Prediction method for flow velocity and Reynolds stress transverse distribution in vegetation river channel

Abstract

The invention discloses a method for predicting flow velocity and Reynolds stress transverse distribution in a vegetation riverway, and belongs to the technical field of hydraulics and river dynamics, and the method comprises the steps: determining a two-dimensional longitudinal flow velocity transverse distribution control equation with average water depth; dividing the riverway into a vegetation area and a non-vegetation area along the direction vertical to water flow by taking the center position of the boundary of the upstream end of the non-submerged vegetation community as an original point; determining a water depth average longitudinal flow velocity transverse distribution analysis model of the vegetation area and the vegetation-free area; providing boundary conditions of the analytical model and solving to obtain transverse flow velocity distribution of each cross section; and constructing a Reynolds stress transverse distribution prediction model based on the predicted flow velocity transverse distribution, and predicting the Reynolds stress transverse distribution. According to the method, the control equation of the flow velocity transverse distribution in the vegetation riverway is deduced from the water flow momentum equation and the continuity equation, solving is carried out according to boundary conditions, and prediction of the flow velocity transverse distribution and Reynolds stress transverse distribution of each cross section is achieved.

Description

Technical Field

[0001] The invention relates to the technical field of hydraulics and river dynamics, and in particular to a method for predicting flow velocity and lateral distribution of Reynolds stress in a vegetated river channel. Background Art

[0002] Vegetation communities often appear in natural rivers, forming vegetated river channels with vegetation communities. The appearance of vegetation communities will affect the water flow structure of the local river channels around them. When water flows toward the vegetation community, it will be subject to the drag force exerted by the vegetation. The upstream flow in front of the vegetation community will be deflected laterally, causing the flow velocity inside the vegetation area to slow down, thereby reducing the sand-carrying capacity of the water flow, and the suspended sediment in the water is easy to deposit inside the vegetation community. On the contrary, in the adjacent river channel outside the vegetation area, the water flow velocity increases, increasing the sand-carrying capacity of the water flow, causing the riverbed outside the vegetation area to be eroded. The velocity difference between the inside and outside of the vegetation community area leads to a large velocity gradient between the vegetation area and the non-vegetated area. The larger the velocity gradient, the greater the Reynolds stress, which is easy to cause the sediment sediment in the riverbed to re-suspend. Therefore, the velocity distribution and Reynolds stress distribution are closely related to the riverbed evolution process.

[0003] Vegetation communities in natural rivers are mostly non-submerged vegetation. Compared with submerged vegetation, non-submerged vegetation has roots rooted in the riverbed sediment under the water surface to absorb nutrients and organic matter deposited in the water. However, non-submerged vegetation has parts above the water surface. Compared with the parts of submerged vegetation located below the water surface and above the riverbed, these branches and leaves can provide more nutrients for vegetation. One is because of light 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 velocity distribution of vegetated rivers, these studies have been conducted by using instruments to measure the velocity distribution at each point. The theoretical calculation model proposed is only used to predict the lateral distribution of velocity in the fully developed area of ​​the vegetated community river channel and the longitudinal distribution of velocity in the vegetated area. It is still impossible to predict the velocity distribution in the entire vegetated river channel. In addition, there is no prediction model for the lateral distribution of Reynolds stress along the vegetated river channel. In addition, carrying out detailed flow velocity measurements requires a lot of manpower, material resources and time. More importantly, in field surveys, many rivers are not suitable for flow velocity measurements due to factors such as rapid water flow and rugged terrain. It is impossible to obtain the flow velocity distribution in rivers with vegetation communities, which hinders further research on the interaction between water flow, sediment and vegetation. Summary of the invention

[0004] The purpose of the present invention is to provide a method for predicting the lateral distribution of flow velocity and Reynolds stress in a vegetated river channel, which not only realizes the prediction of the lateral distribution of flow velocity in each cross section, but also realizes the prediction of the lateral distribution of Reynolds stress.

