Method for predicting sediment transport rate of river bed load sediment under effect of submerged vegetation

Abstract

The invention belongs to the field of hydraulics and river dynamics, and discloses a river bed load sediment transport rate prediction method under the effect of submerged vegetation, which comprises the following steps: firstly determining river near-bottom turbulent kinetic energy under the effect of submerged vegetation, carrying out dimensionless treatment on the river near-bottom turbulent kinetic energy, and then determining a river bed load sediment transport rate prediction model under the effect of submerged vegetation. The method can efficiently and accurately predict the sediment transport rate of the river bed load under the action of submerged vegetation, and provides a theoretical basis for further research on sediment movement characteristics and riverbed evolution rules involved in natural rivers and wetlands with submerged vegetation.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of hydraulics and river dynamics, and relates to submerged river channel near-bottom turbulent kinetic energy and bed load sediment transport rate prediction, in particular to a submerged vegetation action river channel bed load sediment transport rate prediction method. BACKGROUND

[0002] Vegetation is an important component of aquatic ecosystems such as rivers, wetlands, marshes and deltas, and plays a role in adjusting water flow structure, affecting geomorphic evolution, and maintaining ecological corridors. In areas covered by vegetation, sediment interception is a key means to ensure the stability of the ecological system, and many ecological restoration projects (such as river bank protection and wetland reconstruction) use vegetation to stabilize the riverbed, intercept sediment and reshape the landscape. Therefore, it is crucial to understand the sediment transport law in vegetation-covered areas for river physical habitat evolution.

[0003] Many previous methods have focused on sediment transport in emergent vegetation (vegetation occupies the entire water depth), but there is still a lack of analysis methods for sediment movement under submerged vegetation (vegetation height occupies part of the water depth). For river channels with submerged vegetation, the water flowing through the submerged vegetation zone (0 ≤ z ≤ h) is vertically deflected to the upper overflow zone (h < z ≤ H) without vegetation, resulting in a decrease in flow velocity in the submerged vegetation zone and an increase in flow velocity in the overflow zone above the vegetation. The flow velocity difference forms a shear action at the top of the vegetation (z = h), inducing the development of Kelvin-Helmholtz vortices (KH vortices), driving momentum exchange between the vegetation zone and the overflow zone above it, directly changing the water flow turbulence intensity in the near-bottom region of the river channel, and significantly affecting the sediment transport law and riverbed erosion and deposition process. In view of this fact, it is particularly important to understand the influence of submerged vegetation on the water flow turbulence characteristics and sediment movement in the river channel.

[0004] In vegetation-covered areas, the key driving force of sediment transport has changed from the traditional "bed shear stress " of bare riverbed to "near-bottom turbulent kinetic energy k t(nb)However, there is currently no efficient and accurate method to calculate the near-bottom turbulent kinetic energy under the action of submerged vegetation, resulting in a lack of core basis for the quantitative prediction of bed load sediment transport rate. In addition, the bed load sediment transport in the submerged vegetation area is affected by many conditions such as the average flow velocity of the river, the vegetation density, and the vegetation submergence. Under natural conditions, the changes of upstream flow and water depth directly affect the measurement results of the bed load sediment transport rate, making the measurement results not representative. At the same time, the measurement of the bed load sediment transport rate requires a large amount of manpower, material resources and financial resources to carry out continuous sampling work in the submerged vegetation river. Under laboratory conditions, although constant and uniform flow conditions can be obtained, a large amount of funds and time is still needed for data measurement and analysis. Generally speaking, a 4-meter-long, 1-meter-wide submerged vegetation area is constructed in a 17-meter-long, 1-meter-wide test tank, and the related technical personnel need to repeatedly measure the bed load sediment transport rate every 2 hours to determine whether it reaches the sediment transport balance state. The establishment of the balance state requires at least 15 hours, and the longest can be up to 30 hours. If different flow velocities, vegetation densities and vegetation submergence are considered, detailed measurement of the bed load sediment transport rate under the action of submerged vegetation requires two months or even longer.

[0005] Therefore, there is an urgent need for a simple and practical method to analyze the characteristics of river sediment movement under the action of submerged vegetation, which will cover the prediction of near-bottom turbulent kinetic energy and bed load sediment transport rate in submerged vegetation rivers. SUMMARY

[0006] The purpose of the present application is to solve the above technical problems and provide a method for predicting the bed load sediment transport rate in a river under the action of submerged vegetation, which realizes the prediction of near-bottom turbulent kinetic energy and bed load sediment transport rate under the action of submerged vegetation.

