Prediction method of lateral distribution of flow velocity in river channels with vegetated slopes

Abstract

The present invention belongs to the fields of hydraulics and river dynamics and discloses a method for predicting the lateral distribution of flow velocity in a river channel with a vegetated slope. Based on the vegetation zone of the river channel slope, which has a trapezoidal cross-section, the river channel with a vegetated slope is divided into a main channel zone and a vegetation zone. An analytical calculation model for the lateral distribution of flow velocity in the vegetation zone on the river bank slope is constructed. The model is subjected to a dimensionless tempering process and solved using the differential method to obtain the lateral distribution of flow velocity. The lateral distribution model of flow velocity in the vegetation zone constructed by the present invention can efficiently and accurately predict the cross-sectional flow velocity distribution in the main channel zone and the vegetation zone of a river channel with a vegetated slope, filling a research gap in this field.

Description

Technical Field

[0001] The present invention belongs to the fields of hydraulics and river dynamics, relates to flow velocity prediction in non-flooded vegetation areas, and in particular to a method for predicting the lateral distribution of flow velocity in a river channel with a vegetation slope. Background Art

[0002] In the natural environment, vegetation mostly grows near water sources. The banks near the water provide a favorable environment for vegetation growth. In the riverbank area with vegetation, after a long period of water erosion, a bank slope with a certain inclination angle is formed, referred to as a slope. These inclined slopes cause the water depth inside the vegetation to change continuously, which in turn causes more complex water flow adjustments (such as Figure 1 For example, the presence of vegetation will increase the resistance of the vegetation area, resulting in a decrease in the flow velocity inside the vegetation and an increase in the flow velocity outside the vegetation. The velocity difference between the inside and outside of the vegetation will produce a strong shear layer and vortex, accompanied by a large amount of mass and momentum exchange, which will affect the stability of the river bank.

[0003] In order to assess the stability of the riverbank, some scholars have proposed computational models for the lateral distribution of flow velocity in vegetated rivers by combining physical model experiments with theoretical derivations, such as Huai W, Song S, Han J, Zeng Y (2016) Prediction of velocity distribution in straight open-channel flow with partialvegetation by singular perturbation method. Appl Math Mech 37(10): 1315–1324; and Yan, C., Shan, Y., Liu, C., Liu, X., 2022. Analytical model for predicting the lateral profiles of velocities through a partially vegetated channel. Journal of Hydrology 612, 128-137. These models have been shown to have good accuracy in rectangular vegetated channels and composite riverbanks with vegetated banks. However, in natural river channels, it is difficult to obtain flow velocity changes through measurements, and previous computational models cannot describe the impact of such water depth changes.

[0004] Therefore, how to provide an accurate velocity calculation model to predict the lateral velocity distribution in slope vegetation river channels is a technical problem that needs to be solved urgently. Summary of the Invention

[0005] The object of the present invention is to solve the above problems and provide a method for predicting the lateral distribution of flow velocity in a river channel with a vegetated slope. Based on the water momentum equation, considering the blocking effect caused by vegetation, the porosity α (=1–φ) is introduced into the momentum equation. At the same time, considering that in the vegetated area (y≥B-D), affected by the slope, the water depth changes, so the water depth as a function of the slope coefficient s is introduced into the momentum equation, thereby efficiently and accurately predicting the cross-sectional velocity distribution in the main channel area and the vegetated area of the river channel with a vegetated slope, filling the research gap in this field.

[0006] The present invention is applicable to the river channel conditions with a trapezoidal cross-section. In the present invention, a coordinate system is established with the x-axis along the water flow direction, the y-axis horizontally, and the z-axis vertically. Among them, x = 0 is set at the front end of the vegetation, y = 0 is set on the left bank far from the vegetated area, and z = 0 is set at the river bed. The vegetated river channel is divided into a main channel area and a vegetated area. In the main channel area (y < B-D), the water depth is constant. In the vegetated area (y≥B-D), affected by the slope, the water depth is in a changing state. B is the river channel width, and D is the horizontal width of the vegetation.

[0007] Based on the water momentum equation, the present invention first establishes the lateral average velocity models for the main channel area and the vegetated area, and then uses the trial method to obtain the vertical average secondary flow term coefficient in the lateral average velocity models for the main channel area and the vegetated area. Once the vertical average secondary flow term coefficient is determined, the model can be used to predict the lateral distribution of flow velocity in the main channel area and the vegetated area of the river channel with a vegetated slope.

