Method for considering flow characteristics of one-way vortex-driven split flow system

Abstract

The invention provides a method for considering the flow characteristics of a one-way vortex-driven split flow system, which is characterized in that incident irregular waves are reflected by a vertical coast structure with a strong reflection effect on the waves, and a large-scale negative vortex-driven split flow system is formed in the wavelength of a first standing wave in an upstream reflection region of the structure. According to the method, a non-linear gentle slope equation simplified model of GPU parallel acceleration is applied to a one-way vortex-driven split flow system near a simulation structure, the model has accurate dispersivity and also has higher calculation efficiency, and by comparing an incident wave spectrum of irregular waves in the model with a result in an experiment, the calculation efficiency of the model is improved. The random wave generation capability of the model is verified. Different flow characteristics of the one-way vortex-driven flow splitting system compared with common vortex-driven flow splitting systems are displayed based on a numerical model, and the influence of a structure wave reflection coefficient on the flow characteristics of the one-way vortex-driven flow splitting system is analyzed.

Description

Technical Field

[0001] The 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. Most previous studies have 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 short-crest waves and the rip currents between the short-crest waves they cause (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 of multi-section submerged dikes (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 symmetric characteristics of the driving vortex, the distribution characteristics and movement laws of this type of rip current system are easier to predict and describe. However, the rip current movement characteristics of the rip current system driven by an asymmetric unidirectional vortex are often more difficult to consider. This is because the unidirectional vortex movement is more random and no longer shows a slow offshore shedding process, such as the rip current system caused by the oblique movement of the unidirectional vortex at the edge of a single submerged dike (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 the actual marine environment, due to the random wave characteristics, the rip current system driven by the unidirectional vortex often appears, but the existing research has not yet clearly given the relevant consideration method.

[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] In view of the problems existing in the prior art, the purpose of the present invention is to provide a method considering the flow characteristics of a one-way vortex-driven rift flow system. The method applies a simplified model of a nonlinear gentle slope equation accelerated by GPU parallelization to simulate a one-way 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 a one-way vortex-driven rift flow system compared to a common vortex-driven rift flow system are demonstrated, and the influence of the wave reflection coefficient of the structure on the flow characteristics of the one-way vortex-driven flow system is analyzed.

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

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

[0007] Step 1, physical model experiment:

[0008] S11, Experimental arrangement: The experiment was conducted in a laboratory pool containing a wave maker, with the wave maker at one end and a sponge absorbing boundary layer at the other end; two wave guide walls were arranged along the long side of the pool, and a flat slope coast with a slope was built between the two wave guide walls in the center of the pool with concrete, and the coast was rotated at a certain angle relative to the horizontal direction;

[0009] An outlet structure is arranged in a direction perpendicular to the shoreline on the upper side of the flat coast. 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 average 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] The simplified model of nonlinear mild slope equation accelerated by GPU parallelization is used to simulate the physical model experiment in step 1 and verify the model parameters. Finally, the flow characteristics of the unidirectional vortex-driven rift flow system under different configurations are studied by changing the numerical model settings, including:

[0018] S21, simplified model of nonlinear gentle slope equation: adopt Cartesian rectangular coordinate system (x, y, z), where the x-axis is perpendicular to the shoreline direction, the y-axis is parallel to the shoreline direction, and the z-axis is vertically upward. In this coordinate system, the simplified model of nonlinear gentle slope equation accelerated by GPU has the following control equation:

[0019]

[0020] In the formula, 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 takes into account wave breaking, bottom friction and lateral mixing effects;

[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. Then the corresponding source function amplitude D si for:

[0025]

[0026] In the formula, 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] In the formula, 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 absorption boundary, the shore boundary is the wave climbing dynamic boundary, the upstream boundary and the downstream boundary are both solid boundaries, and the downstream boundary can be regarded as a vertical shoreline structure that reflects the incident waves;

[0031] S25, numerical model verification: the above numerical model is used to simulate the physical model experiment, and the numerical model results are compared and analyzed with the physical model experiment results to verify the accuracy of the numerical model; the verification content includes the verification of the wave field and the verification of the flow field. 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 shore direction and along the shore direction and the flow velocity vector in the flow field;

[0032] Step 3: Change the numerical model settings to analyze the flow characteristics of the unidirectional vortex-driven rift 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 reflection coefficient of the structure to the wave, the wave incident angle, and the wave incident height and period on the flow characteristics of the unidirectional vortex-driven rift system is studied.

