A method for predicting the transverse distribution of flow velocity and reynolds stress in a vegetated river channel
By using a two-dimensional longitudinal velocity lateral distribution control equation and a Reynolds stress lateral distribution prediction model, the problem of predicting the lateral distribution of velocity and Reynolds stress in vegetated river channels was solved, achieving high-precision prediction that is applicable to various flow and vegetation conditions.
Patent Information
- Application Number
- CN202411581724.X
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2024-11-07
- Publication Date
- 2026-02-13
- Estimated Expiration
- 2044-11-07
AI Technical Summary
Existing technologies cannot effectively predict the lateral distribution of flow velocity and Reynolds stress in vegetated river channels, especially when field conditions are unsuitable. Furthermore, the high cost and time-consuming nature of measurements hinder research on the interaction between water flow, sediment, and vegetation.
A two-dimensional longitudinal velocity lateral distribution control equation and a Reynolds stress lateral distribution prediction model were adopted. By dividing the area into vegetated and unvegetated zones, the boundary conditions were determined, and the flow velocity and Reynolds stress were predicted using an analytical model and the SKM method.
It achieves high-precision prediction of flow velocity and Reynolds stress in vegetated river channels. The model has wide applicability and high prediction accuracy, and is applicable to different water flow and vegetation conditions.
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Figure CN119476115B_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The present application relates to the technical field of hydraulics and river dynamics, and particularly relates to a prediction method for transverse distribution of flow velocity and Reynolds stress in a vegetated river. BACKGROUND
[0002] Vegetation communities often appear in natural rivers, forming vegetated rivers with vegetation communities. The appearance of vegetation communities will affect the water flow structure of the local river around them. When the water flow flows to the vegetation community, it will be subjected to the drag force exerted by the vegetation, and the incoming flow upstream of the front end of the vegetation community will be laterally deflected, causing the flow velocity inside the vegetation area to slow down, thereby reducing the sediment carrying capacity of the water flow, and the suspended sediment in the water is prone to deposit inside the vegetation community. On the contrary, in the river outside the vegetation area, the water flow velocity increases, increasing the sediment carrying capacity of the water flow, causing the riverbed outside the vegetation area to be eroded. The flow velocity difference between the inside and outside of the vegetation community area causes a large flow velocity gradient at the vegetation area and the non-vegetation area, and the larger the flow velocity gradient, the larger the Reynolds stress, which is prone to cause the re-suspension of the deposited sediment in the riverbed. Therefore, the flow velocity distribution and the Reynolds stress distribution are closely related to the riverbed evolution process.
[0003] The vegetation communities in natural rivers are mostly non-submerged vegetation. Compared with submerged vegetation, both the non-submerged vegetation and the submerged vegetation have root systems that are rooted in the riverbed sediment to absorb nutrients and organic matter deposited in the water. However, the non-submerged vegetation has a part above the water surface, and this part of branches and leaves can provide more nutrients for the vegetation than the part of the submerged vegetation that is located above the riverbed below the water surface. One is because of light and action, and the other is because the oxygen content in the air is higher than that in the water. Although previous studies have been conducted on the flow velocity distribution in vegetated rivers, these studies have measured the flow velocity distribution at each point using instruments, and theoretical calculation models are only used to predict the transverse distribution of flow velocity in the fully developed region of the vegetation community river and the longitudinal distribution of flow velocity in the vegetation area. It is still not possible to predict the flow velocity distribution in the entire vegetated river. In addition, there is no prediction model for the transverse distribution of Reynolds stress along the river in the vegetated river. In addition, detailed flow velocity measurement requires a large amount of manpower, material resources and time, and more importantly, in field investigations, many rivers are not suitable for flow velocity measurement due to factors such as rapid water flow conditions and dangerous terrain, and it is difficult to obtain the flow velocity distribution in the river with vegetation communities, which hinders the further study of the interaction between water flow, sediment and vegetation. SUMMARY
[0004] The present application aims to provide a prediction method for the transverse distribution of flow velocity and Reynolds stress in a vegetated river, which not only realizes the prediction of the transverse distribution of flow velocity at each cross section, but also realizes the prediction of the transverse distribution of Reynolds stress.