[0008] Based on the above analysis, the present invention provides a method for predicting the lateral distribution of flow velocity in a river channel with a vegetated slope, including the following steps:

[0009] S1 Taking the river channel cross-section as trapezoidal, the river channel with a vegetated slope is divided into a main channel area and a vegetated area: Main channel area: 0≤y < B-D; Vegetated area: B-D≤y≤B, where B is the river channel width, D is the width of the vegetation community, and y is the direction perpendicular to the water flow along the river channel horizontal plane.

[0010] S2 Determining the analytical model for the lateral distribution of flow velocity in the river channel with a vegetated slope:

[0011]

[0012] In the formula, α is the porosity (α = 1-φ, where φ is the vegetation density); a is the water-blocking area per unit water body of the vegetation community; g is the acceleration due to gravity; ξ is the water depth, obtained from the formula ; S is the water surface slope; f is the bed surface resistance coefficient; s is the slope coefficient; C d is the vegetation drag force coefficient; λ is the dimensionless eddy viscosity coefficient; is the secondary flow term coefficient; U d is the river channel lateral flow velocity;

[0013] S3 command By non-dimensionalizing formula (1), we can obtain:

[0014]

[0015] Where,

[0016]

[0017] Where U ∞ It is the average flow velocity in the main trough area that is not affected by vegetation, that is, the area where the water flow velocity does not change in the horizontal direction (y direction).

[0018] S4 solves the analytical model of the lateral distribution of flow velocity in the river with the vegetated slope by a difference method to obtain the lateral distribution of the flow velocity in the river; specifically, the steps include:

[0019] S41 divides the effective interval [0,1] of η into several equal parts. Discretization is performed to obtain Discretization representation of ;

[0020] S42 will The discretized representation of is brought into the dimensionless velocity lateral distribution analytical model, and the System of multivariate linear equations;

[0021] S43 determines the lateral boundary conditions of the river channel;

[0022] S44 determines the secondary flow term coefficient;

[0023] S45 is based on the river channel lateral boundary conditions and secondary flow coefficients. The multivariate linear equations are solved to obtain the lateral distribution of river flow velocity.

[0024] In the present invention, in a straight non-submerged vegetation river channel, when the water flow is uniform and stable, according to the momentum equation in the transverse direction (y direction) of the river channel, we have:

[0025]

[0026] Where ρ is the water density; g is the acceleration due to gravity; H is the water depth; S is the water surface slope; f is the bed resistance coefficient; s is the slope coefficient; C d is the vegetation drag coefficient; a is the unit water resistance area of ​​the vegetation community; λ is the dimensionless eddy viscosity coefficient, U d is the average cross-sectional velocity; the secondary flow term is ( is the vertical average secondary flow coefficient).

[0027] Taking into account the blocking effect caused by vegetation, the porosity α (= 1–φ) is introduced into equation (1′), and the result is:

[0028]

[0029] Affected by the slope, the water depth is a function of the slope coefficient s, and ξ is used to represent the changing water depth:

[0030]

[0031] Substituting ξ for H into Equation (2') yields an analytical model for the lateral velocity distribution of a sloping vegetated river channel, namely, Equation (1). When the slope coefficient s = ∞, ξ = H, the water depth remains unchanged, and the river channel assumes a rectangular shape. Therefore, the velocity calculation model proposed in this paper can be used to predict the velocity distribution of a rectangular vegetated river channel.

[0032] For the main channel area away from vegetation, the water depth is constant, the lateral shear stress and the secondary flow term are zero, and Equation (1) can be simplified to:

[0033]

[0034] Where U ∞ It is the average flow velocity in the main trough area that is not affected by vegetation.

[0035] In the above step S3, in order to understand the analytical model more intuitively, equation (1) is dimensionless.

[0036] In the above step S4, the velocity lateral distribution analytical model after the dimensionless processing is about It is difficult to obtain the exact solution of the second-order variable coefficient non-homogeneous linear partial differential equation by solving the differential equation, and it is also difficult to determine whether the prediction model proposed by the present invention is accurate. Therefore, after all the parameters in formula (2) are determined, the present invention adopts the difference method to solve the model. The specific method is: discretize the control equation represented by formula (2) in the valid interval (η∈[0,1]), and discretize the differential equation into a difference equation by using the difference quotient instead of the derivative at each node; obtain the difference equation group under the boundary value condition, so as to solve the numerical approximate solution of the control equation at the node, as shown in the above steps S41-S45.