[0005] To achieve the above object, the present invention provides a method for predicting flow velocity and lateral distribution of Reynolds stress in a vegetated river channel, the steps comprising:

[0006] S1, determine the governing equation for the lateral distribution of the two-dimensional longitudinal velocity averaged at water depth;

[0007] S2, taking the center of the upstream boundary of the non-submerged vegetation community as the origin, divide the river channel into vegetation area and non-vegetation area along the direction perpendicular to the water flow;

[0008] S3, based on the control equation of the lateral distribution of the two-dimensional longitudinal velocity of the average water depth, determine the analytical model of the lateral distribution of the average longitudinal velocity of the water depth in the vegetation area and the non-vegetation area;

[0009] S4, determine the boundary conditions in the analytical model of the lateral distribution of the average longitudinal velocity of the water depth;

[0010] S5. Solve the analytical model of the lateral distribution of the average longitudinal velocity of the water depth based on the boundary conditions to obtain the lateral distribution of the cross-sectional velocity in the vegetation area and the non-vegetation area;

[0011] S6. Based on the obtained lateral distribution of flow velocity in each cross section, a Reynolds stress lateral distribution prediction model is constructed according to the SKM method to predict the Reynolds stress lateral distribution.

[0012] Preferably, the control equation for the lateral distribution of the two-dimensional longitudinal flow velocity in step S1 is:

[0013]

[0014] Where ρ is the density of water, H is the water depth, λ is the dimensionless eddy viscosity coefficient, f is the Darcy drag coefficient, and C d is the drag coefficient, a is the unit water resistance area, which is obtained from the vegetation density n and the diameter d of a single plant, U d is the average velocity of water depth, S is the water surface slope, and K represents the convection term parameter.

[0015] Preferably, the analytical model for the lateral distribution of the average longitudinal velocity of water depth in the vegetation area and the non-vegetation area in step S3 is:

[0016] Area without vegetation:

[0017] Vegetation area:

[0018] In the formula, A1, A2, A3 and A4 are integration constants, which are obtained from the average velocity of water depth in each area at the boundary conditions of two adjacent areas. K1 and K2 represent the dimensionless coefficients of convective exchange in the unvegetated area and the vegetated area, respectively.

[0019] Preferably, in step S4, the boundary condition is used to solve the integral constant, and the boundary condition is:

[0020] At the boundary y=b between the vegetated area and the non-vegetated area, the water flow velocity and water flow gradient are continuous;

[0021] Continuous water flow rate: U bare =U veg ;

[0022] Continuous water flow gradient:

[0023] At the center line y=0 inside the vegetation area,

[0024] At y = 0.95B (inside the exposed channel area, near the side wall), U bare =U d ;

[0025] Where b is 1 / 2 the width of the vegetation community, and B is 1 / 2 the width of the river channel.

[0026] Preferably, solving the analytical model of the lateral distribution of the average longitudinal velocity of the water depth based on the boundary conditions in step S5 includes:

[0027] The values ​​of K1 and K2 are determined by trial and error, and the value of K1 is adjusted. When the calculated velocity of the lateral distribution analytical model of the average longitudinal velocity in the vegetation area is equal to the measured velocity U in the vegetation area, veg When the K1 value is equal to the K2 value, the K1 value is the final value; the K2 value is adjusted, when the calculated flow velocity of the lateral distribution analytical model of the average longitudinal flow velocity in the vegetation-free area is equal to the measured flow velocity U in the vegetation-free area bare When the values ​​of are equal, K2 is the final determined value. The analytical model of the lateral distribution of the average longitudinal velocity at water depth is solved according to K1 and K2 to obtain the lateral distribution of the cross-sectional velocity in the vegetation area and the non-vegetation area.

[0028] Preferably, step S6 constructs a Reynolds stress lateral distribution prediction model based on the obtained lateral distribution of flow velocity in each cross section according to the SKM method, and predicts the Reynolds stress lateral distribution, including:

[0029] The lateral distribution of cross-sectional flow velocity in the vegetation area and the non-vegetation area is defined as U (y) , the Reynolds stress lateral distribution prediction model is constructed according to the SKM method. The SKM formula is:

[0030]

[0031] In the formula, ε yx (=λHU * ) is the lateral average water depth eddy viscosity coefficient, is the friction velocity, U d is the average velocity at water depth;

[0032] The Reynolds stress lateral distribution prediction model is derived from the above formula:

[0033]

[0034] Where 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.