[0007] The present application is applicable to river conditions with submerged vegetation and flow velocity greater than 0 cm / s. In the present application, the flow change is considered to be two-dimensional, that is, only the flow in the flow direction and the vertical (perpendicular to the water surface) direction is changing. In the present application, the coordinate system is established with the flow direction as the x-axis, the direction perpendicular to the flow as the y-axis, and the direction perpendicular to the water surface (vertical direction) as the z-axis, wherein x = 0 represents the front edge of the submerged vegetation area; y = 0 represents the center line of the river and the submerged vegetation area; and z = 0 represents the riverbed surface. The submerged vegetation river is divided into a vegetation area (0 ≤ z ≤ h) and a non-vegetation area (h < z ≤ H), h is the vegetation height, and H is the water depth of the river.

[0008] The present application analyzes the bed surface turbulent kinetic energy k t(b) , the vegetation turbulent kinetic energy k t(v) and the shear turbulent kinetic energy k t(s) to predict the near-bottom turbulent kinetic energy k t(nb)The contribution of submerged vegetation is taken into account to establish a prediction model of near-bottom turbulent kinetic energy under the action of submerged vegetation; and in combination with the near-bottom turbulent kinetic energy of the submerged vegetation river channel and the Meyer-Peter bed load transport formula, a prediction method of bed load sediment transport rate suitable for the submerged vegetation river channel is provided.

[0009] Based on the above analysis, the application provides a prediction method of bed load sediment transport rate of a river channel under the action of submerged vegetation, which comprises the following steps: S1 determining the near-bottom turbulent kinetic energy of the river channel under the action of submerged vegetation and performing dimensionless processing thereon; the step comprises the following sub-steps: S11 determining the average flow velocity U nb of the near-bottom region; S12 determining the bed surface turbulent kinetic energy k t(b) , the vegetation turbulent kinetic energy k t(v) ; S13 defining the sum of the bed surface turbulent kinetic energy k t(b) and the vegetation turbulent kinetic energy k t(v) as k t(bv) , and constructing the proportional relationship between the shear turbulent kinetic energy k t(s) and k t(bv) ; S14 superimposing the bed surface turbulent kinetic energy k t(b) , the vegetation turbulent kinetic energy k t(v) and the shear turbulent kinetic energy k t(s) to obtain the near-bottom turbulent kinetic energy k t(nb) of the river channel under the action of submerged vegetation; S15 performing dimensionless processing on the near-bottom turbulent kinetic energy of the river channel; S2 determining the bed load sediment transport rate of the river channel under the action of submerged vegetation according to the following formula: (1) ; In the formula, k is the dimensionless near-bottom turbulent kinetic energy of the river channel; is the dimensionless critical starting turbulent kinetic energy of the sediment.

[0010] In the above step S11, the average flow velocity U nb of the near-bottom region is determined according to the following steps based on the boundary condition that the flow velocity of the vertical section of the river channel is maximum at the top of the submerged vegetation (z = h):

[0011] S111 defining the submerged vegetation region as 0 ≤ z ≤ h, and constructing a calculation model of the vertical distribution of the flow velocity of the submerged vegetation region based on an exponential decay function in the fully developed region of the water flow: (2) ;

[0012] S112 taking the near-bottom region of the submerged vegetation as 0 ≤ z ≤ z nbFor the calculation domain, the water flow velocity U(z) in the region is integrated along the vertical direction, i.e., the average flow velocity U in the near-bottom region of the submerged vegetation is obtained nb : (3) ; In the formula, U(z) is the water flow velocity at the z position; U s is the internal flow velocity of the submerged vegetation driven only by the hydraulic slope; U h is the water flow velocity at the top of the submerged vegetation (z = h); k u is the attenuation coefficient; h is the vegetation height; is the vertical height of the near-bottom region of the submerged vegetation.

[0013] In this step, the fully developed region of the water flow refers to a stable flow velocity region in which the water flow velocity no longer changes along the path (x direction) after the water flow passes through the submerged vegetation and adjusts for a distance.

[0014] In the above step S111, the internal flow velocity U of the submerged vegetation can be calculated by the following formula: (4) ; (U h -U s ) can be calculated by the following formula: (5) ; (6) ; In the formula, g is the acceleration of gravity; S is the hydraulic slope (i.e., the water surface slope, which refers to the difference between the water depths at the front and rear ends of the river channel divided by the length of the river channel, and can be measured; the larger S is, the stronger the water dynamics of the river channel is); C d is the vegetation drag coefficient, and a is the vertical water-blocking area of the vegetation per unit river bed surface; is the shear flow velocity at the top of the submerged vegetation; and H is the water depth of the river channel.

