the unidirectional vortex motion is more random and no longer exhibits a slow offshore shedding process, such as the rip current system caused by the oblique motion of a unidirectional vortex at the edge of a single submerged breakwater (Brocchini M, Kennedy A, Soldini L, Mancinelli A. Topographically Controlled, Breaking-Wave-Induced Macrovortices. Part 1. Widely Separated Breakwaters. Journal of Fluid Mechanics. 2004, 507:289–307.). In real ocean environments, rip currents driven by unidirectional vortices often occur due to random wave characteristics, but existing research has not yet clearly provided a method for considering these characteristics.

[0003] Therefore, establishing a method to consider the flow characteristics of a unidirectional vortex-driven rip flow system is a problem that needs to be solved. Summary of the Invention

[0004] To address the problems existing in the prior art, the present invention aims to provide a method that considers the flow characteristics of a unidirectional vortex-driven rip flow system. This method applies a simplified model of nonlinear mild-slope equations accelerated by GPU parallelization to simulate unidirectional vortex-driven rip flow systems near structures. This model combines accurate dispersion with higher computational efficiency. By comparing the wave spectrum of the irregular wave incident in the model with experimental results, the ability of the model to generate random waves is verified. Based on a numerical model, the flow characteristics of a unidirectional vortex-driven rip flow system that differ from a common counter-vortex-driven rip flow system are demonstrated, and the influence of the structure's wave reflection coefficient on the flow characteristics of the unidirectional vortex-driven rip flow system is analyzed.

[0005] The purpose of the present invention is achieved through the following technical solutions:

[0006] A method for considering the flow characteristics of a unidirectional vortex-driven rip flow system comprises the following steps:

[0007] Step 1, physical model experiment:

[0008] S11, Experimental setup: The experiment was conducted in a laboratory pool containing a wave generator, with the wave generator at one end and a sponge absorbing boundary layer at the other. Two wave guide walls were placed along the long side of the pool, and a flat, sloped shoreline with a certain angle of rotation relative to the horizontal was built between the two wave guide walls in the center of the pool.

[0009] An outlet structure is arranged on the upper side of the flat coast in a direction perpendicular to the shoreline. When the wave-making plate generates unidirectional irregular waves parallel to the direction of the pool, a triangular wave reflection area will be formed upstream of the outlet structure.

[0010] S12, Experimental wave condition selection and wave generation: Several groups of experimental wave conditions are selected in the experiment, including regular wave conditions and irregular wave conditions; each wave condition contains three cycles, including: H i is the incident wave height in deep water, T p is the spectrum peak period, λ is the theoretical standing wave wavelength corresponding to the spectrum peak period;

[0011] Then the i-th theoretical node line along the coast y=y Ni and the theoretical antinode line y=y Ai The position of the standing wave can be given by the standing wave wavelength λ as follows:

[0012] y Ni =(i-0.5)λ (1)

[0013] y Ai =(i-1)λ (2)

[0014] S13, wave field and flow field measurement: In the experiment, several capacitive wave height meters were selected to measure the wave field inside and outside the wave reflection area, and several Doppler current meters were used to measure the flow field;

[0015] The wave height H in the wave field is calculated by applying the zero-crossing method to the wave surface η recorded by the wave height meter, while the mean water surface rise <η> is obtained by directly taking the time average of η;

[0016] The current meter is placed at a distance of 1 / 3 of the local water depth from the water bottom to measure the average flow velocity at water depth; Step 2, numerical model simulation:

[0017] A simplified nonlinear mild-slope equation model accelerated by GPU parallelism was used to simulate the physical model experiment in step 1 and calibrate the model parameters. Finally, the flow characteristics of the unidirectional vortex-driven rip flow system under different configurations were studied by changing the numerical model settings. Specifically, the following were done:

[0018] S21, simplified model of nonlinear mild slope equation: Using a Cartesian rectangular coordinate system (x, y, z), where the x-axis is perpendicular to the shoreline, the y-axis is parallel to the shoreline, and the z-axis is vertically upward, the GPU-accelerated simplified model of nonlinear mild slope equation has the following governing equation:

[0019]

[0020] Where t is time, and the subscript t represents the derivative with respect to time. is the symbol of the gradient operator in the horizontal direction, U = (U, V) is the horizontal velocity vector at the still water level, U and V are the current velocities in the x and y directions on the still water surface, η is the wave surface, h is the still water depth, g is the acceleration of gravity, k is the wave number, T is the wave period, c is the wave speed, the coefficient n = 1 / 2 + kh / sinh (2kh), and R is the term that takes into account the effects of wave breaking, bottom friction, and lateral mixing;

[0021] S22, GPU parallel accelerated computing: Use the unified computing device architecture CUDA and C language to perform GPU parallel computing on the model;

[0022] S23, irregular wave generation:

[0023] Wave generation is performed by adding the source function F(x, y, t) to the right side of the above equation (3). The specific solution process of F(x, y, t) is as follows:

[0024] Divide the unidirectional irregular wave spectrum JONSWAP spectrum into N = 100 parts in the frequency domain, then for each wave frequency component ω i The incident wave amplitude is Where S(ω i) is the JONSWAP spectrum function. The corresponding source function amplitude D i for:

[0025]

[0026] Where, the subscript i represents the frequency component ω corresponding to each wave i The variable (k x ) i =k i cosα, where k i According to the exact dispersion relation Solve, c i =ω i / k i is the wave speed, n i =1 / 2+k i h / sinh(2k i h) is the wave transmission efficiency, in is a parameter related to the wave width;

[0027] By substituting the source function amplitude D si , we get the expression of the source function F(x,y,t):

[0028]

[0029] Where x s is the position of the source function in the x direction, is the random initial phase of the source function;

[0030] S24, numerical model settings: Determine the coastal width and offshore length of the numerical model calculation domain. The offshore boundary is the sponge layer absorbing boundary, the shore boundary is the wave climbing dynamic boundary, and the upstream and downstream boundaries are both solid boundaries. The downstream boundary can be regarded as a vertical shoreline structure that reflects incident waves.