[0035] Therefore, the present invention adopts the above-mentioned method for predicting the flow velocity and lateral distribution of Reynolds stress in a vegetated river channel, which has the following beneficial effects:

[0036] (1) Starting from the water flow momentum equation and the continuity equation, the present invention not only derives a prediction model for the lateral distribution of the longitudinal flow velocity, but also derives a prediction model for the lateral distribution of the Reynolds stress based on the prediction model, thereby ensuring that the theory is correct and having a high prediction accuracy;

[0037] (2) The constants required to be determined by the analytical calculation model of the present invention are all common calculation variables in this field, and can be determined based on water flow conditions, vegetation conditions and river conditions. The prediction model has wide versatility in this field.

[0038] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 This is a schematic diagram of the longitudinal development of water flow and vortex in a river channel of a vegetation community according to an embodiment of the present invention;

[0040] Figure 2 This is a schematic diagram of the arrangement of a water tank test in an embodiment of the present invention;

[0041] Figure 3 A comparison diagram of the model prediction value and the transverse distribution value of the longitudinal flow velocity actually measured in the flume test in different cross sections under different working conditions of the embodiment of the present invention;

[0042] Figure 4 This is a comparison chart of the model prediction value and the lateral distribution value of turbulent kinetic energy measured in the water tank test in different cross sections under different working conditions in an embodiment of the present invention. DETAILED DESCRIPTION

[0043] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all of the embodiments. The components of the embodiments of the present invention generally described and shown in the drawings here can be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the drawings is not intended to limit the scope of the claimed invention, but merely represents selected embodiments of the present invention. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0044] Example

[0045] The method for predicting the flow velocity and lateral distribution of Reynolds stress in a vegetated river provided by the present invention is applicable to the case where the flow velocity of the river is greater than 0 cm / s, such as Figure 1 shown.

[0046] Based on the momentum equation and the water flow continuity equation, the present invention 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 lateral distribution of the longitudinal flow velocity, and establishes a lateral distribution model of the Reynolds stress along the flow based on the flow velocity model. The specific derivation process is as follows:

[0047] S1. Based on the momentum equation (Equation (1)) and the water flow continuity equation (Equation (2)), the expressions of the two equations are as follows:

[0048]

[0049] where U, V, and W are the time-averaged flow velocities in the x, y, and z directions, respectively; ρ is the density of water; τ is the shear stress term; f x is the drag force generated by vegetation. For a steady flow, the flow velocity no longer changes with time, so

[0050] S2. In the vegetation community area, the additional drag resistance generated by vegetation is expressed as follows:

[0051]

[0052] Among them C d is the drag coefficient, and the unit water resistance area a (= nd) is obtained from the vegetation density (n) and the diameter of a single plant (d).

[0053] S3, shear stress τ in formula (1) xx The expression is:

[0054]

[0055] Among them, p (=-ρgH) is the fluid water pressure, g is the local gravitational acceleration, H is the water depth, and ε is the eddy viscosity.

[0056] S4. Combining formulas (1)-(4) can obtain the control equation (5):

[0057]

[0058] S5. Determine the control equation for the lateral distribution of the two-dimensional longitudinal velocity averaged at the water depth based on equation (5), and integrate equation (5) along the water depth direction, where the vertical velocity W≈0 cm / s at the riverbed (z=0 cm) and the water surface (z=H). Shear stress τ zx It is 0 on the water surface (z = H) and equal to the bed shear stress on the riverbed (z = 0 cm) in is the friction velocity, U d is the average velocity at depth Transverse shear stress term (τ yx ), defined as where ε yx (=λHU * ) is the lateral average water depth eddy viscosity coefficient, λ is the dimensionless eddy viscosity coefficient; f is the Darcy drag coefficient.

[0059] Therefore, integrating equation (5) along the water depth and substituting it into the parameter expressions in S5, the control equation for the lateral distribution of the two-dimensional longitudinal velocity averaged at the water depth can be obtained after simplification:

[0060]

[0061] S6, let the secondary flow term on the right side of the equal sign in equation (6) is K, formula (6) can be simplified to the following formula:

[0062]

[0063] S7. Taking the center of the upstream boundary of the non-submerged vegetation community as the origin, divide the river channel into vegetation area and non-vegetation area along the direction perpendicular to the water flow.