[0005] To achieve the above object, the present application provides a method for predicting the transverse distribution of flow velocity and Reynolds stress in a river channel with vegetation, comprising the following steps:
[0006] S1, determining a control equation for the transverse distribution of water depth averaged two-dimensional longitudinal flow velocity;
[0007] S2, taking the center position of the upstream boundary of the non-submerged vegetation community as the origin, dividing the river channel into vegetation area and non-vegetation area along the direction perpendicular to the water flow;
[0008] S3, determining the analytical model of the transverse distribution of water depth averaged longitudinal flow velocity in the vegetation area and the non-vegetation area based on the control equation for the transverse distribution of water depth averaged two-dimensional longitudinal flow velocity;
[0009] S4, determining the boundary conditions in the analytical model of the transverse distribution of water depth averaged longitudinal flow velocity;
[0010] S5, solving the analytical model of the transverse distribution of water depth averaged longitudinal flow velocity based on the boundary conditions to obtain the transverse distribution of cross-sectional flow velocity in the vegetation area and the non-vegetation area;
[0011] S6, based on the obtained transverse distribution of flow velocity of each cross section, constructing a prediction model for the transverse distribution of Reynolds stress according to the SKM method to predict the transverse distribution of Reynolds stress.
[0012] Preferably, the control equation for the transverse distribution of two-dimensional longitudinal flow velocity in step S1 is:
[0013]
[0014] In the formula, ρ is the density of water, H is the water depth, λ is the dimensionless eddy viscosity coefficient, f is the Darcy resistance coefficient, C d is the drag coefficient, a is the unit water resistance area, which is obtained from the vegetation density n and the diameter of single vegetation d, U d is the water depth averaged flow velocity, S is the water surface slope, and K represents the convection term parameter.
[0015] Preferably, the analytical model of the transverse distribution of water depth averaged longitudinal flow velocity in the vegetation area and the non-vegetation area in step S3 is:
[0016] Non-vegetation area:
[0017] Vegetation area:
[0018] In the formula, A1, A2, A3 and A4 are integral constants, which are obtained from the water depth averaged flow velocity in the adjacent two area boundary conditions, and K1 and K2 respectively represent the dimensionless coefficients of convection exchange in the non-vegetation area and the vegetation area.
[0019] Preferably, the boundary conditions in step S4 are used to solve the integral constants, the boundary conditions are:
[0020] The water flow velocity is continuous and the water flow gradient is continuous at the junction of the vegetation area and the non-vegetation area y=b;
[0021] The water flow velocity is continuous: U bare =U veg ;
[0022] The water flow gradient is continuous:
[0023] At the center line y=0 inside the vegetation area,
[0024] At y=0.95B (close to the side wall inside the bare river area), U bare =U d ;
[0025] In the formula, b is 1 / 2 of the vegetation community width, and B is 1 / 2 of the river width.
[0026] Preferably, the water depth average longitudinal flow velocity transverse distribution analytical model is solved based on the boundary conditions in step S5, which includes:
[0027] The values of K1 and K2 are determined by trial and error, the value of K1 is adjusted, when the calculated flow velocity of the water depth average longitudinal flow velocity transverse distribution analytical model inside the vegetation area is equal to the measured flow velocity U veg inside the vegetation area, the value of K1 is the final determined value; the value of K2 is adjusted, when the calculated flow velocity of the water depth average longitudinal flow velocity transverse distribution analytical model in the non-vegetation area is equal to the measured flow velocity U bare in the non-vegetation area, the value of K2 is the final determined value, the water depth average longitudinal flow velocity transverse distribution analytical model is solved according to K1 and K2, to obtain the transverse distribution of the cross-sectional flow velocity in the vegetation area and the non-vegetation area.
