EXPONENTIAL MODEL-BASED METHOD FOR PREDICTING TWO-DIMENSIONAL FLOW VELOCITY FIELD IN RIVER CHANNEL WITH EMERGENT VEGETATION

Abstract

Provided is an exponential model-based method for predicting a two-dimensional flow velocity field in a river channel with emergent vegetation. The method comprises the following steps: (1) with a center of an upstream boundary of an emergent vegetation patch as an origin, dividing the river channel into a vegetated region and a bare channel in a direction perpendicular to a streamwise direction namely, an x direction; (2) determining a model for predicting flow velocity distribution of a two-dimensional flow velocity field in the vegetated region and the bare channel and (3) determining the flow velocity U.sub.y=b at the side edge of the vegetation patch and the mean flow velocity U.sub.bare over transverse profiles in a streamwise direction of the bare channel.

Claims

1. An exponential model-based method for predicting a two-dimensional flow velocity field in a river channel with emergent vegetation, comprising the following steps: (1) with a center of an upstream boundary of an emergent vegetation patch as an origin, dividing the river channel into a vegetated region and a bare channel in a direction perpendicular to a streamwise direction, namely, an x direction, wherein the vegetated region is: 1>y/b>−1, a central area of the vegetated region is: b−δ.sub.p>y>δ.sub.p−b, the bare channel is: B/2≥y≥b and −b≥y≥−B/2, a side edge of the vegetation patch is: y=b, b denotes half width of a vegetation patch, and B denotes half width of a river channel; and δ.sub.p denotes a penetration distance that lateral vortexes penetrate into a patch through its side edge, and δ.sub.m denotes a width of a mixed layer; (2) determining a model for predicting flow velocity distribution of a two-dimensional flow velocity field in the vegetated region and the bare channel: wherein a model for the vegetated region is: $U_{d\left(1\right)}=U_{\mathrm{veg}}+\left(U_{y=b}-U_{\mathrm{veg}}\right)e^{\frac{y-b}{L_{d\left(\mathrm{veg}\right)}}}$ a model for the bare channel is: $U_{d\left(2\right)}=U_{\mathrm{bare}}+\left(U_{y=b}-U_{\mathrm{bare}}\right)e^{\frac{b-y}{L_{d\left(\mathrm{bare}\right)}}}$ wherein U.sub.d (1) denotes a laterally distributed flow velocity in a streamwise direction at different locations in the vegetated region, U.sub.d (2) denotes a laterally distributed flow velocity in a streamwise direction at different locations in the bare channel, U.sub.veg denotes a mean flow velocity over transverse profiles in a streamwise direction of the vegetated region, U.sub.y=b denotes a flow velocity at the side edge of the vegetation patch, U.sub.bare denotes a mean flow velocity over transverse profiles in a streamwise direction of the bare channel, L.sub.d (veg) and L.sub.d (bare) denote exponential decay lengths of the vegetated region and the bare channel, respectively, wherein $\frac{L_{d\left(\mathrm{veg}\right)}}{{\delta }_p}=0.32\pm 0.04,\frac{L_{d\left(\mathrm{bare}\right)}}{{\delta }_m}=0.64\pm 0.14,$ and the mean flow velocity U.sub.veg over transverse profiles in a streamwise direction of the vegetated region can be determined by a model for predicting longitudinal flow velocity distribution in the river channel with an emergent vegetation patch; and (3) determining the flow velocity U.sub.y=b at the side edge of the vegetation patch and the mean flow velocity U.sub.bare over transverse profiles in a streamwise direction of the bare channel: the flow velocity U.sub.y=b at the side edge of the vegetation patch and the mean flow velocity U.sub.bare over transverse profiles in a streamwise direction of the bare channel are determined according to the following two boundary conditions: a predicted flow velocity satisfies a flow continuity equation at the side edge of the vegetation patch: $\frac{\partial U_{\mathrm{veg}}}{\partial y}=\frac{\partial U_{\mathrm{bare}}}{\partial y};$ a predicted flow velocity in the vegetated region and the bare channel satisfies a flow continuity equation: ∫.sub.0.sup.bU.sub.d(1)dy+∫.sub.b.sup.BU.sub.d(2) dy=BU.sub.0; wherein U.sub.d(1) and U.sub.d(2) denote laterally distributed flow velocities in the vegetated region and the bare channel obtained according to the prediction model in step (2), respectively, U.sub.0 denotes a mean flow velocity at an upper stream of the river channel x<−L.sub.u, and L.sub.u denotes a flow deflection distance at an upper stream of the vegetation patch; and once the flow velocity U.sub.y=b at the edge of the vegetation patch and the mean flow velocity U.sub.bare over transverse profiles in a streamwise direction of the bare channel are determined, the prediction model in step (2) can be used for predicting flow velocity distribution of the two-dimensional flow velocity field in the vegetated region and the bare channel.