[0031] S25, Numerical Model Verification: Use the numerical model to simulate the physical model experiment, and compare and analyze the numerical model results with the physical model experiment results to verify the accuracy of the numerical model; the verification content includes wave field verification and flow field verification. The former is verified by comparing wave height and mean water surface, while the latter is verified by comparing the flow velocity in the perpendicular and along-shore directions and the flow velocity vector within the flow field;

[0032] Step 3: Change the numerical model settings to analyze the flow characteristics of the unidirectional vortex-driven rip flow system:

[0033] Using the experimentally verified GPU parallel accelerated nonlinear mild slope equation simplified model and numerical simulation settings given in step 2, by changing a single setting parameter, the influence of factors such as the structure's reflection coefficient of waves, the wave incident angle, and the wave incident height and period on the flow characteristics of the unidirectional vortex-driven rip current system is studied.

[0034] Furthermore, in step 1, S12, the theoretical standing wave wavelength λ corresponding to the spectrum peak period is calculated according to the Snell theorem using the following formula:

[0035]

[0036] Where L0 is the deep water incident wavelength corresponding to the spectral peak period, and α is the wave incident angle.

[0037] Furthermore, in step 2, S22, the process of GPU parallel computing of the model based on CUDA and C language includes: declaring and defining variables on the host side and the device side, allocating memory space for variables on the host side and the device side, initializing the host side variables, copying the host side data to the device side, calling the device side kernel function in sequence to complete the calculation, copying the device side data back to the host side, and finally outputting the result;

[0038] The number of logically enabled threads in the kernel function call is organized in two levels. The first level specifies the grid size, that is, the number of thread blocks in the grid in the x and y directions. The second level defines the thread block size, that is, the number of threads in a thread block.

[0039] Furthermore, during the verification of S25 in step 2, the flow velocity in the numerical model needs to be converted into the average flow velocity at water depth. The flow velocity is converted using the following formula using the flow conservation principle:

[0040]

[0041] Where <·> represents the time averaging, u = (u, v), where u and v are the average water depth velocities in the x and y directions, respectively.

[0042] The beneficial effects of the present invention compared to the prior art are:

[0043] 1. The present invention provides a simple and effective physical model experiment and numerical model simulation method for forming a unidirectional vortex-driven rip current system. Relying on the strong reflection effect of incident random waves on the structure perpendicular to the coast, uneven coastal surge and strong lateral current are formed upstream of the structure. The lateral current acts on the counterclockwise water flow in the vortex, reducing the counterclockwise vortex and enhancing the clockwise vortex, so that a unidirectional vortex-driven rip current system is formed upstream of the structure.

[0044] 2. In the numerical simulation method of the present invention that considers the flow characteristics of the unidirectional vortex-driven rift current system, the simplified nonlinear mild-slope equation model accelerated by GPU parallelization is applied to the simulation of the unidirectional vortex-driven rift current system near coastal structures. Since the model described in the present invention is a nonlinear mild-slope equation model, it has the characteristics of precise dispersion and can be better applied to the simulation of wave surfaces and water flows near structures far offshore.

[0045] 3. Since the numerical model described in the present invention removes the high-order nonlinear terms and weak nonlinear terms containing the bottom slope in the fully nonlinear gentle slope equation model, the model form is simpler. In addition, since CUDAC is used for GPU parallel computing, the current model has high computational efficiency, ensuring the timeliness of the numerical simulation research on the unidirectional vortex-driven rift flow system near the structure. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] The present invention will be further described below with reference to the accompanying drawings and embodiments:

[0047] Figure 1 The plan layout (a) and cross-section (b) of the physical model experiment are shown;

[0048] Figure 2 This is a schematic diagram of the calculation process of the GPU parallel acceleration model developed based on CUDAC;

[0049] Figure 3 This is a schematic diagram of the calculation domain setting of the numerical model;

[0050] Figure 4 The following is a comparison of the incident wave spectra of irregular waves at the wave height gauge position (x = 12m, y = 9m) in the comparative example and the numerical model; where f (Hz) is the frequency and S (f) is the spectral density;

[0051] Figure 5 Comparison diagrams of the instantaneous free wave fronts given for irregular wave condition A (left figure) and regular wave condition E (right figure) in Example 2; (a) and (b) are the wave fronts in the experiment, and (c) and (d) are the wave fronts given by numerical simulation;

[0052] Figure 6 The wave height (left figure) and water level increase and decrease (right figure) distribution results on different nodes and antinode lines for four groups of irregular wave conditions given in Example 2; the scattered points represent experimental results, and the curves represent numerical simulation results;

[0053] Figure 7 The wave height and water level increase / decrease distribution results for regular wave condition F in Example 2 are given; the definitions of each scatter point and line type are the same as Figure 6 ;

