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1.
Analytic stage–discharge formulae are derived for flow in straight trapezoidal channels, based on the 2D analytic velocity distribution in open channels given by Shiono and Knight [Shiono K, Knight DW, Turbulent open-channel flows with variable depth across the channel. J Fluid Mech 1991;222:617–46]. A simple hand-calculation method is provided. Legendre incomplete elliptic integrals of the first and second kinds and a binomial series expansion are used in the derivation of these analytic formulae, together with physically based hydraulic parameters, such as local friction factor (f), dimensionless eddy viscosity (λ) and secondary flow (Γ). The stage–discharge results obtained from the formulae are shown to be in good agreement with experimental data, as are the corresponding analytic velocity and boundary shear stress distributions. The influences of f, λ and Γ on the stage–discharge relationship are also discussed. 相似文献
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This paper presents an approach to modeling the depth-averaged velocity and bed shear stress in compound channels with emergent and submerged vegetation. The depth-averaged equation of vegetated compound channel flow is given by considering the drag force and the blockage effect of vegetation, based on the Shiono and Knight method (1991) [40]. The analytical solution to the transverse variation of depth-averaged velocity is presented, including the effects of bed friction, lateral momentum transfer, secondary flows and drag force due to vegetation. The model is then applied to compound channels with completely vegetated floodplains and with one-line vegetation along the floodplain edge. The modeled results agree well with the available experimental data, indicating that the proposed model is capable of accurately predicting the lateral distributions of depth-averaged velocity and bed shear stress in vegetated compound channels with secondary flows. The secondary flow parameter and dimensionless eddy viscosity are also discussed and analyzed. The study shows that the sign of the secondary flow parameter is determined by the rotational direction of secondary current cells and its value is dependent on the flow depth. In the application of the model, ignoring the secondary flow leads to a large computational error, especially in the non-vegetated main channel. 相似文献
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A Reynolds stress model for the numerical simulation of compound open-channel flows with vegetation on the floodplain is described. The Reynolds stress model consists of various sub-models such as Speziale et al.’s model, Mellor and Herring’s model, and Rotta’s model for the pressure–strain correlation term, the turbulent diffusion term, and the dissipation term, respectively. For validation of the model, plain compound open-channel flows are simulated. The computed results were compared with measured data by [Tominaga A, Nezu I. Turbulent structure in compound open-channel flows. J Hydraul Eng, ASCE 1991;117(1):21–41] and the results show that the Reynolds stress model successfully simulates the mean flow and turbulence structure of plain compound channel flows. The model was then applied to compound open-channel flows with vegetated floodplains. Good agreement between the simulated results and data from an algebraic stress model by [Naot D, Nezu I, Nakagawa H. Hydrodynamic behavior of partly vegetated open channels. J Hydraul Eng, ASCE 1996;122(11):625–33] was found. However, it was shown that the RSM is capable of predicting the velocity dip and lateral shift in the maximum streamwise velocity, which were not observed in the data from algebraic stress modeling. Finally, a depth-averaged analysis of the streamwise momentum equation was performed to investigate the lateral momentum transfer in compound channel flows with vegetated floodplains. Compared with components by the secondary currents and Reynolds stress, the drag force due to the presence of vegetation appears to be a factor in reducing the bottom shear stress in both main channel and floodplain. 相似文献
4.