[0037] In the above step S41, the valid interval [0,1] of η is divided into n equal parts, the corresponding step length h=1 / n, and the node η i =ih(i=0,1,...,n), where i=0 and n(eta0 and eta n ) represent the lateral boundaries of the river channel; according to the concept of numerical differentiation, we have:

[0038]

[0039] Ignore the truncation error term O(h 2 ),by Approximate substitution After discretization, we get:

[0040]

[0041] In the above step S42, at each node, the central difference quotient is used Replace WeChat business Substituting formula (5) into formula (2), we can obtain:

[0042]

[0043] Where p i ,q i , r i Indicates that at node η i Based on the lateral boundary conditions of the river channel, the boundary values ​​in the above formula are eliminated by iteration. and You can get information about A system of linear equations with n-1 variables:

[0044]

[0045] In the above step S43, the boundary conditions need to be known when using the difference method to solve the multivariate linear equation system. The present invention takes the left side of the main trough area and the right side of the vegetation area as the velocity area boundary, and gives the boundary conditions, that is, the boundary conditions when η=0. and the boundary when η=1

[0046] (1) For y = 0, η = 0, Where ζ is the proportionality coefficient (which can be estimated from experimental data), R bare is the hydraulic radius of the main trough area; It is expressed as follows:

[0047]

[0048] (2) For y = B, η = 1, flow rate boundary It is expressed as follows:

[0049]

[0050] Where U (wall) Indicates the side wall of the river.

[0051] In the above step S44, the secondary flow coefficient It is the key to determine whether the calculation model can accurately predict the lateral distribution law of the vertical average flow velocity, reflecting the momentum exchange between the main channel area and the vegetation area. Its value is related to the intensity, quantity, rotation direction and coverage of the secondary flow. The present invention has an analytical model for the lateral distribution of flow velocity in the river channel with vegetation slope, which involves two secondary flow coefficients, corresponding to the vegetation area and the horizontal distribution of the secondary flow. and main tank area Different regions The value mainly affects its own area and has only a small impact on the adjacent area near the boundary. Here, it is assumed that the mutual influence between the two is ignored, and the trial algorithm is used to obtain the secondary flow term coefficient of the main trough area for different areas. and vegetation areas

[0052] First, a trial algorithm is used to assign the secondary flow coefficient of the main tank area By adjusting the secondary flow coefficient of the vegetation area The lateral velocity U in the vegetation area obtained according to formula (1) is d The calculated value and the measured value reach the minimum error, that is, the optimal secondary flow coefficient is obtained

[0053] Then, the secondary flow coefficient of the vegetation area is assigned by trial and error. By adjusting the secondary flow coefficient of the main tank area The lateral flow velocity U in the main trough area obtained according to formula (1) is d The calculated value and the measured value reach the minimum error, that is, the optimal secondary flow coefficient is obtained

[0054] The above calculation steps are completed by computer, and the computer is used to calculate until the secondary flow item values ​​of the main river channel and the vegetation area with the minimum root mean square error are obtained.

[0055] The error between the calculated value and the measured value is expressed as the root mean square error (RMSD):

[0056]

[0057] Where subscript j = "bare" or "veg" or "total" represents the main trough area or vegetation area or the entire interval, N is the number of samples in different intervals, X m and X p Represent the measured and calculated values ​​respectively. The smaller the RMSD value, the higher the model accuracy.

[0058] In the above step S45, the lateral boundary conditions of the river channel and the secondary flow coefficients of the main channel area and the vegetation area are respectively substituted into the multivariate linear equation group (7), and then the multivariate linear equation group is solved to obtain the numerical approximate solution of the control equation at each node, and the solution is used as the lateral flow velocity at each node, thereby obtaining a lateral distribution prediction model of the flow velocity in the main channel area and the vegetation area of ​​the river channel with vegetation slope.

[0059] When the vegetation bank has a slope, it is currently impossible to obtain a lateral distribution prediction model of the flow velocity in the river with a vegetation slope. The present invention has the following beneficial effects:

[0060] 1. The present invention provides a model for calculating the transverse velocity of uniform flow in an open channel in a sloping vegetated river channel. The model uses a difference method to obtain the numerical approximate solution of the momentum equation at each node.

[0061] 2. The model of the present invention was used to predict the embodiment. The results showed that the model can accurately predict the changes in lateral flow velocity caused by changes in water depth in vegetation areas, and is also applicable to straight vegetated river channels, including rectangular and complex shapes.