[0015] In the above step S111, the attenuation coefficient k u takes different values in rigid vegetation and flexible vegetation (see Nepf, H. M. (2012). Flow and transport in regions with aquatic vegetation. Annual Review of Fluid Mechanics, 44(1), 123-142. https: / / doi.org / 10.1146 / annurev-fluid-120710-101048), so, in order to make the method for predicting the river bed load sediment transport rate under the action of submerged vegetation proposed in the present application applicable to both rigid vegetation and flexible vegetation, the attenuation coefficient k uDetermined according to the following method: When the submerged vegetation is rigid vegetation: (7); When the submerged vegetation is flexible vegetation: (8).

[0016] In the above step S12, the bed surface turbulent energy k t(b) is provided by the bed surface shear stress (τ , ρ is the water density), and the calculation formula is: (9); In the formula, (= 0.19, see Soulsby, R. (1981). Measurement of the Reynolds stress components close to a marine sand bank. Marine Geology, 42(1–4), 35–47. https: / / doi.org / 10.1016 / 0025-3227(81)90157-2) is a proportional parameter; is the bed surface friction coefficient of the riverbed.

[0017] In the above step S12, the vegetation turbulent energy k t(v) is the additional water flow turbulence generated by the vortex of the plant wake, and the calculation formula is: (10); In the formula, γ 2 is a vortex scale parameter; is a shape drag coefficient; d nb is the average diameter of the submerged vegetation near the bottom region; is the volume fraction of vegetation per unit area.

[0018] In the above step S13, k t(bv) The calculation formula is: (11);

[0019] It should be noted that formula (11) does not consider the contribution of shear turbulent energy k t(s) to the near-bottom turbulent energy k t(nb) , but it should be clear that the water flow turbulence generated in the shear layer at the top of the submerged vegetation (z = h) can be transmitted to the riverbed bed surface through the KH vortex structure. With the increase of the shear turbulence generation amount in the submerged vegetation area, the intensity of the water flow turbulence transmitted to the riverbed bed surface also increases. Therefore, in order to quantify the influence of shear turbulent energy k t(s) on the near-bottom turbulent energy k t(nb) , the present application preferably uses shear turbulent energy kt(s) with k t(bv) in a proportional relationship: (12) ; where δ s is a proportional coefficient.

[0020] In the above step S14, the near-bottom turbulent kinetic energy k t(nb) under the submerged vegetation effect of the river channel is calculated by the following formula: (13).

[0021] In the above step S2, the specific derivation process of formula (1) is as follows: (1) Based on the Meyer-Peter bed load transport formula: (14) ; where is the dimensionless bed load transport rate, where ρ s is the sediment density, w s is the sediment particle settling velocity (which can be measured by the settling tube method), d s is the sediment particle size; α0(= 12.0 ± 0.5, see Deal, E., Venditti, J. G., Benavides, S. J., Bradley, R., Zhang, Q., Kamrin, K., & Perron, J. T. (2023). Grain shape effects in bed load sediment transport. Nature, 613(7943), 298–302. https: / / doi.org / 10.1038 / s41586‐022‐05564‐6) is an empirical coefficient; is the dimensionless bed shear stress; is the dimensionless critical bed shear stress corresponding to the sediment incipient motion, determined by the dimensionless sediment particle size , where v(= 0.01 cm 2 / s) is the kinematic viscosity.

[0022] Here, when < 0.3, ; when 0.3 ≤ ≤ 19, ; when 19 < ≤ 50, ; when > 50, .

[0023] (2) the relationship between the near-bottom turbulent kinetic energy and the bed shear stress is: , the formula (14) is converted into the sediment transport rate prediction formula with the near-bottom turbulent kinetic energy as the core parameter, that is, the river bed sediment transport rate prediction model under the action of submerged vegetation is obtained: (1); In the above formula, the dimensionless river near-bottom turbulent kinetic energy and the dimensionless critical starting turbulent kinetic energy of the sediment are respectively:

[0024] The dimensionless river near-bottom turbulent kinetic energy is: (15);

[0025] The dimensionless critical starting turbulent kinetic energy of the sediment is: (16); In the formula, ρ s is the density of the sediment, ρ is the density of the water body, g is the acceleration of gravity, d s is the particle size of the sediment; is the dimensionless critical bed shear stress corresponding to the starting of the sediment, is a proportional parameter.