[0028] Preferably, based on the obtained flow velocity transverse distribution of each cross section, the Reynolds stress transverse distribution prediction model is constructed according to the SKM method in step S6 to predict the Reynolds stress transverse distribution, which includes:
[0029] The obtained transverse distribution of the cross-sectional flow velocity in the vegetation area and the non-vegetation area is defined as U (y) , the Reynolds stress transverse distribution prediction model is constructed according to the SKM method, and the SKM formula is:
[0030]
[0031] In the formula, ε yx (=λHU * ) is the transverse average water depth eddy viscosity coefficient, U is the friction velocity, d U is the average velocity of the water depth;
[0032] A prediction model of the transverse distribution of the Reynolds stress is derived from the above formula, and the formula is:
[0033]
[0034] In the formula, ρ is the density of water, H is the water depth, λ is the dimensionless eddy viscosity coefficient, and f is the Darcy resistance coefficient.
[0035] Therefore, the prediction method for the transverse distribution of the flow velocity and the Reynolds stress in the vegetated river channel has the following beneficial effects:
[0036] (1) The present application is based on the water flow momentum equation and the continuity equation, and not only a prediction model of the transverse distribution of the longitudinal flow velocity is derived, but also a prediction model of the transverse distribution of the Reynolds stress is derived based on the prediction model, which ensures the correctness of the theory and has high prediction accuracy;
[0037] (2) The constants required for the analytical calculation model of the present application are common calculation variables in the field, which can be determined according to the water flow conditions, vegetation conditions and river channel conditions, and the prediction model has wide universality in the field.
[0038] The technical solutions of the present application will be further described in detail below through the drawings and examples. BRIEF DESCRIPTION OF DRAWINGS
[0039] Figure 1 Fig. 1 is a schematic diagram of the water flow and vortex longitudinal development of the vegetated community river channel in the embodiment of the present application;
[0040] Figure 2 Fig. 2 is a schematic diagram of the water tank test arrangement in the embodiment of the present application;
[0041] Figure 3 Fig. 3 is a comparison diagram of the model prediction value and the measured longitudinal flow velocity transverse distribution value in the water tank test in different cross sections in different working conditions in the embodiment of the present application;
[0042] Figure 4 Fig. 4 is a comparison diagram of the model prediction value and the measured turbulent kinetic energy transverse distribution value in the water tank test in different cross sections in different working conditions in the embodiment of the present application. DETAILED DESCRIPTION
[0043] In order to make the purposes, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only some of the embodiments of the present application, rather than all the embodiments. The components of the embodiments of the present application described and shown in the drawings can be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present application provided in the drawings is not intended to limit the scope of the claimed present application, but only represents selected embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the scope of protection of the present application.
[0044] Embodiment
[0045] The present application provides a prediction method for the transverse distribution of flow velocity and Reynolds stress in a vegetated river channel, which is suitable for the case where the flow velocity in the river channel is greater than 0 cm / s, as shown in the following formula (3). Figure 1
[0046] The present application takes the momentum equation and the water flow continuity equation as the derivation basis, considers the additional drag force generated by the vegetation community, proposes the boundary conditions of the analytical model, proposes an analytical calculation model for the transverse distribution of the longitudinal flow velocity, and establishes a model for the transverse distribution of the Reynolds stress based on the flow velocity model. The specific derivation process is as follows:
[0047] S1, taking the momentum equation (formula (1)) and the water flow continuity equation (formula (2)) as the derivation basis, the expressions of the two equations are as follows:
[0048]
[0049] Wherein, U, V, and W are the time-averaged flow velocities in the x, y and z directions respectively; p is the density of water; τ is the shear stress term; f x is the drag force generated by the vegetation, for the constant flow, the flow velocity no longer changes with time, so
[0050] S2, in the vegetation community area, the additional drag force generated by the vegetation is expressed as follows:
[0051]
[0052] Wherein C d is the drag force coefficient, the unit water body resistance area a (=nd) is obtained from the vegetation density (n) and the diameter of a single plant (d).
