CN114357905B - River vegetation area flow velocity and turbulence vertical distribution along-path prediction method under influence of real morphological vegetation - Google Patents
River vegetation area flow velocity and turbulence vertical distribution along-path prediction method under influence of real morphological vegetation Download PDFInfo
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Abstract
The invention discloses a vertical distribution along-path prediction method of flow velocity and turbulence energy of a river vegetation region under the influence of real form vegetation, which is based on a real reed form vegetation region, a water depth average flow velocity, vertical flow velocity and turbulence energy prediction model is constructed, the flow velocity and turbulence energy of a river with real vegetation can be predicted point by point along the cross section of the river, and the river vegetation region has important theoretical value and application prospect for developing river evolution under the effect of vegetation. The vegetation area cross section average flow velocity longitudinal distribution model constructed by the method is an exponential decay function, can meet the rule of hydrodynamic decay, and the vegetation area cross section water depth average flow velocity and turbulence energy distribution obtained by the prediction method is closer to the real flow velocity distribution.
Description
Technical Field
The invention belongs to the field of hydraulics and river dynamics, relates to prediction of flow velocity and turbulence of a non-submerged vegetation zone, and particularly relates to prediction of flow velocity and turbulence of a vegetation zone in a river channel with true morphological vegetation (such as reed).
Background
Aquatic vegetation is widely found in natural rivers, streams, marshes and coastal areas. The vegetation changes the water flow structure and affects the form of the river bed, and is an important component in the river ecosystem. The drag force of vegetation increases resistance, reduces flow rate, but increases turbulence. Compared with a vegetation-free zone, the flow velocity of the vegetation zone is obviously reduced due to vegetation resistance, and sediment deposition is promoted. Meanwhile, wake vortexes generated by vegetation increase turbulence energy, so that sediment re-suspension and sediment bed load re-starting are promoted. The opposite effect of vegetation to river sediment transport leads to the prediction difficulty of the evolution trend of the vegetation area river bed to be increased. Because of the important role of vegetation in the river bed evolution, the influence of vegetation on water flow characteristics is researched, and particularly, the along-way change rule of the vertical distribution of the flow velocity and the turbulence energy of a vegetation area is needed to be researched.
In the prior vegetation area flow velocity and turbulence prediction method, a rigid cylinder is generally adopted to simulate vegetation, and the flow change inside and outside a vegetation area of a model is concerned. Because the vegetation produces extra drag force, the front end of the vegetation zone generates water flow transverse deflection, so that the speed of the vegetation zone is reduced along the path, and the speed of the adjacent vegetation-free zone is increased along the path. The distance at which the flow velocity decreases from the forefront of the vegetation zone to a constant inside the vegetation zone is defined as the vegetation internal water flow regulating zone length L d. The vegetation internal water flow regulating zone length L d is related to the vegetation density C d a and the vegetation zone width b: wherein C d is the drag coefficient, and a d is the water blocking area of vegetation in the unit water body.
On the rear side of the vegetation interior water flow regulation zone (x > L d), the flow speed and the turbulence are not changed any more, and the water flow is fully developed in the zone. For the x > L d region, if the shear layer is strong enough, kelvin-Helmholtz (KH) vortices start to form along the vegetation zone sides. In the fully developed area of water flow, the critical conditions for KH vortex generation are as follows: Wherein U bare and U veg are respectively the water flow stabilizing speeds of the vegetation-free area and the vegetation area of the river channel, and the stabilizing speeds can be determined by the measured speed transverse distribution. When KH vortex is formed, the vortex can penetrate through the edge of the vegetation zone to enter the vegetation zone, and the penetration distance of the vortex is delta p. KH vortices only affect the flow velocity and turbulence over the penetration distance. In the range that the vegetation area b-delta p is more than or equal to 0, the flow speed and the turbulence energy are not influenced by KH vortex, and the technology is used for obtaining the vertical distribution prediction of the water flow speed and the turbulence energy in the area not influenced by KH vortex.
In a vegetation zone consisting of vegetation in a real form, no technology can realize the along-path prediction of the vertical distribution of the flow velocity and the turbulence energy of the vegetation zone at present. The invention takes reed vegetation with a real form as a research object, provides an along-path prediction method for vertical distribution of flow velocity and turbulence energy of a reed vegetation area, fills the blank of a prediction technology for the flow velocity and turbulence energy of the real form vegetation area, and provides a theoretical basis for further developing river evolution research under the action of vegetation.
