Development of a three-dimensional numerical model to solve shallow-water equations in compound channels

Abstract

Velocity gradient between main channel and flood plains in compound channels leads to the formation of a large shear layer and secondary currents between these two subsections. These phenomena in the interaction region bring about a complex three-dimensional nature of the flow in compound channels. To cope with these flows, many numerical investigations have utilized three-dimensional formulations with advanced turbulence models. However, the free surface in many of these models is fixed and rigid-lid assumption has been used. In the present research, three-dimensional shallow water equations were used to calculate the flow field in compound channels. Three-dimensional equations were integrated in layers and were combined with the continuity equation. In this formulation, free-surface elevation was calculated without the need to solve any additional equations. Velocity and bed shear stress distribution and the stage–discharge relationship in compound channels with smooth and rough beds and with different relative depths were analyzed to verify this model, and satisfactory results were obtained.