[0053] S3, the expression of the shear stress τ xx in formula (1) is as follows:
[0054]
[0055] where p (= -pgH) is the fluid water pressure, g is the local gravitational acceleration, H is the water depth, and ε is the eddy viscosity.
[0056] S4, the control equation (5) can be obtained by combining equations (1)-(4).
[0057]
[0058] S5, based on equation (5) to determine the average water depth of two-dimensional longitudinal flow velocity transverse distribution control equation, equation (5) is integrated along the water depth direction, wherein the vertical flow velocity W ≈ 0 cm / s at the riverbed (z = 0 cm) and the water surface (z = H). Shear stress τ zx At the water surface (z = H), it is 0, and at the riverbed (z = 0 cm), it is equal to the bed shear stress where is the friction velocity, U d is the water depth averaged flow velocity The transverse shear stress term (τ yx ) is defined as where ε yx (= λHU * ) is the transverse average water depth eddy viscosity coefficient, λ is the dimensionless eddy viscosity coefficient; f is the Darcy resistance coefficient.
[0059] Therefore, equation (5) is integrated along the water depth and substituted into the expression of each parameter in S5, and after simplification, the water depth averaged two-dimensional longitudinal flow velocity transverse distribution control equation can be obtained:
[0060]
[0061] S6, let the quadratic flow term on the right side of equation (6) K, equation (6) can be simplified as follows:
[0062]
[0063] S7, taking the center position of the upstream end boundary of the non-submerged vegetation community as the origin, the river channel is divided into vegetation area and non-vegetation area along the direction perpendicular to the flow.
[0064] S8, based on the water depth averaged two-dimensional longitudinal flow velocity transverse distribution control equation, the analytical model of water depth averaged longitudinal flow velocity transverse distribution in the vegetation area and the non-vegetation area is determined, and K is K1 in the vegetation area and K2 in the non-vegetation area. The analytical model of the non-vegetation area (U bare ) and the vegetation area (U veg ) is as follows:
[0065]
[0066] wherein, is an integration constant, A1, A2, A3 and A4 are integration constants.
[0067] S9, determining the boundary conditions in the analytical model of the transverse distribution of the average longitudinal velocity of the water flow. To solve the integration constants in equations (8) and (9), four reasonable boundary conditions are needed. The boundary conditions are:
[0068] a the continuity of the velocity of the water flow and the continuity of the gradient of the water flow at the interface between the vegetated area and the non-vegetated area y = b;
[0069] the continuity of the velocity of the water flow: bare = U veg ;
[0070] the continuity of the gradient of the water flow:
[0071] b at the center line inside the vegetated area y = 0,
[0072] c at the inner edge of the bare river channel area close to the side wall y = 0.95B, U bare = U d ;
[0073] wherein b is 1 / 2 of the width of the vegetation community and B is 1 / 2 of the width of the river channel.
[0074] S10, solving the analytical model of the transverse distribution of the average longitudinal velocity of the water flow based on the boundary conditions to obtain the transverse distribution of the velocity of the water flow in the vegetated area and the non-vegetated area.