[0062] 3. Parameters that affect model prediction, including drag coefficient C d , dimensionless eddy viscosity coefficient λ and secondary flow parameters Sensitivity analysis showed that C d The impact on model prediction is not significant, so C d =1 assumption; vegetation area λ veg The difference mainly affects the area near the boundary between vegetation and non-vegetation. If there is no actual measurement, the standard of open channel flow 0.067 can be used as a reference. The secondary flow parameter The impact on the main channel area is more obvious than that on the vegetation area. At the same time, in the slope vegetation river channel, the main channel area and the vegetation area have the same secondary flow direction. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] Figure 1 This is a schematic diagram of the arrangement of vegetated slopes in the river channel;

[0064] Figure 2 Schematic diagram of the arrangement of the flume experiment in the embodiment, wherein (a) is a schematic diagram of the flume with a vegetated slope; (b) is a real picture of the flume;

[0065] Figure 3 is the transverse velocity distribution diagram at different longitudinal distances in working condition B2;

[0066] Figure 4 The comparison diagram of the horizontal flow velocity at half water depth and full water depth in the stable area of ​​working condition B2;

[0067] Figure 5 The different The lateral velocity distribution diagram corresponding to the value, where (a) is different The lateral velocity distribution diagram corresponding to the value; (b) is the different The lateral velocity distribution diagram corresponding to the value;

[0068] Figure 6 The figures are comparison diagrams of the lateral distribution of the measured and calculated flow velocities under the experimental conditions of the present invention, wherein (a) is a comparison diagram of the lateral distribution of the measured and calculated flow velocities in working condition A1; (b) is a comparison diagram of the lateral distribution of the measured and calculated flow velocities in working condition A2; (c) is a comparison diagram of the lateral distribution of the measured and calculated flow velocities in working condition B1; (d) is a comparison diagram of the lateral distribution of the measured and calculated flow velocities in working condition B2; (e) is a comparison diagram of the lateral distribution of the measured and calculated flow velocities in working condition B3; (f) is a comparison diagram of the lateral distribution of the measured and calculated flow velocities in working condition B4; (g) is a comparison diagram of the lateral distribution of the measured and calculated flow velocities in working condition C1; (h) is a comparison diagram of the lateral distribution of the measured and calculated flow velocities in working condition C2; and (i) is a comparison diagram of the lateral distribution of the measured and calculated flow velocities in working condition C3. DETAILED DESCRIPTION

[0069] The following is a clear and complete description of the technical solutions of the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments derived by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts belong to the present invention.

[0070] Example

[0071] This example compares the lateral distribution of flow velocity in a river channel with a vegetated slope obtained through flume tests with the lateral distribution of flow velocity in the main channel area and vegetated area of ​​a river channel with a vegetated slope obtained by the model of the present invention. The above content is described in detail below.

[0072] ①Purpose of the test

[0073] The lateral distribution of flow velocity in the main channel area and vegetation area of ​​the river with vegetation slope is measured through flume tests to form the flow field distribution of the river with vegetation slope. The measured flow field is used to verify the prediction results of the calculation model proposed in this invention.

[0074] ②Test equipment

[0075] The main equipment is shown in Table 1 below.

[0076] Table 1 Flume test apparatus with vegetation slope

[0077]

[0078]

[0079] ③Test conditions

[0080] like Figure 2 As shown in (a), the coordinate system in the flume is defined at the left bank of the riverbed, away from the vegetation. The coordinate in the direction of water flow (longitudinal) is x, with x = 0 representing the front edge of the vegetation. The direction perpendicular to the water flow (transverse) is y, with y = 0 representing the left bank away from the vegetation. The direction perpendicular to the water surface (vertical) is z, with z = 0 representing the riverbed. The flow velocities in the three directions (x, y, and z), u, v, and w, are measured using a three-dimensional acoustic Doppler velocimeter (ADV). A slide rail is installed at the top of the flume's sidewall, and the ADV measurement bracket is mounted. A regulating valve and stilling basin are installed at the head of the flume to adjust the flow rate (Q). The weir flow type is a rectangular thin-walled weir. After the water flows through the weir, it passes through a screen to reduce surface oscillations before entering the flume, producing a uniform horizontal flow. A flat valve is installed at the tail of the flume. Adjusting the valve opening controls the water level (H) to ensure a constant water depth and uniform flow in the test section.