A three-dimensional, hydrostatic, primitive equation numerical model with modern turbulence closures is used to explore lateral circulation and the associated transport of sediments in idealized, moderately to highly stratified estuaries. The model results suggest that boundary mixing on a sloping bottom can drive a significant amount of lateral circulation. This mechanism has received little attention to date in the estuarine literature. Good agreement with an analytical solution and similar vertical structures of lateral flows to observations from the Hudson River estuary support the importance of the boundary mixing mechanism. Boundary mixing is at least as important as differential advection for the modeled scenarios, when the two mechanisms are evaluated using the salt balance equation for model runs without rotation. Linearly superposing analytical solutions for lagged boundary mixing lateral flow and Ekman-forced lateral flow yields a good representation of the near-bottom lateral flow from the model with rotation. The 2 h lag required for the boundary mixing solution is roughly equal to the vertical diffusion time scale, indicating that lateral flow adjustment depends on development of a bottom mixed layer. Sediment dynamics at cross sections seaward and landward of the salt intrusion are very different. Seaward of the salt intrusion, sediments are eroded in the channel and preferentially deposited on the right slope (looking seaward), mainly due to the combination of high sediment concentration in the channel during flood with strong up-slope transport on that side (tidal pumping). Lateral sediment re-distribution landward of the salt intrusion is negligible due to weak residual lateral circulation. 相似文献
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Turbulent flow in a meandering channel is computed with two Computational Fluid Dynamics (CFD) codes solving the Navier–Stokes equations by employing different turbulence closure approaches. The first CFD code solves the steady Reynolds-Averaged Navier–Stokes equations (RANS) using an isotropic turbulence closure. The second code is based on the concept of Large Eddy Simulation (LES). LES resolves the large-scale turbulence structures in the flow and is known to outperform RANS models in flows in which large-scale structures dominate the statistics. The results obtained from the two codes are compared with experimental data from a physical model study. Both, LES and RANS simulation, predict the primary helical flow pattern in the meander as well as the occurrence of an outer-bank secondary cell. Computed primary as well as secondary flow velocities are in reasonably good agreement with experimental data. Evidence is given that the outer-bank secondary cell in a meander bend is the residual of the main secondary cell of the previous bend. However, the RANS code, regardless of the turbulence model employed, overpredicts the size and strength of the outer-bank secondary cell. Furthermore, only LES is able to uphold the outer-bank second secondary cell beyond the bend apex until the exit of the bend as turbulence anisotropy contributes to its persistence. The presence of multiple secondary cells has important consequences for the distribution of shear stresses along the wetted perimeter of the channel, and thereby the sediment transport in meandering channels. Consequently, even though LES is expected to compute the bed-shear stresses along the wetted perimeter of the channel with a higher degree of accuracy than the RANS model, comparisons between LES and RANS computed wall shear stresses agree well. These findings are useful for practitioners who need to rely on RANS model predictions of the flow in meandering channels at field scale. 相似文献
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Analytical solutions for 2D topography-driven flow in stratified and syncline aquifers 总被引：1，自引：0，他引：1
Two analytical solution methods are presented for regional steady-state groundwater flow in a two-dimensional stratified aquifer cross section where the water table is approximated by the topographic surface. For the first solution, the surficial aquifer is represented as a set of dipping parallel layers with different, but piecewise constant, anisotropic hydraulic conductivities, where the anisotropy is aligned with the dip of the layered formation. The model may be viewed as a generalization of the solutions developed by [Tóth JA. A theoretical analysis of groundwater flows in small drainage basins. J Geophys Res 1963;68(16):4795–812; Freeze R, Witherspoon P. Theoretical analysis of regional groundwater flow 1) analytical and numerical solution to the mathematical model, water resources research. Water Resour Res 1966;2(4):641–56; Selim HM. Water flow through multilayered stratified hillside. Water Resour Res 1975;11:949–57] to an multi-layer aquifer with general anisotropy, layer orientation, and a topographic surface that may intersect multiple layers. The second solution presumes curved (syncline) layer stratification with layer-dependent anisotropy aligned with the polar coordinate system. Both solutions are exact everywhere in the domain except at the topographic surface, where a Dirichlet condition is met in a least-squared sense at a set of control points; the governing equation and no-flow/continuity conditions are met exactly. The solutions are derived and demonstrated on multiple test cases. The error incurred at the location where the layer boundaries intersect the surface is assessed. 相似文献
10.
In a recent work [Valiani A, Caleffi V. Depth–energy and depth–force relationships in open channel flows: analytical findings. Adv Water Resour 2008;31(3):447–54], the authors analytically inverted the depth–specific energy and depth–total force relationships for flows in open channels with wide rectangular cross-sections. 相似文献
11.
A large-eddy simulation study has been undertaken to investigate the turbulent structure of open-channel flow in an asymmetric compound channel. The dynamic sub-grid scale model has been employed in the model, with the partial cell treatment being implemented using a Cartesian grid structure to deal with the floodplain. The numerical model was used to predict the: primary velocity and secondary currents, boundary shear stress, turbulence intensities, turbulent kinetic energy, and Reynolds stresses. These parameters were compared with experimental measurements published in the literature, with relatively close agreement being obtained between both sets of results. Furthermore, instantaneous flow fields and large-scale vortical structures were predicted and are presented herein. These vortical structures were found to be responsible for the significant lateral exchange of mass and momentum in compound channels. 相似文献
12.