[0054] Figure 8The numerical simulation vorticity diagram (color filling), nearshore wave surge (red curve) and time-averaged flow field comparison diagram (arrows) given for regular waves (right column) and irregular waves (left column) in Example 2; wherein the red arrow represents the experimental flow velocity, the black arrow represents the numerical simulation flow velocity; the white arrow indicates the non-node-symmetric vorticity for the irregular wave case; the purple arrow indicates the node-symmetric vorticity for the regular wave case; the vertical black solid line represents the theoretical antinode line; the vertical black dashed line represents the theoretical node line;

[0055] Figure 9 This is the irregular wave situation at the position x=3m on the cross section in Example 2 and <v>The coastal distribution of; Among them, the black solid line represents the theoretical antinode line; the black dotted line represents the theoretical node line;

[0056] Figure 10 3 is the vorticity distribution and flow field diagram corresponding to the wave reflection coefficient of different structures in Example 3; wherein, the black solid line represents the theoretical antinode line; and the black dotted line represents the theoretical node line. DETAILED DESCRIPTION

[0057] The preferred embodiments of the present invention will be described in detail below with reference to the examples. It should be understood that the following examples are provided for illustrative purposes only and are not intended to limit the scope of the present invention. Those skilled in the art may make various modifications and substitutions to the present invention without departing from the purpose and spirit of the present invention. Unless otherwise specified, the technical means used in the examples are conventional means well known to those skilled in the art, and the equipment and reagents used are all conventionally commercially available.

[0058] Example 1

[0059] This embodiment provides a method for considering the flow characteristics of a unidirectional vortex-driven rip flow system, including the following steps:

[0060] Step 1, physical model experiment:

[0061] S11, Experimental setup: The experiment was conducted in a laboratory tank containing a wave maker, e.g. Figure 1 As shown in the figure, the pool is 55m long and 34m wide, with a wave maker on the left end and a sponge absorption boundary layer on the right end. Two wave guide walls are arranged along the long side of the pool, with a spacing of 25.2m. A flat sloped coast with a slope is built with concrete between the two wave guide walls in the center of the pool. The coast is rotated 30° relative to the horizontal direction and is arranged 8m away from the wave maker.

[0062] An 18-meter-long water outlet structure was installed perpendicular to the shoreline on the upper side of a flat coast. To ensure total reflection of incident waves, the structure was surfaced with cement mortar. The water depth at the flat bottom was 27.5 cm. At this depth, the total length of the structure in water was 15.7 meters, while the length on the shore was 3 meters. When the wave generator generates unidirectional irregular waves parallel to the pool, the angle α = 30° relative to the perpendicular shoreline is formed upstream of the water outlet structure. This triangular wave reflection region is 9 meters wide on the still water line. For ease of experimental description, a Cartesian coordinate system (x, y, z) is used, with the origin at the intersection of the still water line and the structure, the x-axis on the structure, the y-axis on the still water line along the coast, and the z-axis pointing vertically upward.

[0063] S12, experimental wave condition selection and wave generation: In the experiment of this embodiment, 7 groups of experimental wave conditions are selected, including 3 groups of regular wave conditions and 4 groups of irregular wave conditions; each wave condition contains three cycles, including: H i is the incident wave height in deep water, T p is the spectrum peak period, and λ is the theoretical standing wave wavelength corresponding to the spectrum peak period.

[0064] For the 1.5s period irregular wave condition, two sets of wave heights are considered, while for the other wave conditions, only one set of wave heights is considered. Table 1 gives an introduction to these experimental wave conditions.

[0065] Table 1 Physical model experimental wave conditions

[0066]

[0067] According to Snell's theorem, the theoretical standing wave wavelength λ corresponding to the spectrum peak period is calculated by the following formula:

[0068]

[0069] Where L0 is the deep water incident wavelength corresponding to the spectral peak period, and α is the wave incident angle.

[0070] Then the i-th theoretical node line along the coast y=y Ni (hereinafter referred to as nodes) and the theoretical antinode line y = y Ai The position of the antinode (hereinafter referred to as the antinode) can be given by the standing wave wavelength λ according to the following formula:

[0071] y Ni =(i-0.5)λ (1)

[0072] y Ai =(i-1)λ (2)

[0073] The incident wave in the experiment is a unidirectional narrow spectrum random wave generated by the JONSWAP spectrum with a spectrum peak enhancement factor γ=3.3.

[0074] S13, wave field and flow field measurement: In the experiment of this embodiment, 46 capacitive wave height meters are selected to measure the wave field inside and outside the wave reflection area, and 12 Doppler velocimeters (ADV) are used to measure the flow field.

[0075] The wave height H in the wave field is calculated by applying the zero-crossing method to the wave surface η recorded by the wave height meter, while the mean water level rise <η> is obtained by directly taking the time average of η. In the experiment of this embodiment, the sampling frequency is 50 Hz, and the total sampling time is 327 seconds (corresponding to 16,384 sampling points). The data in the time period of 60 to 300 seconds is used to calculate the wave field results.

[0076] For ease of movement, these measuring instruments are installed on three measuring beams. Beam I is equipped with 18 wave height meters to measure incident wave information at y = 9 m outside the reflection zone. Beams II and III are each equipped with 14 wave height meters to record wave information at nodes and antinodes within the reflection zone. The coastal positions of these nodes and antinodes can be calculated using equations (2) and (3). Table 2 shows the specific offshore locations of the wave height meters on each beam.