Disclosure of Invention
Aiming at the technical situation that the flow velocity and the turbulence distribution of a vegetation area with a real shape are difficult to predict in the prior art, the invention aims to provide an along-path prediction method for the vertical distribution of water flow and turbulence, and the prediction of the flow velocity and the turbulence of the vegetation area with the real shape (such as a reed area) is realized.
The invention is suitable for the working conditions that the water flow velocity of the river is greater than 0cm/s and vegetation is under a non-submerged condition, so that the water flow change can be considered to be two-dimensional, namely only in the water flow direction and the transverse direction (the direction perpendicular to the water flow). In the invention, x and y are respectively denoted as the water flow direction and the transverse direction.
To achieve the above object, the present invention is achieved by the following techniques.
The idea of the invention is as follows: the invention aims at the non-submerged vegetation coverage area of the river channel. Based on reed river channel, analyzing the water depth average flow velocity along the path distribution in the river channel, determining the vertical flow velocity distribution at different positions by using the water depth average flow velocity and vegetation form at different positions along the path, and determining the vertical turbulence energy distribution based on the vertical flow velocity distribution at the points.
The invention provides a river vegetation area flow velocity distribution along-path prediction method under the influence of true morphological vegetation, which comprises the following steps:
s1, obtaining the water depth average flow velocity U d according to the following formula:
Wherein U d(f) is the average flow velocity of water depth in the vegetation interior water fully developed area (x > L d); l d(1) is the e-exponential decay length of vegetation region U d, and L d(1) can be predicted from the relationship of L d(1)＝0.3Ld (Liu et al 2020), where e-exponential decay length is the length of the factor e-exponential decay amount; u d(0) is the water depth average flow rate of the vegetation zone leading edge (x=0);
s2, obtaining the vertical distribution of the flow velocity of each x position of the vegetation zone according to the following formula according to the average flow velocity of the water depth:
In the method, in the process of the invention, A d is the average water blocking area of the water depth, a d =na/H, a is the total water blocking area of the single plant vegetation,A (z) is the vertical variation of the water blocking area of the single plant vegetation (namely the partial water blocking area of the single plant vegetation), and the partial water blocking area of the single plant is determined by the vegetation form; a (z) is the unit water local water blocking area, a (z) = n A (z), and n is the vegetation area unit water vegetation quantity.
In the step S1, the average water depth flow rate of the water flow fully developed area inside the non-submerged vegetation is U d(f), which can be predicted by the following formula:
Wherein g is gravitational acceleration; h is the water depth; s is water surface slope drop; c f is the friction coefficient of the bed layer; c d is the drag coefficient (typically considered as C d =1); phi is the volume percentage of vegetation in the water body of the vegetation zone unit. Firstly, determining the volume of single plant vegetation by using a measuring cylinder and vegetation in combination with a drainage method, and taking the drainage volume of the single plant vegetation in the water body with the same depth unit of a river channel as the volume of the single plant vegetation; then, multiplying the vegetation density n (representing the number of vegetation in the water body of the vegetation zone) by the volume of the single plant vegetation to obtain the total volume of all the vegetation in the water body of the vegetation zone; and finally, dividing the total volume of all vegetation in the unit water body by the volume of the unit water body to obtain the vegetation volume percentage phi.
In the step S1, the water depth average flow rate at the front end (x=0) of the vegetation area is predicted according to the following formula (3):
wherein U 0 is the average river flow rate, and is obtained by measurement.
Equations (1) through (3) have been demonstrated to predict the water depth average flow velocity along the course of a simulated vegetation area (vegetation simulated by a rigid cylinder). However, plants of natural morphology (e.g., reed) have a more complex morphology in the vertical direction (z-direction) than rigid cylinders, and the present invention fully considers the effect of true morphological vegetation on flow rate.
In the step S2, the flow velocity vertical distribution of the non-submerged vegetation area of the river is obtained by the following method:
(1) In the vegetation zone with real shape, the drag force generated by the single plant vegetation can pass through the total water blocking area The water depth average flow rate U d and the water depth average drag coefficient C d(1) are estimated:
(2) The drag force generated by the single plant vegetation can be calculated by integrating the vertical variation A (z) of the water blocking area and the vertical local flow rate U (z):
(3) According to the previous study, assuming that the vertical z-position drag coefficient C d(2) in equation (5) remains unchanged in the vertical direction, equations (4) and (5) are equal, resulting in:
The water depth can be expressed as In the vegetation unit density n region, the depth average water blocking area is defined as a d =na/H, and the local water blocking area is defined as a (z) = n A (z).