[0026] At present, the method for predicting the sediment transport rate of the bed load is mostly an empirical formula, contains multiple fitting parameters, even if the near-bottom turbulent kinetic energy is used to analyze the sediment transport rate of the bed load, the influence of k t(s) is not considered, resulting in significant prediction deviation, the river bed sediment transport rate prediction method under the action of submerged vegetation provided by the application has the following benefits:

[0027] 1、The river bed sediment transport rate prediction method under the action of submerged vegetation provided by the application combines the river near-bottom turbulent kinetic energy and the Meyer-Peter bed load sediment transport formula, meets the physical law of sediment movement and transport, considers many variable factors such as flow velocity, vegetation density and vegetation submergence degree which directly affect the river bed sediment transport rate of the bed load, can directly predict the sediment transport rate of the bed load of the submerged vegetation river, and considers the contribution of k

[0028] 2. The method for predicting the bedload sediment transport rate under the action of submerged vegetation provided by this invention not only considers the influence of bed shear stress and vegetation wake vortices on the turbulent characteristics of river flow and sediment movement under the action of submerged vegetation, but also further incorporates the shear turbulent kinetic energy generated by the KH vortex structure into the analysis, quantifies its enhancement effect on near-bottom turbulent kinetic energy and its driving contribution to sediment movement, and proposes a near-bottom turbulent kinetic energy prediction model under the action of submerged vegetation, thereby making up for the limitations of traditional methods that only focus on a single or partial source of turbulence.

[0029] 3. The method for predicting bedload sediment transport rate in river channels under the influence of submerged vegetation provided by this invention does not require extensive measurements. It only requires basic parameters of the river channel and submerged vegetation (including riverbed friction coefficient, vertical water-blocking area of ​​vegetation per unit riverbed surface, vegetation height, river depth, etc.) to accurately predict the near-bottom turbulent kinetic energy and bedload transport rate of the river channel under the influence of submerged vegetation. This method can not only significantly reduce research costs, but also is applicable to natural river areas where detailed measurements are difficult to implement, and has wide applicability. Attached Figure Description

[0030] Figure 1 Schematic diagram of the experimental flume layout with submerged vegetation: (a) Schematic diagram of the water and sediment cycle experimental flume, where the yellow-green area is vegetation and the brown area represents the sand layer; (b) Submerged model vegetation covers the entire width of the experimental flume; (c) Comparison of natural submerged vegetation (left) and submerged model vegetation (right), with Vallisneria natans as an example; (d) Schematic diagram of sediment transport under the action of submerged vegetation, with the water flow direction from left to right; Figure 2 Near-bottom flow velocity in submerged vegetated river channels A comparison chart of measured and predicted values; Figure 3 Near-bottom turbulent kinetic energy in submerged vegetation channels A comparison chart of measured and predicted values; Figure 4 Dimensionless bedload transport rate in submerged vegetation river channels With dimensionless near-bottom turbulent kinetic energy The graph shows the relationship between the changes, with the solid line representing the changes calculated based on equation (1). Predicted value, indicated by the dashed line. as well as The resulting prediction uncertainty. Marked with a circle or triangle. Measured value. Detailed Implementation

[0031] The technical solutions of various embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0032] Example

[0033] This embodiment compares the near-bottom turbulent kinetic energy and bedload transport rate of submerged vegetated channels obtained through flume tests with the predicted values ​​of near-bottom turbulent kinetic energy and bedload transport rate of submerged vegetated channels obtained by the method of the present invention. The foregoing content will be described in detail below.

[0034] ① Experimental Objective

[0035] The near-bottom turbulent kinetic energy and bedload transport rate of submerged vegetated river channels were measured by flume tests to form the flow field distribution of submerged vegetated river channels. The prediction results of the prediction method proposed in this invention were verified by using the measured flow field.

[0036] ② Test equipment

[0037] The main equipment is shown in Table 1 below.

[0038] Table 1 shows the experimental setup for a water flume with vegetation communities.

[0039]

[0040] ③ Test conditions

[0041] like Figure 1 As shown in Figure a, the coordinate system in the flume defines the coordinates along the direction of water flow as x, the direction perpendicular to the water flow in the horizontal plane as y, and the direction perpendicular to the water surface (vertical) as z. x = 0 represents the foremost edge of the submerged vegetation zone; y = 0 represents the centerline of the flume (submerged vegetation zone); and z = 0 represents the riverbed surface. After bedload transport reaches equilibrium, instantaneous velocities in the three coordinate directions are collected using a Nortek Vectrino profile current meter (probe pointing downwards).