[0077] Table 2 Offshore location of wave height meter

[0078]

[0079] Table 3 Current meter locations along the coast

[0080]

[0081] The current meters have a measurement range of ±1 m / s and a measurement error of ±1 mm / s. These current meters were installed on two measurement racks to measure the flow velocity at five coastal sections near the structure. Table 3 shows the specific locations of the measurement points of these current meters. Among them, the larger measurement range at the x = 3 m section is to measure the distribution characteristics of the rip current in the coastal direction, while the smaller measurement ranges at other sections are to obtain the vortex field characteristics near the structure. In the experiment, these current meters were placed at a distance of 1 / 3 of the local water depth from the bottom to measure the depth-averaged flow velocity. For all wave conditions, the measurement duration was 720 s, and the flow velocity results of 120 to 720 s were averaged to obtain the time-averaged flow velocity.

[0082] Step 2, numerical model simulation:

[0083] A simplified nonlinear mild-slope equation model accelerated by GPU parallelism was used to simulate the physical model experiment in step 1 and calibrate the model parameters. Finally, the flow characteristics of the unidirectional vortex-driven rip flow system under different configurations were studied by changing the numerical model settings. Specifically, the following were done:

[0084] S21, simplified model of nonlinear mild slope equation: Using a Cartesian rectangular coordinate system (x, y, z), where the x-axis is perpendicular to the shoreline, the y-axis is parallel to the shoreline, and the z-axis is vertically upward, the GPU-accelerated simplified model of nonlinear mild slope equation has the following governing equation:

[0085]

[0086] Where t is time, and the subscript t represents the derivative with respect to time. is the symbol of the gradient operator in the horizontal direction, U = (U, V) is the horizontal velocity vector at the still water level, U and V are the flow velocities in the x and y directions on the still water surface, η is the wave surface, h is the still water depth, g is the acceleration of gravity, k is the wave number, T is the wave period, c is the wave speed, the coefficient n = 1 / 2 + kh / sinh (2kh), and R is the term that considers wave breaking, bottom friction, and lateral mixing. Its definition is the same as that given by Xu et al. (Xu J, Zou ZL, Yan SA Set of Fully Nonlinear Mild Slope Equations [J]. Ocean engineering. 2024, 297: 116881.) and will not be repeated here. The above equations (3)-(4) are simplified by removing the high-order nonlinear terms and the weak nonlinear terms containing the bottom slope from the fully nonlinear mild slope equation model of Xu et al., so it has the accurate dispersion performance unique to the mild slope equation, and because its form is simpler, it has higher computational efficiency.

[0087] S22, GPU parallel accelerated calculation: For the above equations (3)-(4), in order to meet the timeliness of rip current risk prediction near structures, it is necessary to further improve the model calculation efficiency. The unified computing device architecture CUDA and C language are used to perform GPU parallel calculation on the model.

[0088] The development platform used is Windows 10 + Intel Complier Visual Studio 2017, the language is C++, the CUDA version used is CUDA 10.2, and the CPU and GPU models and parameters used are as follows:

[0089] CPU: Intel i3-9100f, 4 cores and 4 threads, main frequency is 3.6GHz, single-core turbo frequency is 4.2GHz, and multi-core turbo frequency is 4.0GHz.

[0090] GPU: NVIDIA GeForce RTX 2060 graphics card, Turing 104 architecture, 1920 CUDA cores, core frequency 1755MHz, video memory capacity 6GB, video memory type GDDR6, video memory bus width 192bit, bandwidth 336GB / s, video memory frequency 1.4GHz.

[0091] The present invention is based on the GPU parallel model developed by CUDAC, which roughly follows Figure 2 The calculation process is shown in Figure 5. The most important step in this process, and the process that is mainly different from the CPU serial model, is step 5 - calling the device-side kernel function to complete the calculation. The kernel function is an important concept in CUDA. It is executed by the CUDA core on the device side for matrix operations and is called on the host side. In the process of calling the kernel function, the number of logically enabled threads needs to be organized according to two levels. The first level is to specify the grid size, that is, the number of thread blocks contained in the grid in the x and y directions; the second level is to define the thread block size, that is, the number of threads contained in a thread block. In this model, based on the above development environment, the thread block size was selected as 16×16 after testing, and the grid size can be freely adjusted according to the number of grids contained in the calculation domain.

[0092] S23, irregular wave generation:

[0093] Before applying the above model to simulation experiments, it is necessary to consider the random wave generation problem based on the JONSWAP spectrum. Wave generation is performed by adding the source function F(x, y, t) to the right side of the above equation (3). The specific solution process of F(x, y, t) is as follows:

[0094] Divide the unidirectional irregular wave spectrum JONSWAP spectrum into N = 100 parts in the frequency domain, then for each wave frequency component ω i The incident wave amplitude is Where S(ω i ) is the JONSWAP spectrum function. The corresponding source function amplitude D i for:

[0095]

[0096] Where, the subscript i represents the frequency component ω corresponding to each wave i The variable (k x ) i =k i cosα, where k i According to the exact dispersion relation Solve, c i =ω i / k i is the wave speed, n i =1 / 2+k i h / sinh(2k i h) is the wave transmission efficiency, in is a parameter related to the wave width.

[0097] By substituting the source function amplitude D si , we get the expression of the source function F(x,y,t):

[0098]

[0099] Where x s is the position of the source function in the x direction, is the random initial phase of the source function.

[0100] In order to illustrate the accuracy of irregular wave generation in the above numerical model, the following comparative example 1 gives the comparison results of irregular wave incident wave spectra in the experiment and the numerical model.