Drag coefficients C d(1) and C d(2) are linearly related: Is a ratio parameter. According to the former study, C d(2) can be calculated by the following formula:
Reynolds number of vegetation Can be calculated by the water depth average flow velocity U d and the vegetation equivalent diameter d e (=a/H), η is the water flow viscosity coefficient (η=0.01 cm 2/s). Thus, bringing C d(1)＝βCd(2) into equation (6) yields equation (8):
In the method, in the process of the invention,
And (3) substituting the predicted average water depth speed U d at any x position according to the formula (1) into the formula (8) to predict the vertical flow velocity distribution of any x position of the vegetation area.
The invention further provides a method for predicting the turbulence vertical distribution along the vegetation area of a river under the influence of real morphological vegetation, which comprises the following steps:
And (3) obtaining the vertical turbulence energy distribution of the non-submerged vegetation area according to the vertical flow velocity distribution obtained in the step (S2) and the following formula:
Wherein γ 2 =2.9±0.2 is an empirical constant; l t (z) is the vortex length. For true-form vegetation, below the leaf growth range, l t (z) is equal to the vegetation trunk diameter (i.e., l t (z) =d); over the blade growth range, l t (z) is equal to the blade width. l t (z) can be determined by vegetation morphology. Phi (z) is the vertical variation of the volume percentage of vegetation in the vegetation zone unit water body.
Compared with the prior art, the invention has the following beneficial effects:
At present, no along-path prediction method for vertical distribution of vegetation area flow velocity and turbulence energy in a vegetation river channel in a real form exists, and the method has the following beneficial effects:
1. In nature, natural aquatic vegetation is small in root area, large in stem and leaf area, obvious in vertical water blocking area difference of the vegetation, and cannot be generalized simply by using a cylinder; the natural vegetation is in a natural form of wide stem and leaf and thin root, so that the vegetation root area has small water blocking area and high water flow speed, the near-bottom flow speed is far greater than the vertical average flow speed, and the near-bottom turbulence energy is greater than the vertical average turbulence energy; the prediction method provided by the invention can predict the flow velocity and turbulence energy vertical distribution of the vegetation area of the river with the vegetation in real form point by point along the cross section of the river, and provides an important theoretical basis for researching the evolution rule of the river bed under the vegetation effect.
2. According to the river channel flow velocity and turbulence energy prediction method, the constructed vegetation area water depth average flow velocity longitudinal distribution model is an exponential decay function, so that a hydrodynamic decay rule is met, and the vegetation area water depth average flow velocity longitudinal distribution obtained by the prediction method is closer to the real flow velocity distribution.
3. According to the river channel flow velocity prediction method provided by the invention, the flow velocity measurement is not required to be carried out, and the flow velocity and turbulence distribution of the vegetation region in the river channel with the real form vegetation can be predicted only according to the basic parameters (including the average flow velocity of the river channel, the width of the vegetation region, the vegetation density, the vegetation drag coefficient, the river channel bed surface resistance coefficient and the like) of the river channel and the vegetation. The invention can reduce the research cost, is suitable for river channel areas inconvenient for workers to reach, and has very wide applicability and universality.
Drawings
FIG. 1 is a schematic view showing the vertical distribution of reed structure and water blocking area with real form; wherein, (a) is a single reed photo taken under a white background; (b) Calculating the vertical local water-blocking area distribution A (z) (cm 2/cm) of the single reed, wherein error bars represent the variation ranges of three different single reeds under four different angles; (c) The vertical local vortex length l t (z) of the single reed is set, and error bars represent the variation ranges of three different single reeds under four different angles; (d) The vegetation at different z positions under the conditions of phi=0.005 and 0.019 accounts for the volume percent phi (z); (e) For the generalized distribution diagram of the water tank on the top of the reed canopy, gray points represent the vegetation positions, cross symbols represent ADV measurement positions, and the transverse distance between two rows is dy.