2. The exponential model-based method for predicting a two-dimensional flow velocity field in a river channel with emergent vegetation according to claim 1, wherein in step (2), the mean flow velocity over different transverse profiles in a streamwise direction of the vegetated region is determined according to the following prediction model: wherein the model for the vegetated region is: $U_{\mathrm{veg}}=U_{\mathrm{veg}\left(f\right)}+\left(U_{\mathrm{veg}\left(0\right)}-U_{\mathrm{veg}\left(f\right)}\right)e^{\frac{-x}{L_{d\left(1\right)}}};$ wherein U.sub.veg denotes a mean flow velocity over transverse profiles in a streamwise direction of the vegetated region, U.sub.veg(f) denotes a mean flow velocity of a fully developed region x>L.sub.I within the vegetation patch, U.sub.veg(0) denotes a flow velocity at an upstream boundary x=0 of the vegetated region, L.sub.I denotes a flow deflection distance within the vegetation patch, L.sub.d(1) denotes an exponential decay length within the vegetated region, and L.sub.d(1)/L.sub.I=0.30±0.01.

3. The exponential model-based method for predicting a two-dimensional flow velocity field in a river channel with emergent vegetation according to claim 2, wherein the flow deflection distance L.sub.I within the vegetation patch is determined according to the following formula: $L_I=\left(5.5\pm 0.4\right)\sqrt{{\left(\frac{2}{C_{d}a}\right)}^2+b^2},$ wherein C.sub.d denotes a vegetation drag coefficient, a denotes a frontal area per canopy volume of vegetation per unit water body, and b denotes half width of the vegetation patch.

4. The exponential model-based method for predicting a two-dimensional flow velocity field in a river channel with emergent vegetation according to claim 2, wherein the mean flow velocity U.sub.veg(f) of the fully developed region x>L.sub.I within the vegetation patch is determined according to the following formula: $U_{\mathrm{veg}\left(f\right)}=\sqrt{\frac{ghS}{C_f+\frac{1\mathrm{Cd}ah}{21-\phi }}},$ wherein g denotes gravitational acceleration; h denotes a water depth; S denotes a water surface slope; and C.sub.f denotes a bed friction coefficient.

5. The exponential model-based method for predicting a two-dimensional flow velocity field in a river channel with emergent vegetation according to claim 2, wherein the flow velocity U.sub.veg(0) at the upstream boundary of the vegetated region is determined according to the following formula:
U.sub.veg(0)/U.sub.0=1−(0.15±0.02)√{square root over (C.sub.dab)}; wherein U.sub.0 denotes a mean flow velocity at the upper stream x<−L.sub.u of the river channel, L.sub.u denotes a flow deflection distance at the upper stream of the vegetation patch, C.sub.d denotes a vegetation drag coefficient, a denotes a frontal area per canopy volume of vegetation per unit water body, and b denotes half width of the vegetation patch.

6. The exponential model-based method for predicting a two-dimensional flow velocity field in a river channel with emergent vegetation according to claim 1, wherein the mean flow velocity U.sub.0 over transverse profiles at the upper stream x<−L.sub.u of the river channel is determined according to the following formula: $U_0=\sqrt{\frac{ghS}{C_f}}$ wherein g denotes gravitational acceleration; h denotes a water depth; S denotes a water surface slope; and C.sub.f denotes a bed friction coefficient.

