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1.
V. P. Singh 《水文研究》1995,9(7):783-796
Error equations for the kinematic wave and diffusion wave approximations with lateral inflow neglected in the momentum equation are derived under simplified conditions for space-independent flows. These equations specify error as a function of time in the flow hydrograph. The kinematic wave, diffusion wave and dynamic wave solutions are parameterized through a dimensionless parameter γ which is dependent on the initial conditions. This parameter reflects the effect of initial flow depth, channel-bed slope, lateral inflow, infiltration and channel roughness when the initial condition is non-vanishing; it reflects the effect of bed slope, channel roughness and acceleration due to gravity when the initial condition is vanishing. The error equations are found to be the Riccati equation. The structure of the error equations in the case when the momentum equation neglects lateral inflow is different from that when the lateral inflow is included. 相似文献
2.
V. P. Singh 《水文研究》1995,9(1):1-18
Error equations for the kinematic wave and diffusion wave approximations were derived under simplified conditions for space-independent flows occurring on infiltrating planes or channels. These equations specify error as a function of time in the flow hydrograph. The kinematic wave, diffusion wave and dynamic wave solutions were parameterized through a dimensionless parameter γ which is dependent on the initial conditions. This parameter reflects the effect of initial flow depth, channel bed slope, lateral inflow and channel roughness when the initial condition is non-vanishing; it reflects the effect of bed slope, channel roughness, lateral inflow and infiltration when the initial condition is vanishing. The error equations were found to be the Riccati equation. 相似文献
3.
V. P. Singh 《水文研究》1994,8(4):311-326
Error equations for the kinematic wave and diffusion wave approximations with lateral inflow neglected in the momentum equation are derived under simplified conditions for space-independent flows. These equations specify error as a function of time in the flow hydrograph. The kinematic wave, diffusion wave and dynamic wave solutions are parameterized through a dimensionless parameter γ which is dependent on the initial conditions. This parameter reflects the effect of initial flow depth, channel-bed slope, lateral inflow and channel roughness when the initial condition is non-vanishing; and it reflects the effect of bed slope, channel roughness and acceleration due to gravity when the initial condition is vanishing. The error equations are found to be the Riccati equation. The structure of the error equations in the case when the momentum equation neglects lateral inflow is different from that when the lateral inflow is included. 相似文献
4.
Error equations for kinematic wave and diffusion wave approximations were derived for time‐independent flows on infiltrating planes and channels under one upstream boundary and two downstream boundary conditions: zero flow at the upstream boundary, and critical flow depth and zero depth gradient at the downstream boundary. These equations specify error in the flow hydrograph as a function of space. The diffusion wave approximation was found to be in excellent agreement with the dynamic wave approximation, with errors below 2% for values of KF (e.g. KF ≥ 7·5), where K is the kinematic wave number and F is the Froude number. Even for small values of KF (e.g. KF = 2·5), the errors were typically less than 3%. The accuracy of the diffusive approximation was greatly influenced by the downstream boundary condition. For critical flow depth downstream boundary condition, the error of the kinematic wave approximation was found to be less than 10% for KF ≥ 7·5 and greater than 20% for smaller values of KF. This error increased with strong downstream boundary control. The analytical solution of the diffusion wave approximation is adequate only for small values of K. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
5.
V. P. SINGH 《水文研究》1996,10(7):955-969
Error equations for the kinematic-wave and diffusion-wave approximations were derived under simplified conditions for space-independent flows occurring on infiltrating planes or channels. These equations specify error as a function of time in the flow hydrograph. The kinematic-wave, diffusion wave and dynamic-wave solutions were parameterized through a dimensionless parameter γ which is dependent on the initial conditions. This parameter reflects the effect of initial flow depth, channel-bed slope, lateral inflow and channel roughness when the initial condition is non-vanishing; and it reflects the effect of bed slope, channel roughness, lateral inflow and infiltration when the initial condition is vanishing. The error equations were found to be the Riccati equation. 相似文献
6.