FIG. 2 is a graph showing the comparison of predicted value (solid line) and measured value (black open circle) of the water depth average flow velocity U d in the reed area of the river course; (a) Working condition 1, H=20cm, n=80 plants/m 2; (b) Working condition 2, h=20cm, n=280 strains/m 2; (c) Working condition 3, h=30 cm, n=80 plants/m 2; (d) Working condition 4, h=30 cm, n=280 strains/m 2; the dashed lines represent the predicted value uncertainties corresponding to the change in values of U d(.)、Cd(1) and L d(1).
FIG. 3 is a graph showing the comparison of predicted values (solid lines) and measured values (black open circles) of the vertical distribution U (z) of the flow velocity in the reed area of the river channel; the dashed lines represent the predicted value uncertainties corresponding to the changes in the values of U d, a (z), and a d.
FIG. 4 is a graph showing the comparison of predicted value (solid line) and measured value (black open circle) of turbulence energy vertical distribution k t (z) in a reed area of a river channel; the dashed lines represent the predicted value uncertainties corresponding to the changes in values of γ, U (z), l t (z), and a (z).
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by one of ordinary skill in the art without undue burden on the person of ordinary skill in the art based on the embodiments of the present invention, are within the scope of the present invention.
Examples
The embodiment is used for describing the flow velocity and turbulence energy prediction result of the non-submerged reed area in the reed river channel with the real form obtained through the water tank test in detail.
① Purpose of test
And measuring the flow velocity and the turbulence vertical distribution of different x positions in the reed river channel with the real form through a water tank test, and selecting part of working conditions to measure the flow velocity and the turbulence vertical distribution. And determining the vertical distribution of the flow velocity and the turbulence energy of the reed area of the river under different water depths and different vegetation densities, and obtaining an actual measurement value. The actual measured flow velocity and turbulence and the flow velocity and turbulence data obtained by the method are compared to verify the accuracy of the flow velocity and turbulence distribution prediction method in the reed river channel with the real form.
② Test equipment
The main equipment is shown in table 1 below.
Table 1 test device with reed water tank in real form
③ Test conditions
The embodiment performs experiments under four different working conditions (different water depths, flow rates and vegetation densities) so as to verify the effectiveness of the prediction method provided by the invention. As shown in FIG. 1 (e), the test was conducted in a circulating water tank having a length of 13 m and a width of 1m, and the water tank test section was 7 m long. The vegetation area is composed of plastic reeds with real forms, and the reeds are arranged in a staggered way and fixed on a pre-drilled PVC bottom plate. The PVC plate covers the entire riverbed and has a surface friction coefficient C f =0.005. The series of experiments considered two plant densities: n=280 and 80 strains/m 2. For vegetation of n=280 plants/m 2, a vegetation area length of 3m is arranged, and for vegetation of n=80 plants/m 2, a vegetation area length of 4.4m is arranged. In all working conditions, the reed area width is b=33 cm. The flow of the water tank upstream is measured by an electronic flowmeter, and the water depth is measured by two flowmeters fixed at the front end and the tail of a vegetation area. The test considers two water depths, H=20 and 30cm, corresponding to average river flow rates U 0 =11.5 and 17cm/s, and U 0 is measured at the front end of the vegetation zone, which is not affected by vegetation. In all cases, the Reynolds number of the river channel isAnd 31900, wherein η is the viscosity coefficient of the water flow, here 0.01cm 2/s, R is the hydraulic radius, and the range of Re indicates that the water flow is turbulent; froude number ofAnd 0.1, which indicates that the water flow is slow.
The plastic reed with the real shape used in the present embodiment is shown in fig. 1 (a).
The vertical partial water blocking area A (z) of the single plant vegetation is obtained by the following method: firstly, placing a single reed in a white background for photographing, converting the photo into black and white (wherein the background is completely converted into white), and identifying the water blocking width of the reed at a local vertical position at intervals of 1cm according to the relation between the pixels of the photo and the real length, wherein the water blocking width of the reed is multiplied by the interval of 1cm to obtain the local water blocking area of a corresponding region; then, carrying out the above treatment on three randomly selected single reeds at four different angles to obtain the vertical distribution of the local water blocking areas of the three reeds at different angles; and finally, averaging all the water blocking areas of the obtained three reeds, calculating the standard deviation of the water blocking areas of each point, and finally obtaining the local water blocking area vertical distribution of the reeds. The vertical distribution of the vertical partial water blocking area A (z) of the single plant vegetation is shown in the figure 1 (b). It can be seen that the vertical local water blocking area of the single plant vegetation gradually changes along the vertical direction, especially at the position of 5-15 cm, the change of A (z) is larger. The total water blocking area A can be obtained by summing the local water blocking areas A (z) obtained at each interval, and the calculation results are shown in table 1.