7. The exponential model-based method for predicting a two-dimensional flow velocity field in a river channel with emergent vegetation according to claim 1, wherein the flow deflection distance L.sub.u at the upper stream of the vegetation patch is within a range of 30-50 cm.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0056] FIG. 1 is a schematic diagram of evolution of river flow under two cases of a river channel with emergent vegetation in its center, where b represents half width of vegetation patch, and B represents half width of the river channel.

[0057] FIG. 2 is a schematic diagram of evolution of river flow of a river channel with emergent vegetation at one side, where b represents the width of vegetation patch, and B represents the width of the river channel.

[0058] FIGS. 3A and 3B show a pictures for simulating two cases of a river channel with emergent vegetation according to an embodiment, where FIG. 3(A) shows a picture under case B1, and FIG. 3(B) shows a picture under case C1, where water flows from the bottom to the top.

[0059] FIGS. 4A, 4B and 4C are diagrams illustrating comparison between flow velocity measurements (represented by different symbols) and flow velocity prediction values (represented by solid lines) at different longitudinal (x direction) positions according to an embodiment, where FIG. 4A represents data under case B1, with ϕ=0.015; FIG. 4B represents data under case B2, with ϕ=0.023; FIG. 4C represents data under case B3, with ϕ=0.045, dotted lines represent the edge of vegetation patch, and vegetation length is not represented according to actual scale in the diagram.

[0060] FIGS. 5A and 5B are diagrams illustrating comparison between flow velocity measurements (represented by different symbols) and flow velocity prediction values (represented by solid lines) at different longitudinal (x direction) positions according to an embodiment, where FIG. 5A represents data under case C1, with ϕ=0.025; and FIG. 5B represents data under case C2, with ϕ=0.038, and dotted lines represent the edge of vegetation patch.

DETAILED DESCRIPTION OF THE EMBODIMENTS

[0061] The technical solutions in the examples of the present disclosure are clearly and completely described below with reference to the accompanying drawings. Apparently, the described examples are merely a part rather than all of the examples of the present disclosure. All other embodiments obtained by a person of ordinary skill in the art based on the embodiments of the present disclosure without creative efforts should fall within present disclosure.

[0062] The following embodiment explains in detail the process of obtaining a two-dimensional flow velocity field of the river channel with emergent vegetation patch by the flume test and obtaining a two-dimensional flow velocity field of the river channel with emergent vegetation patch by model prediction and the results thereof.

[0063] I. Test Purpose

[0064] Measure flow velocity distribution of two-dimensional flow velocity fields for a vegetated region and a bare channel in a river channel with an emergent vegetation patch by a flume experiment, measure the detailed two-dimensional flow velocity distribution under certain cases, and compare the flow velocity distribution of the two-dimensional flow velocity fields in the vegetated region and the bare channel with the flow velocity distribution of the two-dimensional flow velocity field obtained by using the prediction model, so as to verify the accuracy of the exponential model-based method for predicting a two-dimensional flow velocity field in a river channel with emergent vegetation according to the present disclosure.

[0065] II. Test Device

[0066] Primary test devices are provided in Table 1.

TABLE-US-00001 TABLE 1 Flume test device with emergent vegetation patch Device name Quantity Remarks Test flume 2 Flume 1: this flume is 23 meters long, 2 meters wide and 1 meter high. Perforated PVC boards are arranged in the whole river channel for the layout of a vegetation patch. Flume II: this flume is 13 meters long, 1 meter wide and 1 meter high. Perforated PVC boards are arranged in the whole river channel for the layout of a vegetation patch. Simulated emergent vegetation 5 cases cases B1-B3: the vegetation patch has a width of patch 30-40 cm, a length of 3-5 m, and a water depth of 17.8 ± 0.2, the mean flow velocity of the river channel is 18.0 ± 0.5 cm/s, and the height of all simulated vegetation is greater than the water depth, cases C1-C2: the vegetation patch has a width of 33 cm and a length of 4.5 m. The water depth under cases Cl and C2 is 20.0 ± 0.2 cm, the mean flow velocity under cases Cl and C2 is 16.6 ± 0.2 cm/s and 19.1 ± 0.2 cm/s, respectively, and the height of all simulated vegetation is greater than the water depth. Acoustic Doppler Current 1 Equipped support and data processing software Profiler