[0034] Further, in step 1, S12, the theoretical standing wave wavelength λ corresponding to the spectrum peak period is calculated according to the Snell theorem by 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 performing GPU parallel computing on the model based on CUDA and C language includes: declaration and definition of host and device variables, allocation of host and device variable memory space, host variable initialization, copying host data to device, calling device kernel functions in sequence to complete the computing, copying device data back to host, and finally outputting the results;

[0038] In the process of calling the kernel function, the number of logically enabled threads is organized at 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 size of the thread block, that is, the number of threads contained in a thread block.

[0039] Furthermore, in 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, and 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] Compared with the prior art, the present invention has the following beneficial effects:

[0043] 1. The present invention provides a simple and effective physical model experiment and numerical model simulation method for forming a unidirectional vortex-driven rift current system. Relying on the strong reflection effect of incident random waves on structures perpendicular to the coast, uneven coastal water surge and strong lateral currents 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 rift current system is formed upstream of the structure.

[0044] 2. In the numerical simulation method considering the flow characteristics of the unidirectional vortex-driven rift current system described in the present invention, the simplified nonlinear gentle slope equation model accelerated by GPU parallelization is applied to the simulation of the unidirectional vortex-driven rift current system near the coastal structure. Since the model described in the present invention is a nonlinear gentle 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 the weak nonlinear terms containing the bottom slope in the completely 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 system near the structure. BRIEF DESCRIPTION OF THE DRAWINGS

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

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

[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 It is a schematic diagram of the calculation domain setting of the numerical model;

[0050] Figure 4 It is the comparison of the irregular wave incident wave spectra of the experiment and the numerical model at the position of the wave height meter in the comparison scale (x=12m, y=9m); where f(Hz) is the frequency and S(f) is the spectrum density;

[0051] Figure 5 : is a comparison diagram of the instantaneous free wave surface given for the irregular wave condition A (left figure) and the regular wave condition E (right figure) in Example 2; wherein (a) and (b) are the wave surfaces in the experiment, and (c) and (d) are the wave surfaces given by the numerical simulation;

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

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

[0054] Figure 8It is the numerical simulation vorticity diagram (color filling), nearshore wave surge (red curve) and time-averaged flow field comparison diagram (arrow) 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 of the irregular wave case; the purple arrow indicates the node-symmetric vorticity of the regular wave case; the vertical black solid line represents the theoretical antinode line; the vertical black dotted line represents the theoretical node line;

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

[0056] Fig.10 It 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 in conjunction with examples. It should be understood that the following examples are provided only for the purpose of illustration 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. If not 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, comprising the following steps:

[0060] Step 1, physical model experiment:

[0061] S11, Experimental setup: The experiment was conducted in a laboratory pool containing a wave maker, e.g. Figure 1 As shown in the figure, the pool is 55m long and 34m wide. There is a wave maker on the left end of the pool 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 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 18m long water outlet structure is arranged in the vertical shoreline direction on the upper side of the flat coast. In order to make the structure have a full reflection function for the incident waves, the surface of the structure is plastered with cement mortar. The water depth at the flat bottom of the experiment is selected as 27.5cm. At this water depth, the total length of the structure in the water is 15.7m, and the length on the beach is 3m. When the wave-making plate generates unidirectional irregular waves parallel to the direction of the pool, the angle of the wave relative to the vertical shoreline direction of the coast is α=30°, so a triangular reflection wave area will be formed upstream of the water outlet structure; the width of this area on the still water line is 9m. In order to facilitate the experimental description, the Cartesian coordinate system of (x, y, z) is adopted. The origin of the coordinate system is located at the intersection of the still water line and the structure, the x-axis is located on the structure, the y-axis is located on the still water line along the coast, and the z-axis is 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] Two sets of wave heights are considered for the irregular wave condition with a period of 1.5 s, while only one set of wave heights is considered for the other wave conditions. Table 1 gives the introduction of 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 antidrome 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 of 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 performing the zero-crossing method on the wave surface η recorded by the wave height meter, and the average water surface rise <η> is obtained by directly performing time averaging on η; in the experiment of this embodiment, the sampling frequency is 50 Hz, and the total sampling time is 327 s (corresponding to 16384 sampling points), wherein the data of the time period of 60 to 300 s are used to calculate the wave field results.

[0076] In order to facilitate movement, these measuring instruments are installed on three measuring beams. Among them, 18 wave height meters are installed on beam I to measure the incident wave information at y = 9m outside the reflection area; beams II and III are equipped with 14 wave height meters to record the wave information on the nodes and antinodes in the reflection area. The coastal positions of these nodes and antinodes can be calculated by equations (2) and (3). Table 2 gives the specific offshore arrangement positions of the wave height meters on each beam.

[0077] Table 2 Wave height meter offshore location

[0078]

[0079] Table 3 Current meter locations along the coast

[0080]

[0081] The current meter has a measurement range of ±1m / s and a measurement error of ±1mm / s. These current meters are installed on two measuring frames to measure the flow velocity of five coastal sections near the structure. Table 3 gives the specific locations of the measurement points of these current meters. Among them, the larger measurement range on the x=3m section is to measure the distribution characteristics of the rip current in the coastal direction, while the smaller measurement range on other sections is 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 of the water to measure the average flow velocity at water depth. For all wave conditions, the measurement time is 720s, and the flow velocity results of 120 to 720s are averaged to obtain the time-averaged flow velocity.

[0082] Step 2, numerical model simulation:

[0083] The simplified model of nonlinear mild slope equation accelerated by GPU parallelization is used to simulate the physical model experiment in step 1 and verify the model parameters. Finally, the flow characteristics of the unidirectional vortex-driven rift flow system under different configurations are studied by changing the numerical model settings, including:

[0084] S21, simplified model of nonlinear gentle slope equation: adopt Cartesian rectangular coordinate system (x, y, z), where the x-axis is perpendicular to the shoreline direction, the y-axis is parallel to the shoreline direction, and the z-axis is vertically upward. In this coordinate system, the simplified model of nonlinear gentle slope equation accelerated by GPU has the following control equation:

[0085]

[0086] In the formula, 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 gravitational acceleration, 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 considering wave breaking, bottom friction and lateral mixing; its definition is the same as the results 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 precise dispersion performance unique to the mild slope equation, and because its form is simpler, the calculation efficiency is higher.

[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, 1755MHz core frequency, 6GB video memory capacity, GDDR6 video memory type, 192bit video memory bus width, 336GB / s bandwidth, and 1.4GHz video memory frequency.

[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, which is also the main difference from the CPU serial model, is step 5 - calling the kernel function on the device side 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 size of the grid, that is, the number of thread blocks contained in the grid in the x and y directions; the second level is to define the size of the thread block, that is, the number of threads contained in a thread block. In this model, based on the above development environment, the thread block size is selected as 16×16 after testing, and the size of the grid 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. Waves are generated 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. Then the corresponding source function amplitude D si for:

[0095]

[0096] In the formula, 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 It 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] In the formula, 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 numerical model.