[0042] The specific layout of the water tank with submerged vegetation is as follows: Figure 1 As shown, the experiment was conducted in a water tank 17 m long and 1 m wide, with a 5 cm thick layer of sand artificially laid at the bottom. Figure 1 As shown in Figure a, the water tank is equipped with independent pipes for water supply and sediment passage to achieve water-sand circulation. Figure 1 b and Figure 1As shown in FIG. c, flexible model vegetation with the same morphological characteristics as the Vallisneria densespicata is arranged in the water tank and fixed on the PVC plate in a staggered manner to form a submerged vegetation area with a length of 4 m and a width of 1 m, and the height of the vegetation is lower than the water depth. The median particle size d s =0.5 mm of the sand in the sand layer is 0.5 mm, and the density p s =2.65 g / cm³. The test sets 10 working conditions (A1-A5, B1-B5, different water depth, water depth, vegetation density, and vegetation submergence, as shown in Table 2), and considers two different water depths, water depth H =20 cm and water depth H =25 cm. When the water depth H =20 cm, the cross-sectional average flow velocity U0 = 23.5-58.9 cm / s; when the water depth H =25 cm, the cross-sectional average flow velocity U0 = 48.8-72.3 cm / s. The unit area vegetation volume fraction =0.009-0.017, and the vegetation density n is 222 m -2 and 444 m -2 . The vertical water resistance area a =nd nb =0.023-0.046 cm -1 of the vegetation on the unit bed surface is 0.023-0.046 cm. It is found that the vegetation height h changes from 15.5 cm to 9.8 cm after being impacted by the water flow, so the vegetation submergence changes in the range of H / h = 1.3-2.6. When x>2 m, the time-averaged velocity and turbulent energy remain uniform, indicating that the 4 m long canopy is sufficient to form a fully developed and stable flow. During the test, as shown in FIG. d, the thickness of the sand layer is always maintained at 2-3 cm, ensuring that the PVC bottom plate is completely buried. Figure 1

[0043] In this embodiment, the Nortek Vectrino profile flow velocity meter is used to measure the instantaneous flow velocity in three directions (x, y, z) at a frequency of 50 Hz for 240 s at each measurement point, and then the MATLAB code is used to decompose the instantaneous flow velocity into time-averaged flow velocity ( , , ) and instantaneous fluctuation flow velocity ( , , ). The turbulent energy is defined as . In the fully developed flow area (x=3 m), in order to effectively reduce the influence of spatial heterogeneity of the water flow between the vegetation, for each vertical (z direction) measurement point, 5 different positions are set in the transverse (y direction) to measure the water flow, so as to obtain the representative average flow velocity and average turbulent energy at each vertical measurement point z position, i.e. , ​. Near-bed velocity U nb and near-bed turbulent kinetic energy k t(nb) , which are obtained by vertical integration in the near-bed region of submerged vegetation, are calculated as follows: ; .

[0044] Before each test, a 5 cm thick sand layer is manually laid on top of the PVC plate. The sand layer has a median particle size d s = 0.5 mm and a density p s = 2.65 g / cm³. During the test, the thickness of the sand layer is always maintained at 2-3 cm, ensuring that the PVC bottom plate is completely submerged (d Figure 1 The bed load sediment transport rate q s is measured as follows: first, the bed load sediment transported in the circulation pipeline is collected in a mesh bag using a T-valve. The sediment collection time AT is flexibly adjusted according to the filling speed of the mesh bag, and is controlled within the range of 30-120 s; then, the collected sediment in the mesh bag is moved into a water container with a volume scale, and the total volume V tot and mass m tot of water and sediment are recorded, where V tot = V w + V s , m tot = pV w + p s V s , V w and V s are the volumes of water and sediment, and p and p s are the densities of water and sediment; the sediment volume is calculated by volume-mass balance: ; finally, the bed load sediment transport rate per unit width of the river channel is calculated based on the sediment volume: , where W is the width of the water tank. To ensure measurement accuracy, each working condition is measured at least 3 times to calculate the average value of q s and its standard deviation. The measurement interval of the bed load sediment transport rate is 2 hours, and repeated measurements are performed until the sediment transport reaches a dynamic equilibrium state: when the q s measured in two consecutive times remains consistent within the allowable error range (< 10%), it is considered that the bed load sediment transport has reached an equilibrium state. The time required to establish this equilibrium state is at least 15 hours and at most 30 hours.

[0045] In all working conditions, the vegetation drag coefficient C , so C is taken as 1.5 in the calculation, and the bed surface friction coefficient C f is calculated from the bed shear stress t and the near-bed velocity Unb Decide, i.e. Yang et al. proposed the Reynolds stress in the xz direction can be measured at a distance of 1 cm above the sand layer, and and the bed shear stress are consistent in size (see Yang, J. Q., Kerger, F., & Nepf, H. M. (2015). Estimation of the bed shear stress in vegetated and bare channels with smooth beds. Water Resources Research, 51(5), 3647-3663. https: / / doi.org / 10.1002 / 2014WR016042). Therefore, in this embodiment, the above formula is used to calculate .

[0046] The test parameters of all working conditions and the measured near-bottom flow velocity U nb , near-bottom turbulent kinetic energy k t(nb) and channel single-width bed load sediment transport rate q s are shown in Table 2.

[0047] (4) Analysis of test results

[0048] The following is a method for predicting the bed load sediment transport rate of a river channel under the action of submerged vegetation provided by the present application, which is based on the above working conditions to obtain the bed load sediment transport rate of a river channel with submerged vegetation, and specifically includes the following steps:

[0049] S1 determines the near-bottom turbulent kinetic energy of the river channel under the action of submerged vegetation and performs dimensionless processing thereon, specifically including the following steps:

[0050] S11 determines the average flow velocity U nb of the near-bottom region.