[0067] III. Test Case

[0068] According to this embodiment, experiments are carried out on two kinds of river channels with emergent vegetation to verify the effectiveness of the prediction method provided by the present disclosure. Under one case, emergent vegetation grows at the center of the river channel, as shown in FIG. 1; and under the other case, emergent vegetation grows at one side of the river channel, as shown in FIG. 2. For this reason, a series of tests under two cases are designed and carried out in two different flumes (flume I and flume II). There is a flow straightener at the entrance of both flumes to produce a vertical and uniform flow in the flume. The water depth is adjusted by adjusting the tailgate and measured along the flume using a water gauge.

[0069] In flume I, a rectangular vegetation patch model is established and placed in the center of the flume. The rectangular vegetation patch model here does not represent a particular vegetation patch in nature, but is only designed and implemented as a generalized model. Therefore, the shape of the vegetation is not the focus of the present disclosure. Under cases B1-B3 created in flume I, a test section has a length of 15 m, and the vegetation patch has a length of L=3-5 m, where L should be greater than the flow deflection distance L.sub.I within the vegetation patch, so as to reappear a fully developed region of flow (corresponding to U.sub.veg (f). L.sub.u and L.sub.I are determined by the longitudinal flow velocity distribution of each case, where the distance from the position where the flow velocity at the upper stream of the vegetation patch begins to change to the front of the vegetation patch is defined as L.sub.u, and the distance from the position where the flow velocity decreases to a constant within the vegetation patch to the front of the vegetation patch is defined as L.sub.I. The L.sub.I values of cases B1-B3 are shown in Table 2. Under cases B1-B3, ½ of the vegetation patch has a width of b=30-40 cm, ½ of the river channel has a width of B=100 cm, and thus the ratio of the width of the vegetation patch to the width of the river channel is b/B=0.3-0.4; the water depth is h=17.8±0.2, the mean flow velocity of the river channel is U.sub.0=18.0±0.5 cm/s, and Reynolds number is Re(=U.sub.0R/v)≈27000, where Froude number of flow is Fr(=U.sub.0/√{square root over (gh)})=0.14, where R denotes a hydraulic radius.

[0070] In flume II, a rectangular vegetation patch model is established and placed on the side of the flume. Under cases C1-C2 created in flume II, a test section has a length of 7 m, and the vegetation patch has a length of L=4.5 m, where L should be greater than the flow deflection distance L.sub.I within the vegetation patch, so as to reappear a fully developed region of flow (corresponding to U.sub.veg (f). L.sub.u and L.sub.I are determined by the longitudinal flow velocity distribution of each case. The L.sub.I values of cases C1-C2 are shown in Table 1. Under cases C1-C2, the vegetation patch has a width of b=33 cm, the river channel has a width of B=100 cm, and thus the ratio of the width of the vegetation patch to the width of the river channel is b/B=0.33; the water depth is h=20.0±0.2, the mean flow velocity of the river channel is U.sub.0=19.1±0.2 cm/s, and Reynolds number is Re(=U.sub.0R/v)≈23000−27000, where R denotes a hydraulic radius, and Froude number of flow is Fr(=U.sub.0/√{square root over (gh)})=0.12 to 0.14, which shows turbulent flow and subcritical flow both occur in the vegetation patch.