[0064] S8. Determine the analytical model of the lateral distribution of the average longitudinal velocity of the water depth in the vegetation area and the non-vegetation area based on the control equation of the lateral distribution of the two-dimensional longitudinal velocity of the water depth average. Let K be K1 in the vegetation area, K2 in the non-vegetation area, and K3 in the non-vegetation area (U bare ) and vegetation area (U veg ) is as follows:

[0065]

[0066] Among them, in the formula: is the integration constant, A1, A2, A3 and A4 are integration constants.

[0067] S9. Determine the boundary conditions in the analytical model of the lateral distribution of the average longitudinal velocity of the water depth. In order to solve the integral constants in equations (8) and (9), it is necessary to select four reasonable boundary conditions. The boundary conditions are:

[0068] a. At the boundary y=b between the vegetated area and the non-vegetated area, the flow velocity and the flow gradient are continuous;

[0069] Continuous water flow rate: U bare =U veg ;

[0070] Continuous water flow gradient:

[0071] b is at the center line y=0 inside the vegetation area,

[0072] c Inside the exposed channel area, near the side wall y = 0.95B, U bare =U d ;

[0073] Where b is 1 / 2 the width of the vegetation community, and B is 1 / 2 the width of the river channel.

[0074] S10. Solve the analytical model of the lateral distribution of the average longitudinal velocity of the water depth based on the boundary conditions to obtain the lateral distribution of the cross-sectional velocity in the vegetation area and the non-vegetation area.

[0075] The four integral constants in analytical expressions (8) and (9) can be solved by the four boundary conditions introduced in (10). Substituting gravity acceleration g, water depth H, water surface slope S, Darcy drag coefficient f, dimensionless eddy viscosity coefficient λ, vegetation drag coefficient C d , the unit water body vegetation water blocking area a (= nd, where n is the vegetation density and d is the vegetation diameter), and the defined parameters K1 and K2. Among them, g, H, S and a can be directly measured through the test water flow conditions and vegetation density n and vegetation diameter d. Darcy resistance coefficient f formula: f = 8gn c 2 / R 1 / 3 Determine, where R is the hydraulic radius, n c (=0.013) is the Manning coefficient, which is determined based on the PVC board laid in the test flume; the dimensionless eddy viscosity coefficient λ can be calculated according to λ=κ / 6, where κ(=0.4) is the Karman constant; the vegetation drag coefficient C d It is closely related to the water flow conditions.d =1+10Re -2 / 3 Calculation. Use the trial algorithm to determine the values ​​of K1 and K2, adjust the K1 value, and when the calculated flow velocity inside the vegetation area by the analytical model of the average longitudinal velocity lateral distribution of the vegetation area is equal to the measured flow velocity inside the vegetation area U veg When the K1 value is equal to the K2 value, the K1 value is the final value; the K2 value is adjusted, when the calculated flow velocity of the lateral distribution analytical model of the average longitudinal flow velocity in the vegetation-free area is equal to the measured flow velocity U in the vegetation-free area bare When the values ​​of are equal, K2 is the final determined value. The analytical model of the lateral distribution of the average longitudinal velocity at water depth is solved according to K1 and K2 to obtain the lateral distribution of the cross-sectional velocity in the vegetation area and the non-vegetation area.

[0076] S11. Based on the obtained lateral distribution of flow velocity in each cross section, a Reynolds stress lateral distribution prediction model is constructed according to the SKM method to predict the Reynolds stress lateral distribution, including:

[0077] The lateral distribution of cross-sectional flow velocity in the vegetation area and the non-vegetation area is defined as U (y) , the Reynolds stress lateral distribution prediction model is constructed according to the SKM method. The SKM formula is:

[0078]

[0079] In the formula, ε yx (=λHU * ) is the lateral average water depth eddy viscosity coefficient, is the friction velocity, U d is the average velocity at water depth;

[0080] The Reynolds stress lateral distribution prediction model is derived from the above formula:

[0081]

[0082] Where 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.

[0083] In order to verify the effectiveness of the prediction method of the present invention, the longitudinal flow velocity and lateral distribution of Reynolds stress along the non-submerged vegetation group obtained by flume test were compared with the prediction method of the present invention.