[0081] The specific arrangement of the water tank with vegetation community is as follows Figure 2 As shown in (b), the test was conducted in an experimental water tank 17 meters long, 1 meter wide, and 0.75 meters high. The slope was a single-sided slope formed by smooth cement plastering, and the vegetation covered the entire slope. Two different slope conditions were set, one with no slope and one with a certain angle. In the case of no slope (working condition A, s = ∞), the vegetation density n = 257m -2 The widths of the two vegetation types are D = 35 and 50 cm. The cross-section of the water flume presents a rectangular shape during operation. The model vegetation is fixed on a PVC board with evenly distributed holes and placed inside the flume. In the case of a slope with a certain angle, the vertical height of the slope is equal to the water depth H. There are two slope coefficients, s = 1.75 and s = 2.5, as shown in the following example. Figure 2 As shown in (a), the water-passing section presents a right-angled trapezoidal shape during the test operation. In working conditions B and C, three groups of vegetation densities n = 0, 257 and 502m -2 , corresponding to vegetation volume fractions φ = 0, 0.013, and 0.025, and the average upstream flow velocity U0 = 18 cm / s. In all cases, the water depth H = 20 cm. In all cases, the river channel Reynolds number Re (= U0R / ν) > 23000, where R is the hydraulic radius of the section, ν (= 0.01 cm 2 / s) is the kinematic viscosity; Froude number Where g is the acceleration due to gravity and H is the water depth. The flow conditions for all operating conditions were fully developed turbulent and subcritical. Specific test conditions and parameters are shown in Table 2.

[0082] In this embodiment, the model vegetation length L = 35 cm, which is greater than the design water depth H = 20 cm, suggesting non-submerged vegetation; the experiment was arranged to be greater than the internal water flow adjustment length L of the rigid vegetation community. I The vegetation length is set to ensure the water flow is stable. Specifically, for the test conditions A1 and A2 with no slope on the beach, the vegetation length is L = 8.0m > L I (For example, in working condition A1, L I =5.9m, L in working condition A2 I =6.6m); For the slope test condition, without knowing the influence of the slope on the water flow adjustment length, a value much larger than L was set. I The vegetation length L = 10.0m. The results show that this length can ensure that the water flow can be stable under different working conditions. Taking working condition B2 as an example, the average flow velocity U of the water depth in multiple cross sections at different positions in the longitudinal direction of the vegetation area (x = 1, 3, 5, 6, 7m) is d The lateral distribution of the flow velocity at different longitudinal distances is measured accordingly. Figure 3 As shown, it can be seen that the water flow reaches stability after 5m.

[0083] The slope vegetation consists of slender stems that resemble the reeds, tree bases, and mangrove roots found in natural river channels. These stems are fixed to a cement-plastered slope with pre-placed holes. The stems are 35 cm long and 8 mm in diameter, which corresponds to the typical diameter range of 0.1-1 cm for individual plants found in natural rivers and floodplain wetlands.

[0084] In order to accurately describe the lateral variation of flow velocity, the flow velocity measurement was selected at the full water depth (z = 0.2m). This is because the flow velocity at the half water depth (z = 0.1m) cannot accurately describe the vertical average flow velocity, especially at the junction of the main channel area and the vegetation area, where the maximum error reaches 11%. Figure 4 Figure 2 shows a comparison of the horizontal flow velocities at half water depth and full water depth under operating condition B2 within the stable region. The water velocity is measured using a velocimeter, and then processed using data processing software to obtain the time-averaged flow velocities u(x), u(y), and u(z) in the three directions.

[0085] The velocity collection method is as follows: In fully developed areas, the velocity is measured by combining a Vectrino profiler and an LGY-Ⅱ intelligent velocity meter. The Vectrino profiler cannot measure when the water depth is less than 5 cm, so the LGY-Ⅱ intelligent velocity meter is required for supplementary measurement. The sampling frequency of the Vectrino profiler is set to 50 Hz and the sampling time is 3 min. The raw data collected are filtered out according to the method of Goring DG, Nikora VI. Despiking acoustic Doppler velocity meter data [J]. Journal of Hydraulic Engineering, 2002, 128 (1): 117-126. The instantaneous velocity data with a correlation of less than 70% and a signal-to-noise ratio of less than 15 dB are filtered out, and the remaining data are processed by MATLAB program to obtain the time-averaged velocity (u, v, w) in the three directions. The LGY-Ⅱ intelligent velocity meter is set to a sampling time of 10 s, and three consecutive measurements are taken and averaged to obtain the time-averaged velocity u (x) in the downstream direction.