[0051] In this step, the average flow velocity U nb of the near-bottom region refers to the average flow velocity in the near-bottom region of the fully developed flow region, which is obtained by the following operation:

[0052] S111 defines the submerged vegetation region as 0 ≤ z ≤ h, and in the fully developed flow region, a vertical flow velocity distribution calculation model of the submerged vegetation region of formula (2) is constructed based on an exponential decay function;

[0053] S112 takes the near-bottom region of the submerged vegetation as the calculation domain, and integrates the vertical flow velocity U(z) of the region, i.e., the average flow velocity U nb.

[0054] More specifically, the internal flow velocity U of the submerged vegetation is calculated by formula (4), (5), (6) and (8) first s , the attenuation coefficient k u and (U h -U s ) are substituted into formula (2) to solve the vertical distribution of the flow velocity U(z) in the submerged vegetation area; then, z nb = 0.3h is selected as the near-bottom area of the submerged vegetation, and in this height range, the water-blocking area A(z) of the submerged vegetation model, the flow velocity U(z) and the turbulent energy k t (z) are uniformly distributed in the vertical direction; finally, formula (2) and (3) are combined to calculate the average flow velocity U nb .

[0055] S12 determines the bed surface turbulent energy k t(b) and the vegetation turbulent energy k t(v) .

[0056] In this step, the near-bottom area average flow velocity U nb determined in step S11 and the riverbed bed surface friction coefficient C f = 0.005 ± 0.001 are substituted into formula (9) to calculate the bed surface turbulent energy k t(b) , and here, the proportion parameter takes the value 0.19.

[0057] The vegetation turbulent energy k t(v) is calculated according to formula (10), and here, γ 2 can be determined by least square fitting based on the flume test data. In this embodiment, for submerged flexible vegetation, γ 2 = 0.5 ± 0.1, which is basically consistent with γ 2 (= 0.52 ± 0.07) determined in the related research on submerged rigid vegetation (see Zhao, T., & Nepf, H. (2024). Turbulence and bedload transport in submerged vegetation canopies. Water Resources Research, 60, e2024WR037694), which fully verifies the rationality of the value of γ 2 in this embodiment. is the shape drag coefficient, and according to Etminan et al. when the vegetation Reynolds number is Re c , the average flow velocity U , the vegetation shape drag force accounts for 90% of the total drag force (see Etminan, V., Ghisalberti, M., & Lowe, R. J. (2018). Predicting bed shear stresses in vegetated channels. Water Resources Research, 54(11), 9187-9206. https: / / doi.org / 10.1029 / 2018WR022811), it can be reasonably considered in the present embodiment that = C d , that is, .

[0058] S13 defines the bed surface turbulent kinetic energy k t(b) and the sum of the vegetation turbulent kinetic energy k t(v) is k t(bv) , the shear turbulent kinetic energy k t(s) and k t(bv) are in a proportional relationship.

[0059] In this step, the bed surface turbulent kinetic energy k t(b) and the vegetation turbulent kinetic energy k t(v) determined in step S12 are substituted into equation (11), and k t(bv) can be calculated. The proportional relationship between the shear turbulent kinetic energy k t(s) and k t(bv) is shown in equation (12).

[0060] In the equation, δ s is the proportional coefficient, δ s = 1.6 ± 0.5. In the present embodiment, for submerged flexible vegetation, δ s is determined by measuring the near-bottom turbulent kinetic energy k t(nb) , calculating k t(bv) from equation (11), and combining the vegetation-related parameters (such as a, h / H) to calculate and determine together from equation (12).

[0061] It should be noted that for submerged rigid vegetation, the shear turbulent kinetic energy generated by it has a significantly higher enhancement effect on the near-bottom turbulent kinetic energy than flexible vegetation, so its proportional coefficient δ s takes a larger value, δ s = 6.7 ± 1.5 (see Zhao, T., & Nepf, H. (2024). Turbulence and bedload transport in submerged vegetation canopies. Water Resources Research, 60, e2024WR037694).

[0062] S14 superimpose bed surface turbulent energy k t(b) , vegetation turbulent energy k t(v) and shear turbulent energy k t(s) , to obtain the river bottom near turbulent energy k t(nb) under the submerged vegetation effect.

[0063] In this step, the river bottom near turbulent energy k t(nb) under the submerged vegetation effect is shown in formula (13).

[0064] S15 the river bottom near turbulent energy is dimensionless.

[0065] In this step, the dimensionless river bottom near turbulent energy k is shown in formula (15).

[0066] S2 determine the river bed load sediment transport rate under the submerged vegetation effect.