[0071] In flume I and flume II, rigid cylinders, specifically cylindrical sticks, are used to simulate vegetation. In flume I, the cylindrical emergent vegetation model has a length of 30 cm, which is greater than the water depth of 17.8 cm; and in flume II, the cylindrical emergent vegetation model has a length of 30 cm, which is greater than the water depth of 20.0 cm. Cylinders do not represent specific species of plants, but they can represent emerging vegetation such as reeds and cattails, which have hard stems. In nature, vegetation usually appears in the form of patch with limited width and length. Field studies show that the length and width of a vegetation patch are generally between 0.5 meters and 5 meters. This embodiment studies approximate two-dimensional flow formed within and around the emergent vegetation patch when the current is shallow enough. The cylindrical diameter d=0.8 cm is set based on the observed diameter range of tender plants at the river shoal and the rhizome of plants in the river (d=0.2 to 1.2 cm, Lightbody and Nepf 2006; Sand-Jensen 1998; Manners et al, 2015). The volume fraction ϕ(=π/4 nd.sup.2) of solids in the test is within a range of ϕ=0.015-0.045, which is consistent with the vegetation parameters (common gladiolus ϕ=0.001-0.04, Grace et al., 1986; Coon et al. 2000) observed by previous scholars in the field, where n denotes vegetation density per unit area of the riverbed. Specifically, ϕ=0.015, 0.023 and 0.045 under cases B1, B2 and B3, respectively, and ϕ=0.025 and 0.038 under cases C1 and C2, respectively.

[0072] The cylindrical stick is fixed on the perforated PVC board at the bottom of the flume, and the PVC board has a thickness of 1 cm. The PVC board covers the whole bed surface of the above two flumes respectively, yielding a bed friction coefficient of C.sub.f=0.006±0.001. Under each case, the length of the vegetation model is larger than the interior flow adjustment distance (that is, L>L.sub.I). Therefore, there are flow adjustment region and fully developed region of flow under each case. The distance L.sub.I of the flow adjustment region is estimated according to the measured velocities. In the fully developed region of flow, Kelvin-Helmholtz (KH for short) vortexes occur along the side of the emergent vegetation patch. In the study of Caroppi et al. (2020), the cases for the occurrence of KH vortexes are:

[00022]$\lambda \left(=\frac{U_{\mathrm{bare}}-U_{veg}}{U_{\mathrm{bare}}+U_{veg}}\right)\ge 0.4$

[0073] In this embodiment, the parameter λ (=0.7 to 0.9) associated with the KH vortices is greater than the threshold (λ≥0.4), indicating that KH vortexes occur under each of the five cases of B1-B3 and C1-C2. The penetration distance δ.sub.p of the KH vortexes is estimated by the measured laterally distributed velocities or formula (2).

[0074] As shown in FIGS. 1-2, coordinates x, y and z denote the longitudinal direction, horizontal direction and vertical direction, respectively. x=0 denotes the upstream edge of the vegetation patch model, and z=0 denotes the surface of the river bed. The definition of coordinate y varies in two cases. Specifically, for a 2 m wide flume (cases B1-B3), y=0 is the center line of the flume and the vegetation model, as shown in FIG. 1. For a 1 m wide flume (cases C1-C2), y=0 represents the side wall of the flume, as shown in FIG. 2.

[0075] The flow velocity data in two flumes are collected at the same time by using the Nortek Vectrino Acoustic Doppler Current Profiler. A downward-looking probe is fixed to half water depth of the river channel (z=h/2). Flow velocity is measured at z=h/2, as the difference between the velocity at z=h/2 in and around the emergent vegetation and the depth-averaged flow velocity U.sub.d is less than 6%. In order to efficiently measure the flow velocity in the river channel, the flow velocity measured at half water depth is taken as the depth-averaged flow velocity in this embodiment. At each measuring point, the velocity is recorded for a period of 150 s at a frequency of 50 Hz. Instantaneous flow velocity data in three directions are processed by the data processing software of the Doppler Current Profiler, so as to obtain time-averaged velocities (u, v and w) in three directions x, y and z).

[0076] The longitudinal distribution of flow velocities is measured at different positions in the y direction. Within the vegetation patch model, in order to eliminate the non-uniformity of spatial flow, a characteristic region is considered at each location, that is, the flow velocity is measured at the positions of y=0 and dy/4, where dy/4 is the transverse distance between two adjacent cylindrical sticks. The probes are placed in the same orientation and at the same relative position to neighboring cylinders to minimize the measurement error induced by spatial flow heterogeneity inside the cylinder arrays. In the vegetation patch, the mean velocity at two locations in a characteristic region is defined as the depth-averaged flow velocity U.sub.d; and outside the vegetation patch, the mean flow velocity at half water depth is defined as the depth-averaged flow velocity U.sub.d. For cases B1-B3, the measuring positions are y=0 m, 0.1 m, 0.2 m, 0.3 m, 0.4, 0.5 m, 0.6 m, 0.7 m, 0.8 m and 0.9 m, and for cases C1 and C2, the measuring positions are y=0.05 m, 0.15 m, 0.25 m, 0.3 m, 0.35 m, 0.4 m, 0.45 m, 0.5 m, 0.55 m, 0.6 m, 0.7 m, 0.8 m and 0.9 m.