The vertical vortex length distribution l t (z) is obtained by the following method: under the growth range of the leaves, l t (z) takes the average value of the diameters of the main stems of three different single-plant reeds under four different angles (namely, takes the average value of the diameters of the main stems of the three different single-plant reeds under four different angles as the diameter of the vegetation main stems); in the growth range of the leaf, l t (z) is taken as the average value of all leaf widths of three different single-plant reeds at four different angles (namely, the average value of all leaf widths at four different angles of the corresponding height is taken as the z-position leaf width), and the statistical result is shown in fig. 1 (c).
The specific measurement of phi is that for each working condition, a measuring cylinder and vegetation are combined with a drainage method to determine the volume of single plant vegetation, and the drainage volume of the single plant vegetation in the water body with the same depth unit as that of the river channel under each working condition is used as the volume of the single plant vegetation; then, multiplying the vegetation density n (representing the number of vegetation in the water body of the vegetation zone) by the volume of the single plant vegetation to obtain the total volume of all the vegetation in the water body of the vegetation zone; finally, dividing the total volume of all vegetation in the unit water body by the volume of the unit water body to obtain the vegetation volume percentage phi, wherein the calculation result is shown in table 1.
The specific measurement of phi (z) is that for any working condition, the volume of the single plant vegetation is determined by combining a measuring cylinder and vegetation with a drainage method, and the drainage volume variation of the single plant vegetation in a unit water body with a given depth interval (1 cm) at the vertical z position is taken as the volume variation of the single plant vegetation; then, multiplying the vegetation density n (representing the number of vegetation in the water body of the vegetation zone) by the volume change of the single plant vegetation to obtain the total volume change of all the vegetation in the water body of the vegetation zone; finally, the total volume change of all vegetation in a unit water body is divided by the unit water body volume of a given depth interval to obtain the vegetation percentage (z), and the statistical result is shown in fig. 1 (d).
Water depth average flow velocity, flow velocity and turbulence vertical distribution measurement
The coordinates x, y and z are longitudinal, transverse and vertical, respectively. x=0 is a vegetation area start position; y=0 is the right wall of the river channel and z=0 is the surface of the river bed (fig. 1 c). The Nortek Vectrino profiler was mounted on the positioning system of the sink and the probe was moved in the x, y and z directions. Vectrino flowmeters the flowrates at different longitudinal positions z=3 cm were acquired. The instantaneous flow rate was measured at 50Hz for 150s at each measurement point. The raw flow rate data with correlation greater than 70% and signal to noise ratio less than 12 is filtered, processed using the methods Gorning and Nikora (2002) and the resulting instantaneous velocity (Goring,D.G.,Nikora,V.I.,2002.Despiking acoustic Doppler velocimeter data.Journal of Hydraulic Engineering,128(1),117–126). at each station decomposes each measured instantaneous velocity (u, v, w) into a time-averaged velocityAnd a pulsating flow rate (u ', v ', w '), the definition of the turbulence k being as follows:
0 is measured at three lateral positions (at the cross symbol in fig. 1 (e)) near the characteristic region of the centerline of the vegetation zone, i.e., y=12, 14 and 16cm, resulting in a vertical distribution of the average velocity and the average turbulence of the characteristic region. Measuring the water depth average flow velocity of a location And turbulent energyThe difference between the average flow velocity and the average turbulence energy of the vegetation area is less than 3 percent and 8 percent respectively. This shows that the characteristic area flow velocity and turbulence average value can reasonably reflect the average flow velocity and turbulence of the vegetation area cross section. The water depth average flow velocity measurement at each location is defined asWhere U (z) is the water depth and flow velocity measurement at each location, the length of the vegetation internal water flow regulating zoneEstimated and summarized in table 1. In the two vegetation sparse working conditions (n=80 plants/m 2), the vegetation region length (=4.4 m) is shorter than the vegetation inner water flow adjustment region length L d (=5.1 and 5.9 m), so that the water flow of the whole vegetation region is adjusted, and the water flow is not fully developed. In contrast, in the two conditions where the vegetation density is high (n=280 plants/m 2), the vegetation region length (=3m) is longer than the vegetation internal water flow regulating region length L d (=2.2 and 2.4 m), resulting in a vegetation internal water flow regulating region (x < L d) and a water flow full development region (x Σ d). In vegetation areas, the flow rate reduction occurs mainly in the vegetation internal water flow regulation zone (x < L d), and therefore the flow rate vertical profile U (z) is measured mainly in the vegetation internal water flow regulation zone. Specifically, in condition 1 (n=80 strains/m 2, h=20 cm), the flow rates were measured at x= 30,140,250,320 and 380 cm; In operating mode 2 (n=280 strains/m 2, h=20 cm), the flow rates were measured at x=50, 90, 140, 180 and 245 cm; in regime 3 (n=80 strains/m 2, h=30 cm), the flow rates were measured at x=64, 180, 213, 280 and 355 cm; in operating mode 4 (n=280 strains/m 2, h=30 cm), the flow rates were measured at x=25, 78, 108, 160 and 230 cm. Wherein x=245 cm in the working condition 2 and x=230 cm in the working condition 4 are positioned in a water flow fully-developed area, and other measuring positions are positioned in a water flow adjusting area inside vegetation, and the design aims at verifying the vertical distribution of the flow velocity and the turbulence at different positions of the vegetation area.
