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Journal ArticleDOI

Mathematical model development of modified flow dispersion stress tensor in 2-D curvilinear flow domain

TL;DR: In this paper, a modified formulation for flow dispersion stress tensor is proposed to simulate curvilinear flow field in curved flow domain, which can lead to more realistic and improved simulation of flow field.
Abstract: For 2-D simulation of curvilinear flow field, use of momentum equations involves flow dispersion stress terms. Dispersion Stress terms take into account the effect of secondary flow variation arisen due to integration of the product of discrepancy between depth averaged velocity and the true velocity distributions. The objective of this paper is to present empirical mathematical functions to evaluate these terms. These terms can be incorporated in the 2D depth averaged flow equations as an additional source/sink term. In this work, the derivation is done to get revised set of empirical relations are later used in development of enhanced 2D numerical model. When compared with earlier investigations, the proposed formulations are simplified and numerically compatible. It is expected that modified formulation for flow dispersion stress tensor will lead to more realistic and improved simulation of flow field in curved flow domain.
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Journal ArticleDOI
TL;DR: In this article, a hydrodynamic stability analysis of the flow in an alluvial channel in which dunes have developed along the bed is presented, and the model offers an explanation of the fact that some channels tend to meander, others to braid.
Abstract: The paper describes a hydrodynamic stability analysis of the flow in an alluvial channel in which dunes have developed along the bed. The purpose is to develop a mathematical model describing the three-dimensional flow leading to instability of an originally straight channel. The model offers an explanation of the fact that some channels tend to meander, others to braid.

176 citations

Journal ArticleDOI
TL;DR: In this article, the vertical distribution of the secondary flow in a shallow curved channel is derived from a logarithmic main velocity profile, and a numerical method for the computation of the depth-averaged flow field and the bed shear stress (magnitude and direction) is developed.
Abstract: Starting from a logarithmic main velocity profile, the vertical distribution of the secondary flow in a shallow curved channel is derived. The secondary circulation turns out to have one vertical and two horizontal components. The horizontal component in the main flow direction arises from the longitudinal acceleration of the main flow; the transverse horizontal component is due to the curvature of the main flow. In addition, a numerical method for the computation of the depth-averaged flow field and the bed shear stress (magnitude and direction) is developed. This model has great flexibility of allowable channel geometry. Its results agree better with experimental data if the bed is not flat than in case of a flat bed.

168 citations

Journal ArticleDOI
TL;DR: In this paper, the authors presented a mathematical model of the flow in rivers of which: i the depth is small compared with the width, ii the width is small with the radius of curvature, iii the horizontal length scale of the bottom variations is of the order of magnitude of the width.
Abstract: The mathematical model presented describes the flow in rivers of which: i the depth is small compared with the width, ii the width is small compared with the radius of curvature, iii the horizontal length scale of the bottom variations is of the order of magnitude of the width. Within these limits, the channel alignment can be arbitrary and it is not necessary that the width is constant. Furthermore, it is assumed that: iv the flow is mainly friction controlled, v the longitudinal component of the velocity is predominant, vi the Froude number is small. The final set of differential equations accounts for the longitudinal convection (Bernoulli effect), the bottom friction, the flow curvature and the transverse convection of momentum by the secondary flow. The numerical integration procedure is straightforward and requires little computation time. Computational results are presented for a large hydraulic model which fulfills the above conditions.

159 citations

Journal ArticleDOI
TL;DR: In this paper, a steady, two-dimensional model of flow and bed topography in an alluvial channel with variable curvature is presented, where the basis is a steady 2D meander flow and planform development.
Abstract: Meander flow and meanderplanform development are described. The basis is a steady, twodimensional model of flow and bed topography in an alluvial channel with variable curvature. The model is devel...

141 citations

Journal ArticleDOI
TL;DR: In this paper, a depth-averaged two-dimensional hydrodynamic model is developed to simulate the inception and development of channel meandering processes, which is the result of the complex interaction between flow, bed sediment, and bank material.
Abstract: The inception of channel meandering is the result of the complex interaction between flow, bed sediment, and bank material. A depth-averaged two-dimensional hydrodynamic model is developed to simulate the inception and development of channel meandering processes. The sediment transport model calculates both bedload and suspended load assuming equilibrium sediment transport. Bank erosion consists of two interactive processes: basal erosion and bank failure. Basal erosion is calculated from a newly derived equation for the entrainment of sediment particles by hydrodynamic forces. The mass conservation equation, where basal erosion and bank failure are considered source terms, was solved to obtain the rate of bank erosion. The parallel bank failure model was tested with the laboratory experiments of Friedkin on the initiation and evolution processes of non-cohesive meandering channels. The model replicates the downstream translation and lateral extension of meandering loops reasonably well. Plots of meandering planforms illustrate the evolution of sand bars and redistribution of flow momentum in meandering channels. This numerical modelling study demonstrates the potential of depth-integrated two-dimensional models for the simulation of meandering processes. Copyright © 2005 John Wiley & Sons, Ltd.

116 citations