[0075] The four integration constants in the analytical expressions (8) and (9) can be solved by the four boundary conditions introduced in (10). Substituting the gravitational acceleration g, the water depth H, the water surface slope S, the Darcy resistance coefficient f, the dimensionless eddy viscosity coefficient λ, the vegetation drag coefficient C d , the unit water body vegetation water resistance area a (= nd, wherein n is the vegetation density and d is the vegetation diameter), the defined parameters K1 and K2. Among them, g, H, S and a can be directly measured by the test water flow conditions and the vegetation density n and the vegetation diameter d. The formula of the Darcy resistance coefficient f is f = 8gn c 2 / R 1 / 3 is determined, wherein R is the hydraulic radius, n c (= 0.013) is the Manning coefficient, which is determined according to the PVC plate laid in the test flume; the dimensionless eddy viscosity coefficient λ can be calculated according to λ = κ / 6, wherein κ (= 0.4) is the Karman constant; the vegetation drag coefficient C d is closely related to the water flow conditions, and is calculated by the formula Cd = 1 + 10Re -2 / 3 Calculation. The values of K1 and K2 are determined by trial method, the value of K1 is adjusted, when the calculated flow velocity of the water depth average longitudinal flow velocity transverse distribution analytical model in the vegetation area is equal to the measured flow velocity U veg of the vegetation area inside, the value of K1 is the final determined value; the value of K2 is adjusted, when the calculated flow velocity of the water depth average longitudinal flow velocity transverse distribution analytical model in the non-vegetation area is equal to the measured flow velocity U bare of the non-vegetation area, the value of K2 is the final determined value, the water depth average longitudinal flow velocity transverse distribution analytical model is solved according to K1 and K2, and the transverse distribution of the cross-sectional flow velocity of the vegetation area and the non-vegetation area is obtained.
[0076] S11, based on the obtained transverse distribution of flow velocity of each cross section, a Reynolds stress transverse distribution prediction model is constructed according to the SKM method, and the Reynolds stress transverse distribution is predicted, comprising:
[0077] The obtained transverse distribution of cross-sectional flow velocity of the vegetation area and the non-vegetation area is defined as U (y) , a Reynolds stress transverse distribution prediction model is constructed according to the SKM method, and the SKM formula is:
[0078]
[0079] In the formula, ε yx ( = λHU * ) is the transverse average water depth eddy viscosity coefficient, is the friction velocity, U d is the water depth average flow velocity;
[0080] The Reynolds stress transverse distribution prediction model is derived from the above formula, and the formula is:
[0081]
[0082] In the formula, ρ is the density of water, H is the water depth, λ is the dimensionless eddy viscosity coefficient, and f is the Darcy resistance coefficient.
[0083] In order to verify the effectiveness of the prediction method of the application, the longitudinal flow velocity and the Reynolds stress transverse distribution along the path obtained by the flume test with non-submerged vegetation group are compared with the prediction method of the application.
[0084] Test purpose
[0085] The longitudinal flow velocity transverse distribution in the multiple cross sections along the path of the vegetation test flume is measured by the flume test, and the prediction results of the model introduced in the disclosure are verified by using the measured longitudinal flow velocity and the Reynolds stress transverse distribution in the multiple cross sections along the path.
[0086] Test equipment
[0087] The main equipment is shown in Table 1 below.
[0088] Table 1. Flume test equipment for non-submerged vegetation communities in the beach area.
[0089]
[0090] Test conditions
[0091] The experiment was conducted in a test flume measuring 13 meters long, 1 meter wide, and 0.5 meters high. The flow development zone was defined as the distance from the inlet to 3 meters from the inlet, and the test zone was defined as the 7-meter distance from 3 meters to 10 meters from the inlet. The vegetation community was positioned at the center of the test area (10 meters from the inlet). A schematic diagram of the vegetation community flume layout is attached. Figure 2 As shown. The water surface gradient S = 44 × 10⁻⁶ -6 The average upstream velocity (U0) in the river channel was measured 5m in front of the vegetation community using an ADV (Advanced Dynamic Velocity Detector) mounted on a flue. This location was chosen because the flow deflection in front of the vegetation community only occurs within a 50cm radius of the vegetation front, i.e., L. u <50cm. Under all operating conditions, the upstream flow rate is 65L / s, the water depth is H=18cm, and the average upstream velocity is U0=18cm / s. The flow is turbulent and slow-moving under all operating conditions.
[0092] In this embodiment, a rectangular model vegetation community was constructed and placed in the center of the water tank. In conditions 1-3, the length of the vegetation community L = 3-4.5m. The selection of L is based on the fact that it is greater than the water flow deflection distance L within the vegetation community. I Therefore, the water flow can remain stable after it has fully developed within the vegetated area. The parameters for operating conditions 1-3 are shown in Table 2.