(II) vertical distribution prediction of Water depth average flow velocity, flow velocity and turbulence
The method provided by the invention can be used for obtaining the along-way change of the flow velocity and turbulence vertical distribution of the vegetation area in the reed river channel with a real form:
(1) Predicting longitudinal flow velocity distribution
The invention fully considers the complex forms of reed, and firstly provides a method for predicting the average flow velocity of water depth of a reed area with a real form.
In the fully developed area of water flow in reed, the prediction method of the water depth average flow velocity U d(f) is as follows:
wherein g is the gravitational acceleration; h is the water depth; s is water surface slope drop; c f is the bed friction coefficient; c d is the drag coefficient, here taken as 1.U d(0) is the average flow velocity of water depth at the front end of vegetation zone (x=0), using the formula And (5) predicting.
The water depth average flow velocity U d along the reed zone can be predicted by the following formula:
wherein U d(f) is the average flow velocity of water depth in the zone of sufficient development of water flow (x > L d) in vegetation; l d(1) is the e-exponential decay length of the vegetation region U d, L d(1) can be predicted by the relationship of L d(1)＝0.3Ld (Liu et al 2020); u 0 is the average flow velocity of the river; u d(0) is the water depth average flow rate at the front end of the vegetation zone (x=0).
(2) Predicting flow velocity vertical distribution
As previously described, the vertical flow velocity profile for each x-position within the vegetation zone is predicted by the following equation:
In the method, in the process of the invention, Beta can be determined by calculation from the water depth H, vegetation morphology (a d and a (z)).
(3) Vertical distribution of predicted turbulence energy
As previously described, the turbulence vertical distribution of each x position of the vegetation zone is predicted by the following formula:
(III) analysis of test results
For quantitative comparison of predicted and measured values, root Mean Square Error (RMSE) is defined as:
Where N is the number of measurements and X p and X m are the predictions and measurements, respectively, of the present invention.
Based on the four sets of operating condition data, the predicted water depth average flow velocity U d, the flow velocity vertical distribution U (z) and the turbulence energy vertical distribution k t (z) are compared with the measured flow velocity and the turbulence energy of the water tank test, as shown in fig. 2,3 and 4 respectively. As can be seen from the figure, the predicted water depth average flow velocity, the vertical flow velocity distribution and the vertical turbulence distribution are all well matched with the measured value.
The test condition calculation parameters are summarized in table 1.
Table 1 summary of calculated parameters for each experimental condition
In Table 1, U 0 is the average river flow rate; h is the water depth; n is the plant density per unit area of the vegetation zone; a is the total water blocking area of a single plant; a d (= n A/H) is a vegetation area depth average water blocking area; phi refers to the volume fraction of vegetation in a unit water body in a vegetation zone, and the volume of a single plant is determined by a drainage method (Archimedes principle); l d is the length of the vegetation internal water flow regulating zone; l is the vegetation zone length.
The water-blocking area of reed is not uniform in the vertical direction and varies along the vertical direction. The prediction method provided by the invention is used for respectively estimating the water depth average flow velocity of the vegetation inner water flow adjustment area and the water flow full development area and the water depth average velocity of the front end of the vegetation area. The root mean square error between the longitudinal distribution of the predicted water depth average flow velocity and the measured value in 4 working conditions is err=11% no matter in sparse and dense vegetation areas, which shows that the predicted value and the measured value of the invention have good matching effect (figure 2).