[0101] S24, numerical model setting: In the numerical model calculation, since there is no restriction on the pool area in the experiment, the beach model can be arranged parallel to the wave-generating boundary. It is only necessary to generate waves with an oblique incidence of 30° during wave generation. Figure 3 A schematic diagram of the computational domain settings for the numerical model of this embodiment is given. The computational domain has a coastal width of 40 m and an offshore length of 21 m. The offshore boundary is a sponge layer absorbing boundary, the shore boundary is a wave climbing dynamic boundary, and both the upstream and downstream boundaries are solid boundaries. The downstream boundary can be regarded as a vertical shoreline structure that reflects incident waves. The internal wave generator is located 3 m below the offshore boundary. When the water depth is set to the depth used in the experiment, the size of the wave reflection area is consistent with that in the experiment, while the size of the non-reflection area is slightly larger than that in the experiment. This is because the influence of the wave shadow area is taken into account.

[0102] In the numerical calculations, the spatial grid size in the x-direction was Δx = 0.05 m, the spatial grid size in the y-direction was Δy = 0.1 m, and the time step interval was Δt = 0.02 s. The total simulation duration remained the same as in the experiment, at 720 s. The results from 120 to 720 s were used to calculate the mean flow field velocity.

[0103] S25, Numerical model verification: Use the above numerical model to simulate the physical model experiment, and compare and analyze the numerical model results with the physical model experiment results to verify the accuracy of the numerical model; the verification content includes wave field verification and flow field verification. The former is verified by comparing the wave height and the average water surface, while the latter is verified by comparing the flow velocity in the perpendicular and along-shore directions and the flow velocity vector within the flow field.

[0104] During the verification process, the flow velocity in the numerical model needs to be converted into the average flow velocity at water depth. The flow velocity is converted using the following formula based on the flow conservation principle:

[0105]

[0106] Where <·> represents the time averaging, u = (u, v), where u and v are the average water depth velocities in the x and y directions, respectively.

[0107] Regarding the above physical model experiment, the specific verification process is shown in Example 2 below.

[0108] Step 3: Change the numerical model settings to analyze the flow characteristics of the unidirectional vortex-driven rip flow system:

[0109] Using the experimentally verified GPU parallel accelerated nonlinear mild slope equation simplified model and numerical simulation settings given in step 2, by changing a single setting parameter, the influence of factors such as the structure's reflection coefficient of waves, the wave incident angle, and the wave incident height and period on the flow characteristics of the unidirectional vortex-driven rip current system is studied.

[0110] Comparative Example 1: Comparison of the incident wave spectra of irregular waves in the experiment and the numerical model

[0111] Since the flow field of the rip current system near the structure is directly affected by the wave field, and the accuracy of the incident random waves directly affects the accuracy of the wave field simulation, this comparative example gives a comparison of the irregular wave incident wave spectra in the experiment and the numerical model to illustrate the consistency of the numerical model incident wave results with the experimental incident wave results.

[0112] Figure 4 For the four sets of irregular wave conditions in the experiment, a comparison of the incident wave spectra from the experimental and numerical simulations at the wave height meter location (x = 12 m, y = 9 m) is presented. As can be seen from the figure, for all four sets of irregular wave conditions, the numerical simulation results closely reproduce the experimental JONSWAP spectra, including the peak frequency locations and their maximum spectral density. The shapes of the two spectra are also largely consistent. These results demonstrate that the numerical simulation method described in this invention is capable of generating random waves consistent with those found in the experiments.

[0113] Example 2 - Characteristic demonstration of a unidirectional vortex-driven rip flow system and numerical model verification

[0114] To demonstrate the feasibility of the unidirectional vortex-driven rip flow system described in the current invention, the wave field, flow field, and vorticity field under irregular waves were compared with those under regular waves. Furthermore, to verify the accuracy of the numerical model, the numerical simulation results were compared with the experimental results. The comparison included both the wave field and the flow field, and the detailed process is described below:

[0115] (1) Wave field characteristics—partial standing wave morphology

[0116] Figure 5 The instantaneous wavefront results of the experiments and numerical simulations are given for regular wave condition A and irregular wave condition E, respectively. As can be seen from the figure, for the regular wave condition, obvious standing wave nodes (i.e., node lines with small wavefront amplitudes and perpendicular to the shoreline) appear at all theoretical nodes (5); for the irregular wave condition, the node characteristics are only displayed at theoretical node 1, while no obvious node characteristics can be distinguished at other theoretical nodes. This result shows that the morphology of the cross-wave field near the upstream of the strong reflective structure depends on the wave type. For the regular wave condition, due to the single wave component, a complete standing wave morphology is formed; for the irregular wave condition, due to the offsetting effect of different wave components, the morphology of the cross-wave field is a partial standing wave morphology - there is only one coastal standing wave within the first theoretical standing wave wavelength. It can also be seen from the figure that the wavefront given by the numerical simulation is relatively close to the experimental wavefront, further verifying the above conclusions and proving the accuracy of the numerical simulation.

[0117] In order to demonstrate the quantitative characteristics of the above standing wave morphology, Figure 6 The experimental and numerical simulation results of wave height and water level distribution on nodes and antinodes are given for all irregular wave conditions. Figure 7 Taking the regular wave condition F as an example, the Figure 6 Similar results are compared. The accuracy of the numerical model is further verified by these two figures. It can also be seen from the figure that for regular waves, the wave heights at all antinodes are greater than the wave height at y = 9m and decrease as they move away from the structure. The wave heights at all nodes are less than the wave height at y = 9m and increase as they move away from the structure. This is because the farther away from the structure, the more severe the attenuation of the reflected waves, so the standing wave field is weaker. For irregular waves, the above characteristics only exist within the first standing wave wavelength, that is, antinodes 1 and 2 are significantly greater than the wave height at y = 9m, node 1 is significantly less than the wave height at y = 9m, and the wave heights at nodes and antinodes other than antinode 2 are not significantly different from the wave height at y = 9m. Under the influence of the above different wave height distribution characteristics, the nearshore surge of irregular waves and regular waves also exhibits different characteristics. For regular waves, the nearshore surge at nodes is smaller than that at antinodes, and the antinode surge decreases with distance from the structure, while the node surge increases with distance from the structure. For irregular waves, the nearshore surge decreases almost entirely with distance from the structure, being less affected by the nodes, and is greatest at the first antinode line (i.e., on the structure boundary). These nearshore surge characteristics can be approximately explained by the offshore momentum conservation equation: the greater the offshore breaking wave height, the greater the nearshore surge. This nearshore surge characteristic also leads to the larger alongshore water surface pressure gradient characteristic of irregular waves, which is the primary driving force behind the unidirectional vortex state.