Errors in the kinematic wave and diffusion wave approximation for time-independent (or steady-state) cases of channel flow with infiltration were derived for three types of boundary conditions: zero flow at the upstream end, and critical flow depth and zero depth gradient at the downstream end. The diffusion wave approximation was found to be in excellent agreement with the dynamic wave approximation, with errors of less than 1·4% for KF20≥7·5, and up to 14% for KF20≤0·75 for the upstream boundary condition of zero discharge and finite depth, where K is the kinematic wave number and F0 is the Froude number. The kinematic wave approximation was reasonably accurate except at the channel boundaries and for small values of KF20 (≤1). The accuracy of these approximations was significantly influenced by the downstream boundary, both in terms of the magnitude of the error and the segment of the channel reach for which these approximations would be applicable. © 1998 John Wiley & Sons, Ltd. 相似文献
7.
Errors in the kinematic wave and diffusion wave approximation for time-independent (or steady-state) cases of channel flow with momentum exchange included were derived for three types of boundary conditions: zero flow at the upstream end, and critical flow depth and zero depth gradient at the downstream end. The diffusion wave approximation was found to be in excellent agreement with the dynamic wave approximation, with errors of less than 1% for KF20≥7·5 and up to 12% for KF20≤0·75 for the upstream boundary condition of zero discharge and finite depth, where K is the kinematic wave number and F0 is the Froude number. The kinematic wave approximation was reasonably accurate except at the channel boundaries and for small values of KF20 (≤1). The accuracy of these approximations was significantly influenced by the downstream boundary condition both in terms of the error magnitude and the segment of the channel reach for which these approximations would be applicable. © 1997 by John Wiley & Sons, Ltd. 相似文献
8.
Errors in the kinematic wave and diffusion wave approximations for time-independent (or steady-state) cases of channel flow were derived for three types of boundary conditions: zero flow at the upstream end, and critical flow depth and zero depth gradient at the downstream end. The diffusion wave approximation was found to be in excellent agreement with the dynamic wave approximation, with errors in the range 1–2% for values of KF (? 7.5), where K is the kinematic wave number and F0 is the Froude number. Even for small values of KF (e.g. KF20 = 0.75), the errors were typically less than 15%. The accuracy of the diffusion wave approximation was greatly influenced by the downstream boundary condition. The error of the kinematic wave approximation was found to be less than 13% in the region 0.1 ? x ? 0.95 for KF = 7.5 and was greater than 30% for smaller values of KF (? 0.75). This error increased with strong downstream boundary control. 相似文献
9.
The behaviour of river waves is described using a simplified dimensionless form of the momentum equation in conjunction with the continuity equation. Three dimensionless parameters were derived based on a quantitative linear analysis. These parameters, which depend on the Froude number of the steady uniform flow and the geometric characteristics of the river, permit quantification of the influence of inertia and pressure in the momentum equation. It was found that dynamic and diffusion waves occur mainly on gentle channel slopes and the transition between them is characterized by the Froude number. On the other hand, the kinematic wave has a wide range of applications. If the channel slope is greater than 1%, the kinematic wave is particularly suitable for describing the hydraulics of flow. Since slopes in natural channel networks are often greater than 1%, an analytical solution of the linearized kinematic wave equation with lateral inflow uniformly distributed along the channel is desirable and was therefore derived. The analytical solution was then implemented in a channel routing module of an existing simple rainfall–runoff model. The results obtained using the analytical solution compared well with those obtained from a non‐linear kinematic wave model. Copyright © 2000 John Wiley & Sons, Ltd. 相似文献
10.
The kinematic‐wave and diffusive‐wave approximations were investigated for unsteady overland flow resulting from spatially varying rainfall excess. Three types of boundary conditions were adopted: zero flow at the upstream end, and critical flow and zero depth‐gradient at the downstream end. Errors were derived by comparing the dimensionless profiles of the flow depth over the plane with those computed from the dynamic‐wave solution. It was found that the mean errors for both the approximations were independent of the type of rainfall excess distribution for KF02 > 5, where K is the kinematic‐wave number and F0 is the Froude number. Therefore, the regions (KF02, F0) where the kinematic‐wave and diffusive‐wave solutions would be fairly accurate and for any distribution of spatially varying rainfall, were characterized. The kinematic‐wave approximation was reasonably accurate, with a mean error of less than 5% and for the critical depth at the downstream end, for KF02 ≥ 20 with F0 ≤ 1; if the rainfall excess was concentrated in a portion of the plane, the field where the kinematic‐wave solution was found accurate, it was more limited and characterized for KF02 > 35 with F0 ≤ 1. The diffusive‐wave solution was in good agreement with the dynamic‐wave solution with a mean error of less than 5%, in the flow depth, for KF02 ≥ 15 with F0 ≤ 1; for rainfall excess concentrated in a portion of the plane, the accuracy of the diffusion wave solution was in a region more restricted and defined for KF02 ≥ 30 with F0 ≤ 1. For zero‐depth gradient at the downstream end, the accuracy field of the kinematic‐wave was found to be greater and characterized for KF02 > 10 with F0 ≤ 1; for rainfall excess concentrated in a portion of the plane, the region was smaller and defined for KF02 > 15 with F0 ≤ 1. The diffusive‐wave solution was found accurate in the region defined for KF02 > 7·5, whereas for rainfall excess concentrated in a portion of the plane, the field of accuracy was for KF02 > 12·5 with F0 ≤ 1. The lower limits of the regions, defined on KF02, can be considered generally valid for both approximations, but for F0 < 1 smaller lower limits were also characterized. Finally, the accuracy of these approximations was influenced significantly by the downstream boundary condition. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献
11.