[0093] In operating conditions 1-3, the lateral distribution of longitudinal velocity in multiple cross-sections was measured between the upstream (x=0cm) and downstream (x=L) of the vegetation area. The values of each cross-section location and the values of K1 and K2 in each cross-section are shown in Table 3.
[0094] Rigid wooden sticks were evenly inserted into perforated PVC boards at the bottom of the water tank to construct the model vegetation community. The Darcy drag coefficient generated by the PVC boards was f = 0.025. The wooden sticks simulating non-submerged vegetation were 30 cm long, which is greater than the water depth of 18 cm. Therefore, the model vegetation communities in this study were all non-submerged vegetation communities, which is consistent with the vegetation communities (non-submerged) commonly observed in natural rivers.
[0095] The rigid wooden sticks used to simulate vegetation do not represent any specific type of vegetation. However, the diameter of the round sticks, d = 0.8 cm, is an intermediate value between 0.1-1 cm for common vegetation diameters in natural river channels, riverbanks, and wetlands. Therefore, the experimental results obtained based on this value are highly representative. The vegetation density was n = 0.05 to 0.15 cm³. 2 The proportion of area occupied by vegetation per unit area The value ranges from 0.025 to 0.076, which coincides with the range of *Typha orientalis* (φ = 0.001-0.08), commonly found in natural river channels. The vegetation drag coefficient was chosen as C. d (≈1-1.2).
[0096] The coordinate system in the river channel is defined at the center of the vegetation community's leading edge. The coordinates along the direction of water flow are x, where x = 0 represents the very front of the vegetation community; the direction perpendicular to the water flow is y, where y = 0 represents the center of the vegetation community; and the direction perpendicular to the water surface is z, where z = 0 represents the riverbed position. The flow velocities in these three directions are U(t), V(t), and W(t), respectively, measured using Doppler velocity measurement (ADV). The flume is equipped with a support frame for the ADV, which can move freely along the x, y, and z directions. The instantaneous flow velocity data in the three directions are processed using the ADV's built-in data processing software to obtain the time-averaged flow velocities (U, V, W) in the three directions (x, y, z). Flow velocity measurements were all taken at a depth of 1 / 2 water (z = 9 cm), because the depth-averaged flow velocity U... d The difference between the measured velocity at 1 / 2 water depth and the average velocity at 1 / 2 water depth is less than 6%. Therefore, it can be assumed that the measured velocity at 1 / 2 water depth is equal to the average velocity U at the water depth. d .
[0097] Table 2 shows the parameters for various operating conditions in the flume experiment with vegetated communities.
[0098]
[0099] In the table: H is water depth, U0 is average upstream channel velocity; b is half the width of the vegetation community; L is the length of the vegetation community; a is the water-blocking area of vegetation per unit water body (a = nd, where n is vegetation density and d is vegetation diameter); C d ab is the vegetation coefficient; φ is the proportion of area occupied by vegetation per unit area; L I This represents the water flow deflection distance within the vegetation community.
[0100] Table 3. Test locations and K1 and K2 values for cross-sectional velocity distribution under various working conditions.
[0101]
[0102] In the table: x is the cross-sectional position; K1 and K2 are the defined secondary flow parameters.