[0086] Specifically, in the non-vegetated area, a measuring line is set every 5 cm, and in the vegetated area, the center between two adjacent vegetation rods is measured to reduce the impact of water flow anisotropy on flow velocity measurement in the spatial distribution of the vegetation area. Figure 2 As shown in (a), the area formed by two adjacent vegetation rods is defined as the characteristic area, and three measuring lines, P1-P3, are set horizontally at the center position, corresponding to 0, 1 / 2d s and d s Position, where d s is the lateral spacing between adjacent vegetation poles, and the average flow velocity is taken as the flow velocity at the center of the characteristic area. The specific survey line positions are as follows: when the vegetation density n = 0, the survey line is located at y = 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95 cm; when n ≠ 0 and D = 35 cm, the survey line is located at y = 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 69, 73, 77, 80, 85, 88, 92 cm; when n ≠ 0 and D = 50 cm, the survey line is located at y = 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 54, 58, 62, 66, 70, 74, 78, 82, 85 cm (some areas cannot be measured due to shallow water depth).

[0087] The test parameters and vegetation parameters of each working condition are summarized in Table 2.

[0088] Table 2 Test conditions and parameters for slope vegetation river channel *

[0089]

[0090] *In the table, s is the slope coefficient; U0 is the average velocity of the upstream incoming flow; U ∞ The average velocity of the main channel area not affected by vegetation (acquired by measuring the flow velocity distribution along the y-direction, and the stable velocity value where there is no (obvious) lateral change in the flow velocity is considered as U ∞ ); H is the water depth; D is the horizontal width of the vegetation; n is the vegetation group density; a (= nd) is the equivalent water-blocking area per unit water body of the vegetation community; φ (= πnd 2 / 4) is the vegetation volume fraction per unit area.

[0091] ④ Analysis of test results

[0092] The lateral distribution of the flow velocity of each measured cross-section in the main channel area and the vegetation area under nine working conditions A1 to C3 is obtained through experimental measurement, as Figure 6 shown. The circles represent the measured values (here, for the convenience of observation, U d / U ∞ is used as the ordinate).

[0093] Next, according to the prediction method of the vegetated slope provided by the present invention, the lateral distribution of the flow velocity in the river channel main channel area and the slope vegetation area is given based on the above working conditions, specifically including the following steps:

[0094] S1 Assuming that the cross-section of the river channel is trapezoidal, the river channel with a vegetated slope is divided into a main channel area and a vegetation area: Main channel area: 0 ≤ y < B - D; Vegetation area: B - D ≤ y ≤ B, where B is the river channel width and D is the width of the vegetation community; y is the direction perpendicular to the flow along the horizontal plane of the river channel.

[0095] S2 Determine the analytical model of the lateral distribution of the flow velocity of the river channel with a vegetated slope, specifically as shown in Equation (1).

[0096] It should be noted that: when the slope coefficient s = ∞, ξ = H, the water depth remains unchanged, and the river channel presents a rectangular shape, corresponding to working conditions A1 and A2 in this embodiment. Therefore, the flow velocity calculation model proposed by the present invention can be used to predict the flow velocity distribution of a rectangular vegetated river channel.

[0097] In addition, for the main channel area far from the vegetation, the water depth is constant, the lateral shear stress and the secondary flow term are zero, and Equation (1) can be simplified as:

[0098]

[0099] Therefore, in a river channel where it is inconvenient to measure the flow velocity, the average flow velocity of the main channel area not affected by vegetation can also be calculated through the above formula.

[0100] S3 Let Formula (1) is dimensionlessly processed to obtain the analytical model of the lateral distribution of velocity after dimensionless processing, as shown in Formula (2).

[0101] S4 solves the analytical model of the lateral distribution of flow velocity in the river with the vegetated slope by a difference method to obtain the lateral distribution of the flow velocity in the river; specifically, the steps include:

[0102] S41 divides the effective interval [0,1] of η into several equal parts. Discretization is performed to obtain Discrete representation of .

[0103] In this step, the effective interval [0,1] of η is divided into n equal parts, the corresponding step size h = 1 / n, and the node η i =ih(i=0,1,…,n), where i=0 and n(eta0 and eta n ) represent the lateral boundaries of the river channel respectively; according to the concept of numerical differentiation, according to the above formulas (4) and (5), we can get The discretization representation of

[0104] S42 will The discretized representation of is brought into the dimensionless velocity lateral distribution analytical model, and the A system of multivariate linear equations.

[0105] In this step, at each node, the central difference quotient is used Replace WeChat business Substituting Equation (5) into Equation (2), we can obtain the analytical model of the lateral distribution of velocity with discrete processing, as shown in Equation (6). Based on the lateral boundary conditions of the river channel, the boundary values ​​in the above equation are eliminated by iteration. and You can get information about The system of multivariate linear equations with n-1 variables is shown in formula (7).

[0106] In order to predict the depth-average velocity U d The horizontal distribution of and river boundary conditions.