地下岩石的速度各向异性影响地震波的传播与成像.横向各向同性(TI)介质为最普遍的等效各向异性模型.引入TI介质拟声波方程可以避免复杂的弹性波方程求解以及各向异性介质波场分离,以满足对纵波成像的实际需要.本文从垂直横向各向同性(VTI)介质弹性波方程出发,推导出正应力表达的拟声波方程以及相应的纵波分量的表达式,进而分析从频散关系得到的拟声波方程的物理意义,而后将拟声波方程扩展到更一般的倾斜横向各向同性(TTI)介质中.波前快照与群速度平面的对比验证了拟声波方程可以很好地近似描述qP波的运动学特征.在此基础上,将拟声波方程应用在逆时偏移中并与其特例声波近似方程进行对比,讨论了计算效率、稳定性等实际问题.数值试验表明VTI介质情况下采用声波近似方程可以提高计算效率,而TTI介质qP-qSV波方程则在效率相当的情况下可以保证稳定性.SEG/HESS模型和逆冲模型逆时偏移试验验证了本文TI介质拟声波方程的实用性. 相似文献
12.
J. H. Daluz Vieira 《Journal of Hydrology》1983,60(1-4):43-58
The solutions of the Saint-Vénant equations are compared with those of the kinematic, diffusion and gravity wave approximations, for a range of constant Froudé and kinematic wave numbers, with two different lower boundary conditions: (1) critical flow; and (2) zero depth gradient. For each lower boundary condition, zones are defined in the F0,k-field in which either kinematic, diffusion or gravity wave solutions may be used to approximate the full Saint-Vénant solutions. 相似文献
13.
《Advances in water resources》2003,26(11):1189-1198
A two-dimensional finite element based overland flow model was developed and used to study the accuracy and stability of three numerical schemes and watershed parameter aggregation error. The conventional consistent finite element scheme results in oscillations for certain time step ranges. The lumped and the upwind finite element schemes are tested as alternatives to the consistent scheme. The upwind scheme did not improve on the stability or the accuracy of the solution, while the lumped scheme provided stable and accurate solutions for time steps twice the size of time steps needed for the consistent scheme. A new accuracy based dynamic time step estimate for the two-dimensional overland flow kinematic wave solution is developed for the lumped scheme. The newly developed dynamic time step estimates are functions of the mesh size, and time of concentration of the watershed hydrograph. Due to lack of analytical solutions, the time step was developed by comparing numerical solutions of various levels of discretization to a reference solution using a very fine mesh and a very small time step. The time step criteria were tested on a different set of problems and proved to be adequate for accurate and stable solutions. A sensitivity analysis for the watershed slope, Manning’s roughness coefficient and excess rainfall rate was conducted in order to test the effect of parameter aggregation on the stability and accuracy of the solution. The results of this analysis show that aggregation of the slope data resulted in the highest error. The roughness coefficient had a smaller effect on the solution while the rainfall intensity did not show any significant effect on the flow rate solution for the range of rainfall intensity used. This work pioneers the challenge of providing guidelines for accurate and stable numerical solutions of the two-dimensional kinematic wave equations for overland flow. 相似文献
14.
15.