[0101] S24, numerical model setting: In the numerical model calculation, since there is no limitation of the pool area in the experiment, the beach model can be arranged parallel to the wave-making boundary, and it is only necessary to generate waves with an incident angle of 30° when making waves. Figure 3 A schematic diagram of the calculation domain setting of the numerical model of this embodiment is given. The calculation domain has a coastal width of 40m and an offshore length of 21m. The offshore boundary is a sponge layer absorption boundary, the shore boundary is a wave climbing dynamic boundary, and the upstream boundary and the downstream boundary are both solid boundaries, among which the downstream boundary can be regarded as a vertical shoreline structure that has a reflective effect on the incident waves; the internal wave-making source is located 3m below the offshore boundary. When the water depth is set to the water depth 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 the area in the experiment. This is because the influence of the wave shadow area is taken into account.

[0102] In the numerical calculation, the spatial grid size in the x direction is △x = 0.05m, the spatial grid size in the y direction is △y = 0.1m, and the time step interval is △t = 0.02s. The total simulation time is consistent with the experiment, which is 720s, of which the results from 120 to 720s are used to calculate the average flow field velocity.

[0103] S25, numerical model verification: the physical model experiment is simulated using the numerical model, and the numerical model results are compared and analyzed with the physical model experiment results to verify the accuracy of the numerical model; the verification content includes the verification of the wave field and the verification of the flow field. 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 shore direction and along the shore direction and the flow velocity vector in the flow field.

[0104] During the verification process, the flow velocity in the numerical model needs to be converted into the average flow velocity of the 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 the following Example 2.

[0108] Step 3: Change the numerical model settings to analyze the flow characteristics of the unidirectional vortex-driven rift 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 reflection coefficient of the structure to the wave, the wave incident angle, and the wave incident height and period on the flow characteristics of the unidirectional vortex-driven rift system is studied.

[0110] Comparative Example 1: Comparison of the incident wave spectra of irregular waves in the experiment and 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 incident wave spectra of irregular waves in the experiment and the numerical model to illustrate the consistency between the incident wave results of the numerical model and the experimental incident wave.

[0112] Figure 4 For the four groups of irregular wave conditions in the experiment, the spectrum comparison results of the irregular wave incident waves in the experiment and the numerical simulation at the wave height meter position (x=12m, y=9m) are given. As can be seen from the figure, for the four groups of irregular wave conditions, the numerical simulation results have reproduced the JONSWAP spectrum in the experiment well, including the frequency position of the spectrum peak and its maximum spectrum density, and the shapes of the two spectra are basically consistent. The above results show that the numerical simulation method described in the present invention has the ability to generate random waves consistent with the experiment.

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

[0114] In order to illustrate the feasibility of forming a unidirectional vortex-driven split flow system as described in the current invention, the wave field, flow field and vorticity field under the action of irregular waves are compared with the results under the action of regular waves; in addition, in order to verify the accuracy of the numerical model, the numerical simulation results are also compared with the experimental results. The comparison includes the wave field and the flow field, and the specific process is given below:

[0115] (1) Wave field characteristics - some standing wave forms

[0116] Figure 5 The instantaneous wave surface results of the experiment and numerical simulation are given for the regular wave condition A and the 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 wave surface amplitude and perpendicular to the shoreline) appear at all theoretical nodes (5); while for the irregular wave condition, the node characteristics are only displayed at the theoretical node 1, and no obvious node characteristics can be distinguished at other theoretical nodes. This result shows that the cross-wave field morphology near the upstream of the strong reflection 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 offset of different wave components, the cross-wave field morphology is a partial standing wave morphology - there is only a coastal standing wave in the first theoretical standing wave wavelength. It can also be seen from the figure that the wave surface given by the numerical simulation is close to the experimental wave surface, which further verifies the above conclusions and proves 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 from 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, and 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 weaker the standing wave field; 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-mentioned different wave height distribution characteristics, the nearshore surge of irregular waves and regular waves also shows different characteristics. For regular waves, the nearshore surge at the node is smaller than the surge at the anti-node, and the surge at the anti-node decreases as it moves away from the structure, while the surge at the node increases as it moves away from the structure; for irregular waves, the nearshore surge almost decreases as it moves away from the structure, is less affected by the node, and is the largest on the first anti-node line (i.e., on the boundary of the structure). The above nearshore surge characteristics can be approximately explained by the offshore momentum conservation equation, that is, the greater the breaking wave height in the offshore direction, the greater the nearshore surge. This nearshore surge characteristic also leads to a larger coastal water surface pressure gradient characteristic of irregular waves, which is also the main driving factor for the unidirectional vortex state.