[0077] The lateral distribution of flow velocities is measured at different positions in the x direction. Specifically, for case B1, the flow velocity distributions over transverse profiles of U.sub.d are measured at x=50 cm, 100 cm, 150 cm, 200 cm, 250 cm, 300 cm, 400 cm and 420 cm; for cases B2 and B3, the measurement positions are x=50 cm, 100 cm, 150 cm, 200 cm and 300 cm; and for cases C1 and C2, the measurement positions are x=50 cm, 100 cm, 150 cm, 200 cm, 250 cm, 300 cm, 350 cm, 400 cm and 450 cm. Under cases B1-B3, the vegetation model is placed in the center of the flume, so the velocity is symmetrical along the centerline of the flume and vegetation, which is confirmed by measurement. Therefore, at each x, the lateral distribution of velocity is measured only on the left side (B≥y≥0) of the vegetation patch and the river channel.

[0078] IV. Model Prediction

[0079] Flow velocity distributions of a two-dimensional flow velocity field in the vegetated region and the bare channel of the river channel with a vegetation patch are obtained through a prediction model:

[0080] (1) with a center of an upstream boundary of an emergent vegetation patch as an origin, divide the river channel into a vegetated region and a bare channel along a direction perpendicular to a streamwise direction, namely, an x direction, where the vegetated region is: 1>y/b>−1, a central area of the vegetated region is: b−δ.sub.p>y>δ.sub.p−b, the bare channel is: B/2≥y≥b and −b≥y≥−B/2, a side edge of the vegetation patch is: y=b, b denotes half width of a vegetation patch, and B denotes half width of a river channel; and δ.sub.p denotes a penetration distance that lateral vortexes penetrate into a patch through its side edge;

[0081] (2) determine a model for predicting flow velocity distribution of a two-dimensional flow velocity field in the vegetated region and the bare channel:

[0082] where the model for the vegetated region is:

[00023]$U_{d\left(1\right)}=U_{veg}+\left(U_{y=b}-U_{veg}\right)e^{\frac{y-b}{L_{d\left(veg\right)}}}$

[0083] the model for the bare channel is:

[00024]$U_{d\left(2\right)}=U_{\mathrm{bare}}+\left(U_{y=b}-U_{\mathrm{bare}}\right)e^{\frac{b-y}{L_{d\left(\mathrm{bare}\right)}}},$

where U.sub.d(1) denotes a laterally distributed flow velocity in a streamwise direction at different locations in the vegetated region, U.sub.d(2) denotes a laterally distributed flow velocity in a streamwise direction at different locations in the bare channel, U.sub.veg denotes a mean flow velocity over transverse profiles in a streamwise direction of the vegetated region, U.sub.y=b denotes a flow velocity at the side edge of the vegetation patch, U.sub.bare denotes a mean flow velocity over transverse profiles in a streamwise direction of the bare channel, L.sub.d(veg) and L.sub.d(bare) denote exponential decay lengths of the vegetated re ion and the bare channel, respectively, where

[00025]$\frac{L_{d\left(\mathrm{veg}\right)}}{{\delta }_p}=0.32\pm 0.04,\frac{L_{d\left(\mathrm{bare}\right)}}{{\delta }_m}=0.64\pm 0.14,$

and the mean flow velocity U.sub.veg over transverse profiles in a streamwise direction of the vegetated region can be determined by a model for predicting longitudinal flow velocity distribution in the river channel with an emergent vegetation patch; and

[0084] (3) determine the flow velocity U.sub.y=b at the side edge of the vegetation patch and the mean flow velocity U.sub.bare over transverse profiles in a streamwise direction of the bare channel.