[0107] h, f, λ, C d It can be determined by conventional methods disclosed in the art. First, the choice of step size h determines the calculation accuracy. The smaller h is, the finer the effective interval division is, the larger the calculation amount is, and the higher the model accuracy is. According to the experimental conditions of this chapter, the step size h = 0.001 is selected for differential calculation. The bed resistance coefficient f is divided into the main groove area (f bare ) and vegetation areas (f veg ), according to the formula The estimation is performed, where the subscript j = "bare" or "veg" represents the main trough area or the vegetation area. The dimensionless eddy viscosity coefficient λ (=κ / 6, ​​where κ is the Karman constant) is taken as a constant of 0.067. The vegetation drag coefficient C d Use the following formula to estimate: (where Re d (=(U d d) / ν) is the vegetation Reynolds number, U d is the local velocity inside the vegetation, d is the diameter of a single plant, ν(=0.01cm 2 / s 2 ) is the viscosity coefficient); the resistance coefficient varies within the range of C d =1.0-1.4; In this embodiment, the vegetation drag coefficient is selected as C d =1.

[0108] Next, the lateral boundary conditions of the river channel and the secondary flow term coefficient are determined through steps S43 and S44.

[0109] S43 determines the lateral boundary conditions of the river channel.

[0110] The left side of the main trough area and the right side of the vegetation area are used as the velocity region boundaries. The boundary conditions are given by the above equations (8) and (9), that is, the boundary conditions when η = 0 are: and the boundary when η=1

[0111] S44 determines the secondary flow term coefficient.

[0112] The analytical model of the lateral distribution of flow velocity in a river with a vegetated slope involves two secondary flow coefficients, corresponding to the vegetation area and the and main tank area Different regions The value mainly affects its own area and has only a small impact on the adjacent area near the boundary. Here, it is assumed that the mutual influence between the two is ignored, and the trial algorithm is used to obtain the secondary flow term coefficient of the main trough area for different areas. and the secondary flow coefficient of the vegetation area

[0113] For example, first give 0.04 and 0.06, and solve equation (1) to obtain the corresponding lateral flow velocities U in the vegetation area. d The calculated value is compared with the U measured by the tachometer. d Compare the two values ​​and take the one with the smallest error. value.

[0114] Similarly, give -0.001 and -0.003, solve equation (1) and obtain the corresponding main trough area lateral flow velocity U d The calculated value is compared with the U measured by the tachometer. d Compare the two values ​​and take the one with the smallest error. value.

[0115] The error between the calculated value and the measured value is expressed as the root mean square error RMSD:

[0116]

[0117] Where subscript j = "bare" or "veg" or "total" represents the main trough area or vegetation area or the entire interval, N is the number of samples in different intervals, X m and X p Represent the measured and calculated values, respectively. The smaller the RMSD value, the higher the model accuracy.

[0118] different The lateral velocity distribution diagram corresponding to the value is shown in Figure 5 According to the error calculation, the secondary flow coefficient of the main tank area can be determined and the second-order coefficient of vegetation area

[0119] The secondary flow coefficient of the main tank area under the above working conditions obtained by the above trial calculation and the secondary flow coefficient of the vegetation area As shown in Table 3.

[0120] Table 3 Main tank area under different working conditions and vegetation areas

[0121]

[0122] S45 is based on the river channel lateral boundary conditions and secondary flow coefficients. The multivariate linear equations are solved to obtain the lateral distribution of river flow velocity.

[0123] When the river boundary conditions and the parameters of the main channel area and vegetation area After determination, they are substituted into the multivariate linear equation group (7) respectively, and then the multivariate linear equation group is solved to obtain the numerical approximate solution of the control equation at each node, and it is used as the lateral flow velocity at each node, and then the lateral distribution prediction model of the flow velocity in the main channel area and vegetation area of ​​the river with vegetation slope is obtained. The prediction results are shown in Figure 6 shown.

[0124] from Figure 6Comparing the predicted values ​​with the measured values, the prediction method proposed in the present invention can accurately predict the lateral distribution of average water depth and flow velocity in vegetation areas and non-vegetation areas along the river channel with different densities of vegetation communities, regardless of whether the vegetation bank has a slope.

[0125] It should be noted that previous studies have also proposed excellent calculation models for vegetated river channels, such as Huai W, Song S, Han J, Zeng Y (2016) Prediction of velocity distribution in straight open-channel flow with partial vegetation by singular perturbation method. Appl Math Mech 37(10):1315–1324. However, these models can only calculate the case where the bank vegetation has no slope (i.e., s = ∞, corresponding to the operating condition series A), and cannot describe the lateral change of flow velocity under the influence of slope vegetation (i.e., s ≠ ∞, corresponding to the operating conditions series B and C). Therefore, the model of the present invention has a wider applicability.