[0067] In this step, first, the dimensionless critical bed surface shear stress corresponding to the sediment incipient motion is determined , which is converted into the dimensionless sediment critical incipient motion turbulent energy ; then, the bottom near turbulent energy k t(nb) determined in step S1 (formula (13)) is dimensionless, that is , the dimensionless bottom near turbulent energy k and the dimensionless sediment critical incipient motion turbulent energy are substituted into formula (1), and the dimensionless bed load sediment transport rate under the submerged vegetation effect is calculated.

[0068] To verify the accuracy of the river bed load sediment transport rate prediction method under the submerged vegetation effect proposed in the present application, including the near bottom flow velocity U nb , the near bottom turbulent energy k t(nb) and the river bed load sediment transport rate q s prediction method, 10 groups of flume test data (A1~A5, B1~B5 in Table 2) collected in the submerged flexible vegetation in this embodiment and the existing research test data C1~C6 in Table 2 are used to test the prediction effect. It should be noted that the research objects C1~C6 are submerged rigid vegetation, therefore, the attenuation coefficient k u in step S11 is calculated by formula (7); when calculating the shear turbulent energy k t(s) in step S13, the proportionality coefficient δ s = 6.7 ±1.5.

[0069] As Figure 2As shown, equations (2) to (8) can be used to accurately predict the average flow velocity U in the near-bottom area of ​​submerged vegetation. nb Whether for flexible or rigid vegetation, the model predictions of this invention agree well with the measured values; the average flow velocity U in the near-bottom region... nb The relative errors between predicted and measured values ​​were 8.5% (flexible vegetation, conditions A1~A5, B1~B5) and 16.7% (rigid vegetation, conditions C1~C6), respectively. This was based on the average flow velocity U in the near-bottom region. nb The prediction results are obtained by using equations (9) to (13) to predict the near-bottom turbulent kinetic energy k. t(nb) . Figure 3 The comparison between predicted and measured near-bottom turbulent kinetic energy under submerged vegetation is presented: for flexible vegetation (conditions A1~A5, B1~B5), the average relative error is 20.5%; for rigid vegetation (conditions C1~C6), the relative error is 24.5%, indicating that the near-bottom turbulent kinetic energy prediction method proposed in this invention has reliable and accurate prediction capabilities. Finally, this invention combines dimensionless near-bottom turbulent kinetic energy... and dimensionless critical initiation turbulent kinetic energy of sediment Equation (1) is used to predict the bedload transport rate of submerged vegetation channels. Figure 4 As shown, whether it is submerged flexible vegetation ( Figure 4 a) or rigid vegetation ( Figure 4 b) Dimensionless bedload transport rate The measured values ​​agree well with the predicted values ​​obtained by the method of this invention. Furthermore, if the model does not consider the contribution of shear turbulent kinetic energy to the near-bottom turbulent kinetic energy, it will lead to an increase in the near-bottom turbulent kinetic energy k. t(nb) The sediment transport rate q in submerged vegetation channels is underestimated. s The predicted value is 30% lower than the measured value (e.g. Figure 4 (As shown in the inset a) This result confirms that the method for predicting bedload sediment transport rate under submerged vegetation proposed in this invention significantly reduces prediction errors by introducing quantitative calculations of the contribution of shear kinetic energy. It is also applicable to various aquatic environments, such as submerged flexible vegetation and submerged rigid vegetation, and has wide applicability and versatility.

[0070] Table 2 Test conditions and parameters for submerged vegetated river channels

[0071]

[0072] In the table: n is vegetation density; H is water depth; It is the vegetation volume fraction per unit area; h is the vegetation height, and U0 is the average flow velocity of the river cross-section; U nb It is the average flow velocity in the near-bottom region of the river channel; k t(nb) It is the near-bottom turbulent kinetic energy of the river channel; q sis the sediment transport rate per unit width of the river channel.

[0073] Those skilled in the art will appreciate that the embodiments described herein are presented for purposes of illustration and understanding of the principles of the application and should not be construed as limiting the scope of the application to such specifically enumerated embodiments. Various other specific adaptations and combinations of features can be made in accordance with the techniques disclosed herein without departing from the spirit of the application, and it is the intent that all such variations and combinations be included within the scope of the application.