[0085] The flow velocity U.sub.y=b at the side edge of the vegetation patch and the mean flow velocity U.sub.bare over transverse profiles in a streamwise direction of the bare channel are determined according to the following two boundary conditions:

[0086] a predicted flow velocity satisfies a flow continuity equation at the side edge of the vegetation patch:

[00026]$\frac{\partial U_{\mathrm{veg}}}{\partial y}=\frac{\partial U_{\mathrm{bare}}}{\partial y};$

[0087] a predicted flow velocity in the vegetated region and the bare channel satisfies a flow continuity equation: ∫.sub.0.sup.bU.sub.d(1)dy+∫.sub.b.sup.BU.sub.d(2) dy=BU.sub.0;

[0088] where U.sub.d (1) and U.sub.d (2) denote laterally distributed velocities in the vegetated region and the bare channel obtained by the prediction model, respectively, U.sub.0 denotes a mean flow velocity at an upper stream of the river channel x<−L.sub.u, and L.sub.u denotes a flow deflection distance at an upper stream of the vegetation patch.

[0089] Once the flow velocity U.sub.y=b at the edge of the vegetation patch and the flow velocity U.sub.bare in the bare channel are determined, the prediction model in step (2) can be used for predicting flow velocity distribution of the two-dimensional flow velocity field in the vegetated region and the bare channel.

[0090] For the mean flow velocity U.sub.veg over transverse profiles in the streamwise direction within the vegetated region in step (2), under the five cases, U.sub.veg is determined according to the following existing prediction model U.sub.veg:

[00027]$U_{\mathrm{veg}}=U_{\mathrm{veg}\left(f\right)}+\left(U_{\mathrm{veg}\left(0\right)}-U_{veg\left(f\right)}\right)e^{\frac{-x}{L_{d\left(1\right)}}};$

[0091] U.sub.veg(f) denotes a mean flow velocity of a fully developed region x>L.sub.I within the vegetation patch, U.sub.veg(0) denotes a flow velocity at an upstream boundary x=0 of the vegetated region, L.sub.I denotes a flow deflection distance within the vegetation patch, L.sub.d(1) denotes an exponential decay length within the vegetated region,

[00028]$L_{d\left(1\right)}/L_I=0.3\pm 0.01,$$L_I=\left(5.5\pm 0.4\right)\sqrt{{\left(\frac{2}{C_{d}a}\right)}^2+b^2},$

C.sub.d denotes a vegetation drag coefficient, a denotes a frontal area per canopy volume of vegetation per unit water body, and b denotes half width of the vegetation patch (for cases C1-C2, b denotes width of the vegetation patch).

[0092] Under the five cases, the mean flow velocity U.sub.veg(f) in the fully developed region within the vegetation patch involved in the foregoing prediction model U.sub.veg may be determined according to the following formula:

[00029]$U_{veg}\left(f\right)=\sqrt{\frac{ghS}{C_f+\frac{1\mathrm{Cd}ah}{21-\phi }}}$

[0093] where g denotes gravitational acceleration; h denotes a water depth; S denotes a water surface slope; and C.sub.f denotes a bed friction coefficient.

[0094] Under the five cases, the flow velocity U.sub.veg(0) at the upstream boundary of the vegetated region involved in the above prediction model U.sub.veg is determined according to the following formula:

U.sub.veg(f)/U.sub.0=1−(0.15±0.02)√{square root over (C.sub.dab)};

[0095] where U.sub.0 denotes a mean flow velocity at the upper stream of the river channel, C.sub.d denotes a vegetation drag coefficient, a denotes a frontal area per canopy volume of vegetation per unit water body, and b denotes half width of the vegetation patch.

[0096] Under the five cases, the mean flow velocity U.sub.0 at the upper stream of the river channel involved in the foregoing prediction model U.sub.veg can either be determined according to the existing formula, or obtained by measurement. In this embodiment, U.sub.0 data are obtained via actual measurement, and U.sub.0 under each case is shown in Table 2.