[0103] Analysis of test results
[0104] The longitudinal flow velocity and the Reynolds stress along the path and the transverse distribution of the three working conditions in the examples were predicted by using the prediction model of the application, and the model prediction values are shown in Figs. 6-8. Figure 3 and 4 The measured values of the longitudinal flow velocity distribution of the flume test are shown in Figs. 6-8. Figure 3 and 4 The measured values of the longitudinal flow velocity distribution of the flume test are shown in Figs. 6-8. Figure 3 Figs. 6-8 are comparison diagrams of the model prediction values and the measured values of the longitudinal flow velocity transverse distribution in different cross sections in different working conditions of the examples, (a) working condition 1, C d ab=1.32; (b) working condition 2, C d ab=1.98; (c) working condition 3, C d ab=3.96. The gray vertical line represents the boundary of the vegetation community, the black curve is the model prediction value, the black circle is the test measured value, and x=50 cm, x=100 cm and x=150 cm in the figure respectively represent the selected flow velocity transverse distribution test cross section positions under each working condition. Figure 4 Figs. 6-8 are comparison diagrams of the model prediction values and the measured values of the longitudinal flow velocity transverse distribution in different cross sections in different working conditions of the examples, (a) working condition 1, C d ab=1.32; (b) working condition 2, C d ab=1.98; (c) working condition 3, C d ab=3.96. The gray vertical line represents the boundary of the vegetation community, the black curve is the model prediction value, the black circle is the test measured value, and x=50 cm, x=100 cm and x=150 cm in the figure respectively represent the selected flow velocity transverse distribution test cross section positions under each working condition.
[0105] When the calculation is carried out, the parameter values in formulas (8) and (9) are shown in Tables 4 and 5. The Reynolds stress is calculated based on the flow velocity values of formulas (8) and (9). From the comparison of the measured values and the model prediction values in Figs. 6-8, the prediction model of the longitudinal flow velocity and the Reynolds stress along the path and the transverse distribution of the vegetated river channel proposed by the application can accurately predict the longitudinal flow velocity and the Reynolds stress along the path and the transverse distribution of the vegetated area under the influence of different density vegetation communities. Figure 3 and 4 When the calculation is carried out, the parameter values in formulas (8) and (9) are shown in Tables 4 and 5. The Reynolds stress is calculated based on the flow velocity values of formulas (8) and (9). From the comparison of the measured values and the model prediction values in Figs. 6-8, the prediction model of the longitudinal flow velocity and the Reynolds stress along the path and the transverse distribution of the vegetated river channel proposed by the application can accurately predict the longitudinal flow velocity and the Reynolds stress along the path and the transverse distribution of the vegetated area under the influence of different density vegetation communities.
[0106] Table 4 Summary of calculation parameters of each working condition
[0107]
[0108] In the table, g is the local gravitational acceleration; H is the water depth; S is the water surface slope; a is the water resistance area of the unit water body vegetation (a=nd, wherein n is the vegetation density and d is the vegetation diameter); C dC d is the vegetation drag coefficient; φ is the area proportion of vegetation per unit area; f is the Darcy resistance coefficient; λ is the dimensionless eddy viscosity coefficient.
[0109] Table 5: Summary of integral constants of each cross-sectional area A1, A2, A3 and A4 in each working condition
[0110]
[0111] In the table: x is the cross-sectional position; A1, A2, A3 and A4 are integral constants.
[0112] Therefore, the present application adopts the above-mentioned method for predicting the transverse distribution of flow velocity and Reynolds stress in a vegetated river channel, derives the control equation of the transverse distribution of flow velocity in a vegetated river channel from the water flow momentum equation and the continuity equation, and solves it according to the boundary conditions, thereby not only realizing the prediction of the transverse distribution of flow velocity of each cross section, but also realizing the prediction of the transverse distribution of Reynolds stress, ensuring the correctness of the theory while having higher prediction accuracy.
[0113] Finally, it should be noted that: the above examples are only used to illustrate the technical solutions of the present application rather than limiting them, although the present application has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that: the technical solutions of the present application can still be modified or replaced by equivalents, and these modifications or equivalent replacements cannot make the modified technical solutions deviate from the spirit and scope of the technical solutions of the present application.