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

[0119]

[0120] In the formula, H A (i) and H A (i+1) are the breaking wave heights on the i-th and i+1-th antinode lines, respectively, 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 close to 1, while for regular waves, the value is still significantly greater than 1, which indicates that the standing wave characteristics of the former almost disappear, 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, while outside this area 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 by the following formula:

[0126]

[0127] from Figure 8 It can be seen that the flow field near the structure mainly consists of two parts: 1) "ejection flow" (i.e. deflection rip current) outside the reflection zone. This type of offshore current is formed by the coastal current driven by oblique incident waves, which deflects offshore after meeting the lateral current near the boundary of the reflection zone, and flows to the open sea and never returns to the wave breaking zone; 2) "circulation" formed by node rip current (occurring near the theoretical node line of the standing wave field) and Euler onshore current in the reflection zone. This type of offshore current is called "circulation" because it circulates in the wave breaking zone. For regular waves and irregular waves, the morphology and distribution of "ejection flow" are not much different, but the "circulation" in the reflection zone is significantly different.

[0128] From the vorticity distribution in the first standing wave field in the figure, we can see that for the regular wave case, a set of vortex pairs with opposite directions symmetrical about the node will be formed on both sides of the node (indicated by the purple circle in the figure), where the node rift flow is the offshore flow between the vortex pairs. This vortex pair structure caused by short-crest wave breaking waves has been deeply studied by many scholars at home and abroad (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.). Here, due to its vortex structure characteristics of symmetrical pairs appearing about the node, we call it the "opposite vortex" flow state. However, for the irregular wave case (indicated by the white circle in the figure), the above two vortices with opposite directions symmetrical about the node show significantly different characteristics: the clockwise negative vortex (i.e., the blue range in the figure) increases significantly to nearly the entire standing wave range, while the counterclockwise positive vortex decreases significantly or even disappears (opposite wave condition A). In this case, the node rift, as the offshore flow 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 rift form in which the irregular wave situation is only driven 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 deflected rift flow and node rift flow in the unidirectional vortex driven rift flow system, Fig. 9 For the case of irregular waves, the vertical shore velocity at the section x = 3m is given: and alongshore velocity <v>The results of the coastal distribution. In the figure, the deflected rip flow range and the node rip flow range are marked with blue rectangles and red rectangles respectively according to the experimentally measured flow velocity. It can be seen that there is only one node rip flow for all irregular wave conditions. Driven by the unidirectional vortex, the position of the node rip flow deviates from the theoretical node away from the structure. Outside the node rip flow, the deflected rip flow shows a relatively dispersed continuous distribution feature. 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 mass transfer flow to the shore will flow to the open sea in the form of bottom return flow.

[0130] (3) Quantitative description of the accuracy of numerical models

[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] In the formula, f c (i) and f t (i) represents the ith numerical simulation result and the experimental result, n is the number of data, and the superscript "—" indicates the average value of n data. The larger the value of IOA, the better the agreement between the numerical simulation result and the experimental result. When IOA=1, it means perfect agreement. It is generally believed that IOA>0.6 corresponds to a better agreement result.