[0084] Purpose of the test

[0085] The lateral distribution of the longitudinal flow velocity in multiple cross sections along the vegetation test flume was measured through a flume test, and the prediction results of the model introduced in the invention content were verified using the longitudinal flow velocity and lateral distribution of Reynolds stress measured in multiple cross sections along the flume.

[0086] Test equipment

[0087] The main equipment is shown in Table 1 below.

[0088] Table 1 Flume test equipment with non-submerged vegetation communities in the beach

[0089]

[0090] Test conditions

[0091] The test was conducted in a test flume 13 meters long, 1 meter wide, and 0.5 meters high. The distance from the entrance to 3 meters from the entrance is the water flow development area, and the 7 meters from 3 meters to 10 meters from the entrance is the test area. The front end of the vegetation community is arranged in the center of the test area (10 meters from the entrance). The schematic diagram of the layout of the vegetation community flume is attached. Figure 2 As shown. Water surface gradient S = 44×10 -6 The average upstream velocity (U0) in the river channel was measured at 5 m in front of the vegetation community by ADV mounted on the flume. This location was chosen because the water flow deflection in front of the vegetation community only occurs within 50 cm in front of the vegetation, that is, L u <50cm. In all working conditions, the upstream flow is 65L / s, the water depth is H=18cm, and the average flow velocity in the upstream of the river is U0=18cm / s. The water flow in all working conditions is turbulent and slow.

[0092] In this embodiment, a rectangular model vegetation community is formed and placed in the center of the water tank. In working 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 inside the vegetation community. I , so the water flow can remain stable after fully developing inside the vegetation area. The parameters of working conditions 1-3 are shown in Table 2.

[0093] In working conditions 1-3, the lateral distribution of the longitudinal flow velocity in multiple cross sections was measured between the upstream of the vegetation area (x=0cm) and the downstream of the vegetation area (x=L). The values ​​of each cross section position and the values ​​of K1 and K2 in each cross section are shown in Table 3.

[0094] Rigid logs were inserted evenly into the perforated PVC board at the bottom of the tank to construct the model vegetation community. The Darcy drag coefficient generated by the PVC board was f = 0.025. The logs simulating non-submerged vegetation were 30 cm long, which was greater than the water depth of 18 cm. Therefore, the model vegetation communities of the components 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 a specific type of vegetation, but the diameter of the round wooden sticks d = 0.8 cm is the middle value of the diameter of common vegetation d = 0.1-1 cm in natural rivers, river beaches and wetlands. Based on this, the test results obtained are highly representative. The density of vegetation is n = 0.05 to 0.15 cm 2 The proportion of vegetation per unit area The vegetation drag coefficient is 0.025 to 0.076, which is consistent with the range of cattail φ (= 0.001-0.08) commonly found in natural rivers. d (≈1-1.2).

[0096] The coordinate system in the river channel is defined at the center of the front end of the vegetation community. The coordinate of the water flow direction is x, and x=0 represents the front end of the vegetation community; the direction perpendicular to the water flow is y, and y=0 is the center of the vegetation community; the direction perpendicular to the water surface is z, and z=0 is the riverbed position. The flow velocities in the three directions are U(t), V(t) and W(t), respectively, and are measured using Doppler velocity measurement (ADV). The flume is equipped with a bracket for mounting ADV, which can be moved arbitrarily in the x, y, and z directions. The instantaneous flow velocity data in the three directions are processed using the data processing software provided by ADV, and the time-averaged flow velocities (U, V, W) in the three directions (x, y, z) are obtained respectively. The flow velocity measurements are all at 1 / 2 the water depth (z=9 cm), because the average flow velocity at the water depth U d The difference between the velocity at 1 / 2 water depth and the velocity at 1 / 2 water depth is less than 6%. Therefore, it can be considered that the measured velocity at 1 / 2 water depth is equal to the average velocity at water depth U d .

[0097] Table 2 Parameters of various working conditions in flume test with vegetation community

[0098]

[0099] In the table: H is the water depth, U0 is the average flow velocity of the upstream river; b is the 1 / 2 width of the vegetation community; L is the length of the vegetation community; a is the water blocking area of ​​the vegetation per unit water body (a=nd, where n is the vegetation density and d is the vegetation diameter); C d ab is the vegetation coefficient; φ is the area ratio of vegetation per unit area; L I is the water flow deflection distance within the vegetation community.