In a compound meandering channel, patterns of flow structures and bed variations change with increasing water depth owing to complex momentum exchange between high-velocity flow in a main channel and low-velocity flows in flood plains. We have developed a new quasi-three-dimensional model without the shallow water assumption, i.e., hydrostatic pressure distribution; our method is known as the general bottom velocity computation (BVC) method. In this method, a set of depth-integrated equations, including depth-integrated momentum and vorticity equations, are prepared for evaluating bottom velocity and vertical velocity distributions. The objective of this study is to develop a bed variation calculation method for both single and compound meandering channels by using the BVC method coupled with a sediment transport model. This paper shows that the BVC method can reproduce the pattern change of bed variation in a compound meandering channel flow with increasing relative depth. The variation in sediment transport rate due to overbank flow is explained by experimental and computational results. 相似文献
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Analytical study of the transverse distribution of along-channel and transverse residual flows in tidal estuaries 总被引：2，自引：0，他引：2
We present an analytical model to decompose complex along-channel and transverse residual flows into components induced by individual mechanisms. The model describes the transverse distribution of residual flows in tidally dominated estuaries. Scaling and perturbation techniques are used to obtain analytical solutions for residual flows over arbitrary across-channel bed profiles. The flows are induced by horizontal density gradients, tidal rectification processes, river discharge, wind, channel curvature and the earth's rotation. These rectification processes induce residual flows that are up-estuary to the right and down-estuary to the left of an estuarine channel (looking up-estuary in the northern hemisphere). The tidal rectification processes fundamentally change the transverse structure of along-channel residual flows in many tidal estuaries, as these processes cause the flows to be internally asymmetric about the mid-axis of the channel for relatively large tidal velocities, steep channels or narrow estuaries. In addition, velocity scales are derived from the analytical solutions to estimate the relative importance of the various residual flow mechanisms from estuarine parameters. A case study of a transect across the Upper Chesapeake Bay showed that important features of the residual flow observed in that transect are reproduced and explained by the analytical model. The velocity scales were able to identify the relevant residual flow mechanisms as well. The tidal rectification processes considered here result from advection of along-channel tidal momentum by Coriolis-induced transverse tidal currents. 相似文献
14.
This study is aimed at investigating the vertical velocity profile of flow passing over a vegetal area by an analytical approach. The soil ground is considered as pervious and thus non-zero velocity at the ground surface can be estimated. The soil and vegetation layers are regarded as homogeneous and isotropic porous media. Therefore the solution of the flow can be obtained by applying the theory of turbulent flow and Biot’s theory of poroelasticity after dividing the flow field into three layers: homogenous water, vegetation and pervious soil. The velocity distribution is compared with the experimental data of [Rowiński PM, Kubrak J. A mixing-length model for predicting vertical velocity distribution on flows through emergent vegetation. J Hydrol Sci 2002;47(6):893–904] to show its validity. In addition, five dimensionless parameters denoting the variation of slope, permeability of soil, Reynolds stress, density of vegetation, and relative height of vegetation are proposed to reveal their effects on the surface water flow. The analytical solutions of flow velocity can also be simplified into simpler expressions to describe the flow passing over a non-vegetated area. 相似文献
15.
A 2D depth‐averaged hydrodynamic, sediment transport and bed morphology model named STREMR HySeD is presented. The depth‐averaged sediment transport equations are derived from the 3D dilute, multiphase, flow equations and are incorporated into the hydrodynamic model STREMR. The hydrodynamic model includes a two‐equation turbulence model and a correction for the mean flow due to secondary flows. The suspended sediment load can be subdivided into different size classes using the continuum (two‐fluid) approach; however, only one bed sediment size is used herein. The validation of the model is presented by comparing the suspended sediment transport module against experimental measurements and analytical solutions for the case of equilibrium sediment‐laden in a transition from a rigid bed to a porous bed where re‐suspension of sediment is prevented. On the other hand, the bed‐load sediment transport and bed evolution numerical results are compared against bed equilibrium experimental results for the case of a meander bend. A sensitivity analysis based on the correction for secondary flow on the mean flow including the effect of secondary flow on bed shear stresses direction as well as the downward acceleration effect due to gravity on transverse bed slopes is performed and discussed. In general, acceptable agreement is found when comparing the numerical results obtained with STREMR HySeD against experimental measurements and analytical solutions. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
16.
Abstract The acceptability of zero potential vorticity models as approximations for natural systems of small, but finite, potential vorticity is studied for bounded frontal flows of arbitrary profile. It is demonstrated that all (infinitely) long-wave solutions of the zero potential vorticity front are asymptotic limits for some (not necessarily long-wave) solutions of the small potential vorticity front. In contrast, for downstream-varying solutions there is no simple way of demonstrating this property. These findings suggest that the use of zero potential vorticity models should be carefully examined in other, non-frontal, problems as well. Finally we show that the longwave solutions of the zero potential vorticity flow are at most neutral (quasi-stable). 相似文献
17.