[0118] In order to further quantitatively describe the above standing wave morphological characteristics, the standing wave intensity parameter δ at the i-th node is introduced here. H (i), which is defined as

[0119]

[0120] Where H A (i) and H A (i+1) are the breaking wave heights on the i-th and i+1-th antinode lines, H N (i) is the breaking wave height on the i-th node line. H The value of (i) can quantitatively reflect the strength of the standing wave: H (i) The larger the value, the stronger the standing wave intensity. H When (i) = 1, there is no standing wave feature.

[0121] Table 4 shows the δ at the first three nodes of the four groups of irregular wave conditions and regular wave conditions F in the experiment. H (i) The value of. At the first node, the irregular wave δ H (i) is about 1.5 to 1.8, which is significantly greater than 1, indicating the obvious standing wave field characteristics at node 1, but the value is still smaller than the result of regular waves; at nodes 2 and 3, for irregular waves, δ H The value of (i) is already close to 1, while for regular waves, it is still significantly greater than 1, indicating that the standing wave characteristics of the former have almost disappeared, while the latter still have standing wave characteristics. The above results show that the standing wave morphology of irregular waves only exists within the first standing wave wavelength and is weaker than that of regular waves. Outside this region, it exhibits random wave field characteristics.

[0122] Table 4 δ at the first three nodes in the experiment H The value of (i).

[0123]

[0124] (2) Flow field characteristics—unidirectional vortex state

[0125] Figure 8 For regular waves and irregular waves, numerical simulation vorticity diagrams, nearshore wave surge, and time-averaged flow field comparison diagrams are given respectively. The vorticity Ω is defined as follows:

[0126]

[0127] from Figure 8 As can be seen in the figure, the flow field near the structure consists of two main components: 1) "ejective flow" (i.e., deflected rip current) outside the reflection zone. This rip current is formed by the longshore current driven by obliquely incident waves, which meets the lateral current near the boundary of the reflection zone and is deflected offshore. It flows out to sea and does not return to the wave breaking zone. 2) "girth current" within the reflection zone, formed by node rip current (occurring near the theoretical node line of the standing wave field) and Euler onshore current. This type of rip current is called a "girth current" because it circulates within the wave breaking zone. For regular and irregular waves, the morphology and distribution of the "ejective flow" are similar, but the "girth current" within the reflection zone exhibits significant differences.

[0128] From the vorticity distribution within the first standing wave field in the figure, we can see that for regular waves, a pair of vortices (indicated by the purple circles in the figure) forms on either side of the node, symmetrically oriented in opposite directions. The node rip current is the offshore current between the vortex pairs. This vortex pair structure caused by short-crest breaking waves has been extensively studied by numerous scholars both domestically and internationally (Wei Z, Dalrymple RA, Munan X, Roland G, Morteza D. Short-Crested Waves in the Surf Zone [J]. Journal of Geophysical Research: Oceans. 2017, 122: 4143–4162.). Due to the characteristic vortex structure of the paired vortices symmetrical about the node, we refer to it as a "counter-vortex" flow pattern. However, for irregular waves (indicated by the white circles in the figure), the two vortices, symmetrically oriented in opposite directions about the node, exhibit distinctly different characteristics: the clockwise negative vortex (indicated by the blue area in the figure) significantly increases to nearly the entire standing wave range, while the counterclockwise positive vortex significantly decreases or even disappears (counter-wave condition A). In this case, the node rift, as the offshore part of the above-mentioned negative vortex, also deviates from the position of the theoretical node 1 to a position close to the theoretical antinode 2. Therefore, according to the vorticity distribution characteristics in the first standing wave field, the above-mentioned rift form in which the irregular wave is driven only by a large-scale unidirectional negative vortex can be called a "unidirectional vortex" driven rift form, and the rift system is called a unidirectional vortex driven rift system.

[0129] In order to further demonstrate the distribution characteristics of deflection rift flow and node rift flow in the unidirectional vortex driven rift flow system, Figure 9 For the case of irregular waves, the vertical bank velocity at the x = 3m section is given as and alongshore current velocity <v>The coastal distribution results are shown in Figure 1. The blue and red rectangles in the figure respectively indicate the range of deflected rip currents and node rip currents based on the experimentally measured flow velocities. It can be seen that for all irregular wave conditions, there is only one node rip current. Driven by the unidirectional vortex, the position of this node rip current deviates from the theoretical node away from the structure. Outside this node rip current, the deflected rip current exhibits a relatively dispersed and continuous distribution. This is due to the influence of the bottom return flow. That is, when the wave height outside the antinode 2 is relatively uniformly distributed along the coast, the onshore mass transfer flow will flow to the open sea in the form of bottom return flow.