Claims
1. A method for predicting the lateral distribution of flow velocity and Reynolds stress in vegetated river channels, characterized in that, This method is applicable when the river flow velocity is greater than 0 cm / s. The steps include: S1. Determine the governing equations for the transverse distribution of the two-dimensional longitudinal velocity with average water depth. The formula is: In the formula, ρ is the density of water, H is the water depth, λ is the dimensionless eddy viscosity coefficient, f is the Darcy drag coefficient, Cd is the drag force coefficient, a is the water-blocking area per unit water body, which is obtained from the vegetation density n and the diameter of a single vegetation plant d, U d Let S be the average velocity at water depth, S be the water surface slope, and K be the convection parameter. S2. Taking the center of the upstream boundary of the non-submerged vegetation community as the origin, the river channel is divided into a vegetated area and a non-vegetated area along the direction perpendicular to the water flow. S3. Based on the governing equations for the transverse distribution of the two-dimensional longitudinal velocity with average water depth, the analytical models for the transverse distribution of the average longitudinal velocity with average water depth are determined for vegetated and unvegetated areas. The formula is as follows: Unvegetated areas: Vegetation area: In the formula, A1, A2, A3 and A4 are integral constants, which are obtained from the average flow velocity of water depth in each region under the boundary conditions of two adjacent regions. K1 and K2 represent the dimensionless coefficients of convective exchange in the unvegetated area and the vegetated area, respectively. S4. Determine the boundary conditions in the analytical model for the transverse distribution of the average longitudinal velocity at water depth. S5. Solve the analytical model of the lateral distribution of the average longitudinal velocity of water depth based on the boundary conditions to obtain the lateral distribution of cross-sectional velocity in vegetated and unvegetated areas. S6. Based on the obtained transverse velocity distribution of each cross section, a transverse Reynolds stress distribution prediction model is constructed according to the SKM method to predict the transverse Reynolds stress distribution, specifically including: The transverse velocity distribution of the obtained cross-sectional flow in vegetated and unvegetated areas is defined as U. (y) A prediction model for the transverse distribution of Reynolds stress is constructed based on the SKM method. The SKM formula is as follows: In the formula, ε yx (=λHU * () represents the eddy viscosity coefficient at the transverse average water depth. For frictional flow velocity, U d The average velocity at water depth; The Reynolds stress transverse distribution prediction model is derived from the above formula, and the formula is: In the formula, ρ is the density of water, H is the water depth, λ is the dimensionless eddy viscosity coefficient, and f is the Darcy drag coefficient.
2. The method for predicting the lateral distribution of flow velocity and Reynolds stress in a vegetated river channel according to claim 1, characterized in that, In step S4, the boundary conditions are used to solve for the integration constant. The boundary conditions are as follows: At the boundary y=b between vegetated and unvegetated areas, the water flow velocity and gradient are continuous. Continuous water flow velocity: U bare =U veg ; Continuous flow gradient: At the center line y=0 within the vegetated area Within the exposed river channel area, near the sidewall at y = 0.95B, U bare =U d ; In the formula, b is 1 / 2 the width of the vegetation community, and B is 1 / 2 the width of the river channel.
3. The method for predicting the lateral distribution of flow velocity and Reynolds stress in a vegetated river channel according to claim 2, characterized in that, Step S5 involves solving the analytical model for the lateral distribution of the average longitudinal velocity at water depth based on boundary conditions, including: The values of K1 and K2 were determined using a trial-and-error method. The value of K1 was then adjusted. The calculated flow velocity within the vegetated area, based on the analytical model of the average longitudinal velocity distribution across the vegetated area, was compared with the measured flow velocity U within the vegetated area. veg When they are equal, the value of K1 is the final determined value; adjust the value of K2 so that the calculated velocity of the analytical model for the lateral distribution of the average longitudinal velocity of water depth in the vegetated area is equal to the measured velocity U in the vegetated area. bare When the values of K1 and K2 are equal, the value of K2 is the final determined value. Based on K1 and K2, the analytical model of the transverse distribution of the average longitudinal velocity of the water depth is solved to obtain the transverse distribution of the cross-sectional velocity in the vegetated area and the unvegetated area.