[0100] Table 3 Cross-sectional velocity distribution test locations and K1 and K2 values ​​for each operating condition

[0101]

[0102] In the table: x is the cross-sectional position; K1 and K2 are the defined secondary flow parameters.

[0103] Test results analysis

[0104] The prediction model of the present invention is used to predict the longitudinal flow velocity and the transverse distribution of Reynolds stress along the three working conditions in the embodiment. The model prediction values ​​are shown in the attached figure. Figure 3 and 4 The measured values ​​of the longitudinal velocity distribution in the flume test are shown in the attached figure. Figure 3 and 4 Shown in the middle circle. Figure 3 The figure is a comparison diagram of the model prediction value and the transverse distribution value of the longitudinal flow velocity measured in the flume test in different cross sections under different working conditions of the embodiment of the present invention, (a) working condition 1, C d ab=1.32; (b) Condition 2, C d ab=1.98; (c) Condition 3, C d ab = 3.96. The gray vertical line indicates the boundary of the vegetation community, the black curve is the model prediction value, the black circle is the experimental measurement value, and x = 50 cm, x = 100 cm and x = 150 cm in the figure respectively represent the cross-sectional positions of the velocity lateral distribution test selected under various working conditions. Figure 4 The embodiment of the present invention is a comparison of the model prediction value and the measured lateral distribution value of turbulent kinetic energy in different cross sections under different working conditions. (a) Working condition 1, C d ab=1.32; (b) Condition 2, C d ab=1.98; (c) Condition 3, C d ab = 3.96. The gray vertical line indicates the boundary of the vegetation community, the black curve is the model prediction value, the black circle is the test measurement value, and x = 50 cm, x = 100 cm and x = 150 cm in the figure respectively indicate the selected cross-sectional positions of the Reynolds stress lateral distribution test under various working conditions.

[0105] When carrying out the calculation, 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 ​​in formulas (8) and (9). Figure 3 and 4 By comparing the measured values ​​with the model prediction values, the prediction model for the longitudinal flow velocity and the lateral distribution of Reynolds stress along the vegetated river channel proposed in the present invention can accurately predict the longitudinal flow velocity and the lateral distribution of Reynolds stress along the vegetated river channel in areas with or without vegetation under the influence of vegetation communities of different densities.

[0106] Table 4 Summary of calculation parameters for each working condition

[0107]

[0108] In the table, g is the local gravity acceleration; H is the water depth; S is the water surface slope; a is the water blocking area of ​​vegetation per unit water body (a=nd, where n is the vegetation density and d is the vegetation diameter); C dis the vegetation drag coefficient; φ is the area ratio of vegetation per unit area; f is the Darcy drag coefficient; λ is the dimensionless eddy viscosity coefficient.

[0109] Table 5 Summary of the integral constants of A1, A2, A3 and A4 for each cross-sectional area in each operating condition

[0110]

[0111] In the table: x is the cross-sectional position; A1, A2, A3 and A4 are integration constants.

[0112] Therefore, the present invention adopts the above-mentioned method for predicting the lateral distribution of flow velocity and Reynolds stress in a vegetated river channel. Starting from the water flow momentum equation and the continuity equation, the control equation for the lateral distribution of flow velocity in a vegetated river channel is derived, and solved according to the boundary conditions. It not only realizes the prediction of the lateral distribution of flow velocity in each cross section, but also realizes the prediction of the lateral distribution of Reynolds stress, ensuring the correctness of the theory while having a high prediction accuracy.

[0113] Finally, it should be noted that the above embodiments are 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 embodiments, those skilled in the art should understand that they can still modify or replace the technical solution of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solution to deviate from the spirit and scope of the technical solution of the present invention.