Zhihua Xie 《Ocean Dynamics》2017,67(10):1251-1261
Wind effects on periodic breaking waves in the surf zone have been investigated in this study using a two-phase flow model. The model solves the Reynolds-averaged Navier–Stokes equations with the k ? ?? turbulence model simultaneously for the flows both in the air and water. Both spilling and plunging breakers over a 1:35 sloping beach have been studied under the influence of wind, with a focus during wave breaking. Detailed information of the distribution of wave amplitudes and mean water level, wave-height-to-water-depth ratio, the water surface profiles, velocity, vorticity, and turbulence fields have been presented and discussed. The inclusion of wind alters the air flow structure above water waves, increases the generation of vorticity, and affects the wave shoaling, breaking, overturning, and splash-up processes. Wind increases the water particle velocities and causes water waves to break earlier and seaward, which agrees with the previous experiment. 相似文献
18.
This study numerically investigates effects of cutting riparian vegetation on flow characteristics by using a two-dimensional numerical model. The numerical model is based on depth-averaging the time- and volume-averaged Navier–Stokes equation with turbulent effects determined by the standard k–ε turbulence model. Drag forces exerted by the flow on vegetation are considered by adding source terms into momentum equations. In a rectangular channel and compound channel with vegetation along one side, numerical predictions show are in good agreement with those of previous studies. Five cutting scenarios, including the original, cutting along the main channel side, cutting along the bank side, alternative cutting, and reducing vegetative density, are analyzed in this study. The influences of the cutting scenarios on hydrodynamic behaviors are evaluated via numerical simulations. Simulation results suggest that cutting along the main channel side is the most effective scenario for reducing water depth and flow velocities. 相似文献
19.
This numerical investigation was carried out to advance mechanistic understanding of sediment transport under sheet flow conditions. An Euler–Euler coupled two-phase flow model was developed to simulate fluid–sediment oscillatory sheet flow. Since the concentration of sediment particles is high in such flows, the kinematics of the fluid and sediment phases are strongly coupled. This model includes interaction forces, intergranular stresses and turbulent stress closure. Each phase was modeled via the Reynolds-Averaged Navier–Stokes equations, with interphase momentum conservation accounting for the interaction between the phases. The generation and transformation of turbulence was modeled using the two-equation k–ε turbulence model. Concentration and sediment flux profiles were compared with experimental data for sheet flow conditions considering both symmetric and asymmetric oscillatory flows. Sediment and fluid velocity variations, concentration profiles, sediment flux and turbulence parameters of wave-generated sheet flow were studied numerically with a focus on sediment transport characteristics. In all applications, the model predictions compared well with the experimental data. Unlike previous investigations in which the flow is driven by a horizontal pressure gradient, the present model solves the Navier–Stokes equations under propagating waves. The model’s ability to predict sediment transport under oscillatory sheet flow conditions underscores its potential for understanding the evolution of beach morphology. 相似文献
20.
Nonlinear analysis of two-dimensional steady flows with density stratification in the presence of gravity is considered. Inadequacies of Long's model for steady stratified flow over topography are explored. These include occurrence of closed streamline regions and waves propagating upstream. The usual requirements in Long's model of constant dynamic pressure and constant vertical density gradient in the upstream condition are believed to be the cause of these inadequacies. In this article, we consider a relaxation of these requirements, and also provide a systematic framework to accomplish this. As illustrations of this generalized formulation, exact solutions are given for the following two special flow configurations: the stratified flow over a barrier in an infinite channel; the stratified flow due to a line sink in an infinite channel. These solutions exhibit again closed-streamline regions as well as waves propagating upstream. The persistence of these inadequacies in the generalized Long's model appears to indicate that they are not quite consequences of the assumptions of constant dynamic pressure and constant vertical density gradient in Long's model, contrary to previous belief. On the other hand, solutions admitted by the generalized Long's model show that departures from Long's model become small as the flow becomes more and more supercritical. They provide a nonlinear mechanism for the generation of columnar disturbances upstream of the obstacle and lead in subcritical flows to qualitatively different streamline topological patterns involving saddle points, which may describe the lee-wave-breaking process in subcritical flows and could serve as seats of turbulence in real flows. The occurrences of upstream disturbances in the presence of lee-wave-breaking activity described by the present solution are in accord with the experiments of Long (Long, R.R., “Some aspects of the flow of stratified fluids, Part 3. Continuous density gradients”, Tellus 7, 341--357 (1955)) and Davis (Davis, R.E., “The two-dimensional flow of a stratified fluid over an obstacle”, J. Fluid Mech. 36, 127–143 ()). 相似文献