[0097] By substituting U.sub.veg calculated in the foregoing step into the prediction model in step (2), and then determining U.sub.y=b and U.sub.bare in step (3), the flow velocity distribution of the two-dimensional flow velocity field in the river channel can be calculated. FIG. 4 shows a flow velocity distribution curve of two-dimensional flow velocity fields in the vegetated region and bare channel under cases B1-B3, and FIG. 5 shows a flow velocity distribution curve of two-dimensional flow fields in the vegetated region and bare channel under cases C1-C2.

[0098] V. Analysis of Test Results

[0099] In order to quantitatively compare the predicted and measured flow velocities, the Root Mean Square Error (RMSE) is defined as:

[00030]$RMSE=\sqrt{\frac{1}{N}{.Math.}_1^N{\left(X_p-X_m\right)}^2}$

[0100] where N denotes the number of points predicted and measured, and X.sub.p and X.sub.m denote the predicted and measured flow velocities, respectively.

[0101] First, based on the data under cases B1-B3, the predicted flow velocity is compared with the measured flow velocity collected in the center of the flume, as shown in FIG. 4. It can be seen from the figure that the predicted flow velocity exactly matches the measured flow velocity.

[0102] Second, as shown in FIG. 5, the model is verified using measurement data under cases C1 and C2, where the vegetation model is located at one side of the flume. It can be seen from the figure that the predicted flow velocity exactly matches the measured flow velocities at different longitudinal positions.

[0103] The predicted flow velocity, measured flow velocity, and the ratio of root mean square error to velocity RMSE/U.sub.0 are shown in Table 2.

TABLE-US-00002 TABLE 2 Summary table of calculation parameters for each test case Longitudinal RMSE/ U.sub.o L b B n a L.sub.l δ.sub.p δ.sub.m measurement RMSE U.sub.o Case (cm/s) (cm)) (cm) (cm) (cm.sup.−2) (cm.sup.−1) ϕ (cm) (cm) (cm) position, x(cm) (cm/s) (%) B1 18 500 40 100 0.03 0.024 0.015 390 20 26 50, 100, 150, 200, 250, 2.8 16 300, 400, 420 B2 18 400 30 100 0.045 0.036 0.023 330 14 25.7 50, 100, 150, 200, 300 2.6 14 B3 18 300 30 100 0.09 0.072 0.045 230 7 25.5 50, 100, 150, 200, 300 1.5 8 C1 16.6 500 33 100 0.05 0.04 0.025 330 12 25.7 50, 100, 150, 200, 250, 2.2 13 300, 350, 400, 450 C2 19.1 500 33 100 0.076 0.06 0.038 260 8 21.1 50, 100, 150, 200, 250, 1.5 8 300, 350, 400, 450

[0104] As shown in Table 2, U.sub.0 denotes a mean flow velocity at an upper stream of a river channel; L denotes a length of a vegetation patch; b denotes half width of the vegetation patch under cases B1-B3 or cases C1-C2; B denotes the width of the river channel under cases B1-B3 or cases C1-C2; n denotes cylinder density in the vegetation patch; a(=nd) denotes a frontal area per canopy volume of a single vegetation patch, where d denotes the diameter of a single plant; L.sub.I denotes an interior flow adjustment distance of the vegetation, which is defined as the distance between a front edge of the vegetation and a point where the internal velocity of the vegetation reaches the minimum or constant value, which is estimated by measured velocities; δ.sub.p denotes a penetration distance estimated according to measured values; and δ.sub.m denotes a distance of a mixed layer distance estimated according to measured values. RMSE is estimated according to a formula, and calculated based on measured and predicted flow velocities.

[0105] As can be seen from Table 2, in all cases, the Root Mean Square Error (RMSE) ranges from 0.4 to 3.1, and the ratio RMSE/U.sub.0 of root mean square error to velocity is between 4% and 16%. The results show that the model of the present disclosure can better predict the two-dimensional flow velocity field of the river channel with partial vegetation.

[0106] Those of ordinary skill in the art will understand that the embodiments described herein are intended to help readers understand the principles of the present disclosure, and it should be understood that the protection scope of the present disclosure is not limited to such special statements and embodiments. Those of ordinary skill in the art may make other various specific modifications and combinations according to the technical teachings disclosed in the present disclosure without departing from the essence of the present disclosure, and such modifications and combinations still fall within the protection scope of the present disclosure.