[0126] Those skilled in the art will appreciate that the embodiments described herein are intended to help readers understand the principles of the present invention, and it should be understood that the scope of protection of the present invention is not limited to such specific descriptions and embodiments. Those skilled in the art can make various other specific variations and combinations based on the technical teachings disclosed in the present invention without departing from the essence of the present invention, and such variations and combinations are still within the scope of protection of the present invention.

Claims

1. A method for predicting the lateral distribution of flow velocity in a river with a vegetated slope, characterized in that: It includes the following steps: S1 With the cross-section of the river channel in a trapezoidal shape, the river channel with a vegetated slope is divided into a main channel area and a vegetated area. Main channel area: 0 ≤ y < B - D, Vegetated area: B - D ≤ y ≤ B, where B is the width of the river channel, D is the width of the vegetation community, and y is the direction perpendicular to the water flow along the horizontal plane of the river channel; S2 Determine the analytical model of the transverse distribution of the flow velocity in the river channel with a vegetated slope: In the formula, α is the porosity; a is the water-blocking area per unit water body of the vegetation community; g is the acceleration due to gravity; ξ is the water depth, according to the formula Get; S is the water surface slope; f is the bed resistance coefficient; s is the slope coefficient; C d is the vegetation drag coefficient; λ is the dimensionless eddy viscosity coefficient; is the secondary flow coefficient; U d is the lateral velocity of the river channel; S3 command By non-dimensionalizing formula (1), we can obtain: Where, Where U ∞ is the average flow velocity in the main trough area not affected by vegetation; S4 Solve the analytical model of the transverse distribution of the flow velocity in the river channel with a vegetated slope by the finite difference method to obtain the transverse distribution of the flow velocity; specifically, it includes the following sub-steps: S41 divides the effective interval [0,1] of η into several equal parts. Discretization is performed to obtain Discretization representation of ; S42 will The discretized representation of is brought into the dimensionless velocity lateral distribution analytical model, and the System of multivariate linear equations; S43 Determine the lateral boundary conditions of the river channel; S44 Determine the coefficient of the secondary flow term; S45 is based on the river channel lateral boundary conditions and secondary flow coefficients. The multivariate linear equations are solved to obtain the lateral distribution of river flow velocity.

2. The method for predicting the lateral distribution of flow velocity in a river with a vegetated slope according to claim 1, characterized in that: In step S41, the valid interval [0,1] of η is divided into n equal parts, the corresponding step length h = 1 / n, and the node η i =ih(i=0,1,...,n), where i=0 and n(eta0 and eta n ) represent the lateral boundaries of the river channel; according to the concept of numerical differentiation, we have: Ignore the truncation error term O(h 2 ),by Approximate substitution After discretization, we get:

3. The method for predicting the lateral distribution of flow velocity in a river with a vegetated slope according to claim 2, characterized in that: In step S42, at each node, the central difference quotient is used Replace WeChat business Substituting formula (5) into formula (2), we can obtain: Where p i ,q i , r i Indicates that at node η i The value at Based on the lateral boundary conditions of the river channel, the boundary values ​​in the above formula are eliminated by iteration. and Get about A system of linear equations with n-1 variables:

4. The method for predicting the lateral distribution of flow velocity in a river with a vegetated slope according to claim 1, characterized in that: In step S43, the lateral boundary of the river channel satisfies the following conditions: (1) For the boundary y = 0, η = 0, in is the proportionality coefficient, R bare is the hydraulic radius of the main trough area; It is expressed as follows: (2) For the boundary y = B, η = 1, the flow rate boundary It is expressed as follows: Where U (wall) Indicates the side wall of the river.

5. The method for predicting the lateral distribution of flow velocity in a river with a vegetated slope according to claim 1, characterized in that: In step S44, calculate the coefficient of the secondary flow direction by the trial method, including: First, a trial algorithm is used to assign the secondary flow coefficient of the main trough area By adjusting the secondary flow coefficient of the vegetation area The lateral velocity U in the vegetation area obtained according to formula (1) is d The calculated value and the measured value reach the minimum error, that is, the optimal secondary flow coefficient is obtained Then continue to use the trial algorithm to assign the secondary flow coefficient to the vegetation area By adjusting the secondary flow coefficient of the main tank area The lateral flow velocity U in the main trough area obtained according to formula (1) is d The calculated value and the measured value reach the minimum error, that is, the optimal secondary flow coefficient is obtained

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