[0130] (3) Quantitative description of numerical model accuracy

[0131] The above verification of the accuracy of the numerical model is only for the qualitative description. Here, the conformity coefficient IOA is introduced to quantitatively describe the conformity of the numerical simulation results to verify the model. The expression of IOA is as follows:

[0132]

[0133] Where, f c (i) and f t (i) represents the i-th numerical simulation result and experimental measurement result, respectively. n is the number of data points. The superscript "—" indicates the average of n data points. A larger IOA value indicates better agreement between the numerical simulation and the experimental results. When IOA = 1, it indicates perfect agreement. It is generally believed that an IOA greater than 0.6 corresponds to good agreement.

[0134] Table 5 gives the root mean square wave height H at the first three nodes and antinodes, the average water surface <η>, and the vertical bank direction current velocity at sections x = 2, 3, 4, 5, and 6 m for the four groups of irregular wave conditions in the experiment. and alongshore current velocity <v>It can be seen that all the calculated IOA values in the table are greater than 0.8 and the average IOA value of each wave condition is greater than 0.9, which shows the accuracy and applicability of the current numerical model in describing the wave height, water increase and decrease, and flow field of the unidirectional vortex-driven rip current system with irregular wave conditions.

[0135] Table 5 IOA values for irregular wave conditions

[0136]

[0137] Example 3 - Effect of structure wave reflection coefficient on unidirectional vortex-driven rip current system

[0138] Although only vertical coastal structures with full wave reflection were considered in the experiment, in reality, due to protective measures (such as riprap), structures often only have partial wave reflection. This example uses irregular wave condition B as an example to investigate the effect of the structure's wave reflection coefficient on the aforementioned unidirectional vortex-driven rip current system through numerical simulation.

[0139] The effect of different reflection intensities of the structure to the incident wave is achieved by placing two layers of digital sponge with different grid widths on the boundary of the structure. The wave attenuation coefficient D at the grid point in the sponge layer is s The expression is as follows

[0140]

[0141] Where, S=2△y is the width of the sponge layer, d s (values of 0, △y and 2△y) represent the grid point position from the sponge layer boundary, k s It is an adjustable parameter that controls the attenuation strength of the sponge layer. By multiplying the η, U and V calculated on each time layer by the above attenuation coefficient D s , the effect of different reflection intensities of waves on the structure can be achieved.

[0142] Through analysis, it can be found that when k s =+∞, corresponding to D s =1, the structure has a total reflection effect on the waves; and when k s =0, corresponding to D s = 0, the structure does not reflect the waves. s The wave reflection coefficient C of the structure is taken as the value R It can be approximated by the breaking wave height H at antinode 1 T Estimate, i.e. C R =(H T -H I ) / H I , where H I is the incident wave height at antinode 1. I The value of can be approximated by the breaking wave height H at the antinode 1 in the total reflection case (wave condition B) TB Estimation, that is, H I =H TB / 2.

[0143] Through numerical simulation, it is found that as the wave reflection coefficient of the structure decreases, the unidirectional vortex driven rip current system will gradually transform into the counter-vortex driven rip current system. For the wave condition B considered in this embodiment, its critical structure wave reflection coefficient is approximately D s =0.75(corresponding to k s =5.0). Figure 10 The transformation process of vorticity distribution characteristics is given for wave reflection coefficients of different structures, where k s =1000 corresponds to the total reflection situation. As can be seen from the figure, as k s As the value of k decreases, the positive vortex in the unidirectional vortex-driven rift system gradually increases and moves closer to node 1, while the range of the negative vortex gradually decreases until k s = 5.0, the positive vortex and the negative vortex are almost symmetrical about node 1, and the flow field is completely transformed into a counter-vortex driven rip flow system. It should also be noted that as k s The value continues to decrease until there is almost no reflection (corresponding to k in the figure s =3.0), the positive vortex in the reflection zone will completely disappear, and the deflected rip current will appear near the boundary of the structure. This situation is also what many scholars have considered (Scott T, Austin M, Masselink G, Russell P. Dynamics of Rip Currents Associated with Groynes-Field Measurements, Modelling and Implications for Beach Safety. Coastal Engineering. 2016, 107: 53–69.).

[0144] The above results show that the unidirectional vortex-driven rip current system near the structure caused by the reflection of irregular incident waves by the structure is essentially determined by the wave reflection coefficient of the structure. When the structure exhibits a strong reflection effect on waves with a reflection coefficient greater than 0.75, a unidirectional vortex-driven rip current system will be formed within a standing wave wavelength near the structure.

[0145] Finally, it should be noted that the above is only used to illustrate the technical solution of the present invention and is not limiting. Although the present invention is described in detail with reference to the preferred arrangement scheme, ordinary technicians in this field should understand that the technical solution of the present invention (such as the use of various formulas, the sequence of steps, etc.) can be modified or replaced by equivalents without departing from the spirit and scope of the technical solution of the present invention.< / v> < / v> < / v>