Claims

1. A method for predicting the bedload sediment transport rate in river channels under the influence of submerged vegetation, characterized in that, Includes the following steps: S1 determines the near-bottom turbulent kinetic energy of the river channel under the influence of submerged vegetation and performs dimensionless processing; this step includes the following sub-steps: S11 determining the average flow velocity U of the near-bottom region nb ; S12 determines the bed surface turbulent energy k t(b) , vegetation turbulent energy k t(v) ; S13 defines the bed shear energy k t(b) The sum of the vegetation shear energy k t(v) t(bv) The shear energy k t(s) t(bv) The ratio of k​​ S14 superimposed bed surface turbulent energy k t(b) , vegetation turbulent energy k t(v) and shear turbulent energy k t(s) , get the river near the bottom turbulent energy k t(nb) under the action of submerged vegetation S15 performs dimensionless processing on the near-bottom turbulent kinetic energy of the river channel; S2 The sediment transport rate of the river channel under the action of submerged vegetation is determined according to the following formula: ； In the formula, The dimensionless near-bottom turbulent kinetic energy of the river channel; It is the dimensionless critical initiation turbulent kinetic energy of sediment.

2. The method for predicting river bedload sediment transport rate under the action of submerged vegetation according to claim 1, characterized in that, In the step S11, the average flow velocity U in the near-bottom region is determined according to the following steps based on the boundary condition that the flow velocity in the vertical section of the river is the largest at the top of the submerged vegetation (z = h) nb : S111 defines the submerged vegetation zone as 0 ≤ z ≤ h. In the zone with fully developed water flow, a calculation model for the vertical distribution of water flow velocity in the submerged vegetation zone is constructed based on the exponential decay function: ； S112 takes the near-bottom region of the submerged vegetation as the calculation domain, and integrates the water flow velocity U(z) along the vertical direction of the region, i.e. obtains the average flow velocity U of the near-bottom region nb : ； In the formula, U(z) is the water flow velocity at position z; U s U represents the internal flow velocity of submerged vegetation driven solely by hydraulic gradient. h The velocity of the water flow at z = h, where the top of the vegetation is submerged; k u is the attenuation coefficient; h is the vegetation height; The vertical height of the near-bottom area of ​​the submerged vegetation.

3. The method for predicting the bedload sediment transport rate in river channels under the action of submerged vegetation as described in claim 2, characterized in that, In step S111 above, the flow velocity inside the submerged vegetation It can be calculated using the following formula: ； (U) h -U s It can be calculated using the following formula: ； ； In the formula, g is the acceleration due to gravity; S is the hydraulic gradient; C d denoted as the vegetation drag coefficient, where a is the vertical water-blocking area of ​​vegetation per unit riverbed surface; H represents the shear velocity that submerges the top of the vegetation; H represents the river channel depth.

4. The method for predicting the sediment transport rate of riverbed under the action of submerged vegetation according to claim 2, characterized in that, In step S111 above, the attenuation coefficient k u Determine using the following method: When the submerged vegetation is rigid vegetation: ； When the submerged vegetation is flexible vegetation: ； in, C d This is the vegetation drag coefficient. a It refers to the vertical water-blocking area of ​​vegetation on the riverbed surface.

5. The method for predicting the bedload sediment transport rate in river channels under the action of submerged vegetation according to claim 1, characterized in that, In step S12, the turbulent kinetic energy k of the bed surface t(b) The calculation formula is: ； In the formula, This is a proportional parameter; The coefficient of friction of the riverbed surface.

6. The method for predicting the bedload sediment transport rate in river channels under the action of submerged vegetation according to claim 1, characterized in that, In step S12, the vegetation turbulent kinetic energy k t(v) The calculation formula is: ； In the formula, γ 2 For vortex scale parameters; d is the shape drag coefficient; nb The average diameter of the near-bottom area of ​​the submerged vegetation; This represents the vegetation volume fraction per unit area.

7. The method for predicting the bedload sediment transport rate in river channels under the action of submerged vegetation according to claim 1, characterized in that, In step S13, k t(bv) The calculation formula is: ； Shear kinetic energy k t(s) With k t(bv) The proportional relationship is: ； In the formula, δ s This is the proportionality coefficient; a The vertical water-blocking area of ​​vegetation on a unit riverbed surface; h The height of the vegetation; H The river is deep.

8. The method for predicting the sediment transport rate of riverbed under the action of submerged vegetation according to claim 7, characterized in that, In step S14, the near-bottom turbulent kinetic energy k of the river channel under the influence of submerged vegetation t(nb) The calculation formula is: 。 9. The method for predicting the sediment transport rate of riverbed under the action of submerged vegetation according to any one of claims 1 to 8, characterized in that, The formulas for calculating the dimensionless near-bottom turbulent kinetic energy and the dimensionless critical initiation turbulent kinetic energy of sediment are as follows: Dimensionless near-bottom turbulent kinetic energy of the river channel: ; Dimensionless critical initiation turbulent kinetic energy of sediment: ; In the formula, ρ s ρ is the density of sediment, ρ is the density of water, g is the acceleration due to gravity, and d is the density of sediment. s The particle size of the sediment; The dimensionless critical bed shear stress corresponds to the initiation of sediment transport. This is a proportional parameter.

Images