Claims

1. A method for predicting the lateral distribution of flow velocity and Reynolds stress in a vegetated river channel, characterized in that the steps include: S1, determine the governing equation for the lateral distribution of the two-dimensional longitudinal velocity averaged at water depth; S2, taking the center of the upstream boundary of the non-submerged vegetation community as the origin, divide the river channel into vegetation area and non-vegetation area along the direction perpendicular to the water flow; S3, based on the control equation of the lateral distribution of the two-dimensional longitudinal velocity of the average water depth, determine the analytical model of the lateral distribution of the average longitudinal velocity of the water depth in the vegetation area and the non-vegetation area; S4, determine the boundary conditions in the analytical model of the lateral distribution of the average longitudinal velocity of the water depth; S5. Solve the analytical model of the lateral distribution of the average longitudinal velocity of the water depth based on the boundary conditions to obtain the lateral distribution of the cross-sectional velocity in the vegetation area and the non-vegetation area; S6. Based on the obtained lateral distribution of flow velocity in each cross section, a Reynolds stress lateral distribution prediction model is constructed according to the SKM method to predict the Reynolds stress lateral distribution.

2. The method for predicting flow velocity and lateral distribution of Reynolds stress in a vegetated river channel according to claim 1, characterized in that: The control equation for the lateral distribution of the two-dimensional longitudinal velocity in step S1 is: Where ρ is the density of water, H is the water depth, λ is the dimensionless eddy viscosity coefficient, f is the Darcy drag coefficient, and C d is the drag coefficient, a is the unit water resistance area, which is obtained from the vegetation density n and the diameter d of a single plant, U d is the average velocity of water depth, S is the water surface slope, and K represents the convection term parameter.

3. The method for predicting flow velocity and lateral distribution of Reynolds stress in a vegetated river channel according to claim 2, characterized in that: The analytical model of the lateral distribution of the average longitudinal velocity of water depth in the vegetation area and the non-vegetation area in step S3 is: Area without vegetation: Vegetation area: In the formula, A1, A2, A3 and A4 are integration constants, which are obtained from the average velocity of water depth in each area at the boundary conditions of two adjacent areas. K1 and K2 represent the dimensionless coefficients of convective exchange in the unvegetated area and the vegetated area, respectively.

4. The method for predicting flow velocity and lateral distribution of Reynolds stress in a vegetated river channel according to claim 3, characterized in that: In step S4, the boundary conditions are used to solve the integral constant, and the boundary conditions are: At the boundary y=b between the vegetated area and the non-vegetated area, the water flow velocity and water flow gradient are continuous; Continuous water flow rate: U bare =U veg ; Continuous water flow gradient: At the center line y=0 inside the vegetation area, Inside the exposed channel area, near the side wall at y = 0.95B, U bare =U d ; Where b is 1 / 2 the width of the vegetation community, and B is 1 / 2 the width of the river channel.

5. The method for predicting flow velocity and lateral distribution of Reynolds stress in a vegetated river channel according to claim 4, characterized in that: In step S5, solving the analytical model of the lateral distribution of the average longitudinal velocity of the water depth based on the boundary conditions includes: The values ​​of K1 and K2 are determined by trial and error, and the value of K1 is adjusted. When the calculated velocity of the lateral distribution analytical model of the average longitudinal velocity in the vegetation area is equal to the measured velocity U in the vegetation area, veg When the K1 value is equal to the K2 value, the K1 value is the final value; the K2 value is adjusted, when the calculated flow velocity of the lateral distribution analytical model of the average longitudinal flow velocity in the vegetation-free area is equal to the measured flow velocity U in the vegetation-free area bare When the values ​​of are equal, K2 is the final determined value. The analytical model of the lateral distribution of the average longitudinal velocity at water depth is solved according to K1 and K2 to obtain the lateral distribution of the cross-sectional velocity in the vegetation area and the non-vegetation area.

6. The method for predicting flow velocity and lateral distribution of Reynolds stress in a vegetated river channel according to claim 5, characterized in that: Step S6 constructs a Reynolds stress lateral distribution prediction model based on the obtained lateral distribution of flow velocity in each cross section according to the SKM method, and predicts the lateral distribution of Reynolds stress, including: The lateral distribution of cross-sectional flow velocity in the vegetation area and the non-vegetation area is defined as U (y) , the Reynolds stress lateral distribution prediction model is constructed according to the SKM method. The SKM formula is: In the formula, ε yx (=λHU * ) is the lateral average water depth eddy viscosity coefficient, is the friction velocity, U d is the average velocity at water depth; The Reynolds stress lateral distribution prediction model is derived from the above formula: Where 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.

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