Claims

1. A method considering the flow characteristics of a unidirectional vortex-driven rip flow system, characterized in that: The method comprises the following steps: Step 1, physical model experiment: S11, Experimental setup: The experiment was conducted in a laboratory pool containing a wave generator, with the wave generator at one end and a sponge absorbing boundary layer at the other. Two wave guide walls were placed along the long side of the pool, and a flat, sloped shoreline with a certain angle of rotation relative to the horizontal was built between the two wave guide walls in the center of the pool. An outlet structure is arranged on the upper side of the flat coast in a direction perpendicular to the shoreline. When the wave-making plate generates unidirectional irregular waves parallel to the direction of the pool, a triangular wave reflection area will be formed upstream of the outlet structure. S12, Experimental wave condition selection and wave generation: Several groups of experimental wave conditions are selected in the experiment, including regular wave conditions and irregular wave conditions; each wave condition contains three cycles, including: H i is the incident wave height in deep water, T p is the spectrum peak period, λ is the theoretical standing wave wavelength corresponding to the spectrum peak period; Then the i-th theoretical node line along the coast y=y Ni and the theoretical antinode line y=y Ai The position of the standing wave can be given by the standing wave wavelength λ as follows: y Ni =(i-0.5)λ (1) y Ai =(i-1)λ (2) S13, wave field and flow field measurement: In the experiment, several capacitive wave height meters were selected to measure the wave field inside and outside the wave reflection area, and several Doppler current meters were used to measure the flow field; The wave height H in the wave field is calculated by applying the zero-crossing method to the wave surface η recorded by the wave height meter, while the mean water surface rise <η> is obtained by directly taking the time average of η; The current meter is placed at a distance of 1 / 3 of the local water depth from the water bottom to measure the average flow velocity at water depth; Step 2, numerical model simulation: A simplified nonlinear mild-slope equation model accelerated by GPU parallelism was used to simulate the physical model experiment in step 1 and calibrate the model parameters. Finally, the flow characteristics of the unidirectional vortex-driven rip flow system under different configurations were studied by changing the numerical model settings. Specifically, the following were done: S21, simplified model of nonlinear mild slope equation: Using a Cartesian rectangular coordinate system (x, y, z), where the x-axis is perpendicular to the shoreline, the y-axis is parallel to the shoreline, and the z-axis is vertically upward, the GPU-accelerated simplified model of nonlinear mild slope equation has the following governing equation: Where t is time, and the subscript t represents the derivative with respect to time. is the symbol of the gradient operator in the horizontal direction, U = (U, V) is the horizontal velocity vector at the still water level, U and V are the current velocities in the x and y directions on the still water surface, η is the wave surface, h is the still water depth, g is the acceleration of gravity, k is the wave number, T is the wave period, c is the wave speed, the coefficient n = 1 / 2 + kh / sinh (2kh), and R is the term that takes into account the effects of wave breaking, bottom friction, and lateral mixing; S22, GPU parallel accelerated computing: Use the unified computing device architecture CUDA and C language to perform GPU parallel computing on the model; S23, irregular wave generation: Wave generation is performed by adding the source function F(x, y, t) to the right side of the above equation (3). The specific solution process of F(x, y, t) is as follows: Divide the unidirectional irregular wave spectrum JONSWAP spectrum into N = 100 parts in the frequency domain, then for each wave frequency component ω i The incident wave amplitude is Where S(ω i ) is the JONSWAP spectrum function, then the corresponding source function amplitude D i for: Where, the subscript i represents the frequency component ω corresponding to each wave i The variable (k x ) i =k i cosα, where k i According to the exact dispersion relation Solve, c i =ω i / k i is the wave speed, n i =1 / 2+k i h / sinh(2k i h) is the wave transmission efficiency, in is a parameter related to the wave width; By substituting the source function amplitude D i , we get the expression of the source function F(x,y,t): Where x s is the position of the source function in the x direction, is the random initial phase of the source function; S24, numerical model settings: Determine the coastal width and offshore length of the numerical model calculation domain. The offshore boundary is the sponge layer absorbing boundary, the shore boundary is the wave climbing dynamic boundary, and the upstream and downstream boundaries are both solid boundaries. The downstream boundary can be regarded as a vertical shoreline structure that reflects incident waves. S25, Numerical Model Verification: Use the numerical model to simulate the physical model experiment, and compare and analyze the numerical model results with the physical model experiment results to verify the accuracy of the numerical model; the verification content includes wave field verification and flow field verification. The former is verified by comparing wave height and mean water surface, while the latter is verified by comparing the flow velocity in the perpendicular and along-shore directions and the flow velocity vector within the flow field; Step 3: Change the numerical model settings to analyze the flow characteristics of the unidirectional vortex-driven rip flow system: Using the experimentally verified GPU parallel accelerated nonlinear mild slope equation simplified model and numerical simulation settings given in step 2, by changing a single setting parameter, the effects of the structure's reflection coefficient of waves, the wave incident angle, and the wave incident height and period factors on the flow characteristics of the unidirectional vortex-driven rip current system are studied.

2. The method according to claim 1, characterized in that In step 1, S12, the theoretical standing wave wavelength λ corresponding to the spectral peak period is calculated according to the Snell theorem as follows: Where L0 is the deep water incident wavelength corresponding to the spectral peak period, and α is the wave incident angle.

3. The method according to claim 1, characterized in that In step 2, S22, the process of GPU parallel computing of the model based on CUDA and C language includes: declaring and defining host and device variables, allocating memory space for host and device variables, initializing host variables, copying host data to device, calling device kernel functions in sequence to complete the calculation, copying device data back to the host, and finally outputting the results. The number of logically enabled threads in the kernel function call is organized in two levels. The first level specifies the grid size, that is, the number of thread blocks in the grid in the x and y directions. The second level defines the thread block size, that is, the number of threads in a thread block.

4. The method according to claim 1, wherein During the S25 verification process in step 2, the flow velocity in the numerical model needs to be converted into the average flow velocity at water depth. The flow velocity is converted using the following formula based on the flow conservation principle: Where <·> represents the time averaging, u = (u, v), where u and v are the average water depth velocities in the x and y directions, respectively.

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