[0134] Table 5 gives the root mean square wave height H, the average water surface <η>, and the vertical shore velocity at sections x = 2, 3, 4, 5, and 6 m for the four groups of irregular wave conditions in the experiment. and alongshore velocity <v>It can be seen that all the calculated values ​​of IOA in the table are greater than 0.8 and the average value of IOA for each group of wave conditions 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 in 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 reflection function for incident waves are considered in the experiment, in reality, due to the existence of protective measures (such as riprap protection), structures often have only partial reflection intensity for waves. This embodiment takes irregular wave condition B as an example to consider the influence of the structure wave reflection coefficient on the above-mentioned unidirectional vortex driven rip current system through numerical simulation method.

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

[0140]

[0141] In the formula, S = 2△y is the width of the sponge layer, d s (values ​​are 0, △y and 2△y) represents 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 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 of 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 a 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). Fig.10 The transformation process of vorticity distribution characteristics is given for wave reflection coefficients of different structures, where k s = 1000 corresponds to total reflection. 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 flow 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 vortex-driven rift 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 one-way vortex-driven rift 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 one-way vortex-driven rift 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 rather than to limit it. Although the present invention has been described in detail with reference to the preferred arrangement scheme, a person skilled in the art 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 for 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 arrangement: The experiment was conducted in a laboratory pool containing a wave maker, with the wave maker at one end and a sponge absorbing boundary layer at the other end; two wave guide walls were arranged along the long side of the pool, and a flat slope coast with a slope was built between the two wave guide walls in the center of the pool with concrete, and the coast was rotated at a certain angle relative to the horizontal direction; An outlet structure is arranged in a direction perpendicular to the shoreline on the upper side of the flat coast. 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 average water surface rise <η> is obtained by directly taking the time average of η; The current meter was placed at a distance of 1 / 3 of the local water depth from the bottom of the water to measure the average velocity at depth; Step 2, numerical model simulation: The simplified model of nonlinear mild slope equation accelerated by GPU parallelization is used to simulate the physical model experiment in step 1 and verify the model parameters. Finally, the flow characteristics of the unidirectional vortex-driven rift flow system under different configurations are studied by changing the numerical model settings, including: S21, simplified model of nonlinear gentle slope equation: adopt Cartesian rectangular coordinate system (x, y, z), where the x-axis is perpendicular to the shoreline direction, the y-axis is parallel to the shoreline direction, and the z-axis is vertically upward. In this coordinate system, the simplified model of nonlinear gentle slope equation accelerated by GPU has the following control equation: In the formula, 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 takes into account wave breaking, bottom friction and lateral mixing effects; 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 si for: In the formula, 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 si , we get the expression of the source function F(x,y,t): In the formula, 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 absorption boundary, the shore boundary is the wave climbing dynamic boundary, the upstream boundary and the downstream boundary are both solid boundaries, and the downstream boundary can be regarded as a vertical shoreline structure that reflects the incident waves; S25, numerical model verification: the above numerical model is used to simulate the physical model experiment, and the numerical model results are compared and analyzed with the physical model experiment results to verify the accuracy of the numerical model; the verification content includes the verification of the wave field and the verification of the flow field. 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 shore direction and along the shore direction and the flow velocity vector in the flow field; Step 3: Change the numerical model settings to analyze the flow characteristics of the unidirectional vortex-driven rift 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 influence of factors such as the reflection coefficient of the structure to the wave, the wave incident angle, and the wave incident height and period on the flow characteristics of the unidirectional vortex-driven rift system is studied.

2. The method according to claim 1, characterized in that In step 1, S12, the theoretical standing wave wavelength λ corresponding to the spectrum peak period is calculated according to the Snell theorem by the following formula: 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: declaration and definition of host and device variables, allocation of host and device variable memory space, host variable initialization, copying host data to device, calling device kernel functions in sequence to complete the calculation, copying device data back to host, and finally outputting the result; In the process of calling the kernel function, the number of logically enabled threads is organized at 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 size of the thread block, that is, the number of threads contained in a thread block.

4. The method according to claim 1, characterized in that 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 using 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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