Vijay P. Singh 《水文研究》2002,16(17):3437-3466
Using kinematic wave equations, analytical solutions are derived for flow resulting from storms moving either up or down the plane and covering it fully or partially. By comparing the flow resulting from a moving storm with that from a stationary storm of the same duration and areal coverage, the influence of storm duration, direction and areal coverage is investigated. It is found that the direction, duration and areal coverage of storm movement have a pronounced effect on the discharge hydrograph. The runoff hydrographs resulting from storms moving downstream are quite different from those from storms moving upstream. Likewise, the areal coverage of the storm has a pronounced effect on the runoff hydrograph. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献
16.
V. P. Singh 《水文研究》2002,16(7):1479-1511
Using kinematic wave equations, analytical solutions are derived for flow due to a storm moving up or down an infiltrating plane and covering it completely. The storm duration is assumed in two ways. First, the plane is covered everywhere for the same duration by the storm. Second, the plane is covered in a linearly decreasing manner from the beginning of its coverage of the plane to the other end of the plane. By comparing the flow due to this storm with that due to a stationary storm of the same duration, the influence of storm duration, direction and velocity on flow hydrograph is investigated. It is found that storm movement has a pronounced effect on runoff hydrograph. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献
17.
V. P. Singh 《水文研究》1998,12(1):147-170
Using kinematic wave equations, analytical solutions are derived for flow owing to storms moving up and down a plane. By comparing the flow owing to a moving storm with that to an equivalent stationary storm, the influence of storm direction is investigated. The direction of storm movement exercises a significant influence on the peak flow and time to peak flow, as well as the shape of the overland flow hydrograph. © 1998 John Wiley & Sons, Ltd. 相似文献
18.
V. P. Singh 《水文研究》2005,19(4):969-992
Using kinematic wave equations analytical solutions are derived for flow resulting from a storm moving either up or down an infiltrating plane but not fully covering it. By comparing the flow resulting from this storm with that from a stationary storm of the same duration the influence of storm duration, direction and velocity is investigated. It is found that the direction of storm movement, duration and velocity of storms, as well as basin infiltration, have a pronounced effect on the discharge hydrograph. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
19.
The concept of a spatially distributed unit hydrograph is based on the fact that the unit hydrograph can be derived from the time–area curve of a watershed by the S-curve method. The time–area diagram is a graph of cumulative drainage area contributing to discharge at the watershed outlet within a specified time of travel. Accurate determination of the time–area diagram is made possible by using a GIS. The GIS is used to describe the connectivity of the links in the watershed flow network and to calculate distances and travel times to the watershed outlet for various points within the watershed. Overland flow travel times are calculated by the kinematic wave equation for time to equilibrium; channel flow times are based on the Manning and continuity equations. To account for channel storage, travel times for channel reaches are increased by a percentage depending on the channel reach length and geometry. With GIS capability for rainfall mapping, the assumption of a uniform spatial rainfall distribution is no longer necessary; hence the term, spatially distributed unit hydrograph. An example of the application for the Waiparous Creek in the Alberta Foothills is given. IDRISI is used to develop a simple digital elevation model of the 229 km2 watershed, using 1 km × 1 km grid cells. A grid of flow directions is developed and used to create an equivalent channel network. Excess rainfall for each 1 km × 1 km cell is individually computed by the Soil Conservation Service (SCS) runoff curve method and routed through the equivalent channel network to obtain the time–area curve. The derived unit hydrograph gave excellent results in simulating an observed flood hydrograph. The distributed unit hydrograph is no longer a lumped model, since it accounts for internal distribution of rainfall and runoff. It is derived for a watershed without the need for observed rainfall and discharge data, because it is essentially a geomorphoclimatic approach. As such, it allows the derivation of watershed responses (hydrographs) to inputs of various magnitudes, thus eliminating the assumption of proportionality of input and output if needed. The superposition of outputs is retained in simulating flood hydrographs by convolution, since it has been shown that some non-linear systems satisfy the principle of superposition. The distributed unit hydrograph appears to be a very promising rainfall runoff model based on GIS technology. 相似文献
20.
This study investigates divering overland flow utilizing kinematic wave theory, which does not appear to have been dealt with previously. Explicit analytical solutions are derived in dimensionless form for space-time invariant rainfall. Analytical solutions do not seem to be tractable for time-varying rainfall. Depending upon the duration of rainfall, equilibrium and partial equilibrium cases are distinguished explicitly. The effect of divergence parameter on the hydrograph shape is shown. The adequacy of kinematic approximation for characterization of diverging overland flow is tested against laboratory watershed results. The diverging overland flow model is found to yield results which compare well with observations and with those of a plane model. 相似文献