Substituting predicted average water depth flow rate U d intoTo predict the local vertical flow velocity U (z) at each x position. Inside the vegetation zone, whether in the water flow adjustment zone (x < L d) or the water flow full development zone (x is greater than or equal to L d), the root mean square error between the vertical distribution predicted value and the measured value of all working condition flow rates is ERR=26%. The error value of the vertical flow rate is acceptable. Note that the present model further predicts the flow velocity vertical distribution using the predicted water depth average flow velocity U d; if measurement U d is used, the root mean square error is reduced to 19% and the predicted and measured flow velocity vertical profiles are compared in FIG. 3. In summary, the invention provides a prediction method for vertical distribution of flow velocities at different x positions of a vegetation area based on local water depth average flow velocity and vegetation water blocking area.
Based on the predicted vertical distribution of flow velocity, the vertical distribution of turbulence energy can be obtained byAnd (5) predicting. For sparse and dense vegetation, FIG. 4 compares the predicted and measured turbulence vertical distributions, and the predicted turbulence (solid line) changes vertically, which is consistent with the measured value (circle) in the uncertainty range, indicating that the method provided by the invention can predict the turbulence vertical distribution inside the vegetation in real form.
Those of ordinary skill in the art will recognize that the embodiments described herein are for the purpose of aiding the reader in understanding the principles of the present invention and should be understood that the scope of the invention is not limited to such specific statements and embodiments. Those of ordinary skill in the art can make various other specific modifications and combinations from the teachings of the present disclosure without departing from the spirit thereof, and such modifications and combinations remain within the scope of the present disclosure.
Claims (4)
1. The river vegetation area flow velocity along-path prediction method under the influence of the true morphological vegetation is characterized by comprising the following steps:
s1, obtaining the water depth average flow velocity U d according to the following formula:
Wherein x is the water flow direction, U d(f) is the average water depth flow velocity of the vegetation inner water flow fully developed area x > L d; l d(1) is the e exponential decay length of the vegetation region U d, and L d(1) can be predicted by the relation of L d(1)＝0.3Ld; l d is the length of the vegetation internal water flow regulating zone, U d(0) is the water depth average flow rate of the vegetation zone leading edge x=0;
S2, according to the water depth average flow velocity, obtaining the vertical flow velocity distribution of each x position in the vegetation canopy according to the following formula:
In the method, in the process of the invention, H is water depth, a d is depth average water blocking area, z is vertical direction, a d =na/H, n is vegetation density, a is total water blocking area of single plant vegetation,A (z) is the vertical variation of the water blocking area of the single plant vegetation; a (z) is a partial water blocking area, a (z) = n A (z).
2. The method for predicting the flow velocity along the vegetation area of a river under the influence of a true morphological vegetation according to claim 1, wherein in step S1, the average water depth flow velocity U d(f) of the water flow fully developed area inside the non-submerged vegetation is predicted by the following formula:
Wherein g is gravitational acceleration; h is the water depth; s is water surface slope drop; c f is the friction coefficient of the bed layer, C d is the drag coefficient, and phi is the volume percentage of vegetation in the vegetation zone unit water body.
3. The method for predicting the flow velocity along the vegetation zone of a river under the influence of a true morphological vegetation according to claim 1, wherein the average flow velocity of the water depth at the front end of the vegetation zone is predicted according to the following formula:
Wherein U 0 is the average river flow velocity, C d is the drag coefficient, and b is the vegetation zone width.
4. A method for predicting turbulence vertical distribution along path of a river vegetation area under the influence of real morphological vegetation is characterized by comprising the following steps:
A vertical flow velocity distribution U (z) obtained by a river vegetation region flow velocity prediction method under the influence of the true morphological vegetation according to any one of claims 1 to 3, wherein the vertical turbulence distribution of the non-submerged vegetation region is obtained according to the following formula:
Wherein γ 2 =2.9±0.2 is an empirical constant; l t is the vortex length; for true morphological vegetation, l t (z) is equal to the diameter of the vegetation main rod below the leaf growth range; in the growth range of the blade, l t (z) is equal to the width of the blade, C d(2) is the drag coefficient at the vertical z position, a (z) is the local water blocking area, and phi (z) is the vertical variation of the volume percentage of vegetation in the vegetation zone unit water body.
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