Simulation of main flow and secondary flow in a curved open channel

Abstract

Knowledge of the secondary flow is essential for predictions about the morphology of alluvial bottoms in tidal channels. In this research the determination of the secondary flow is based on a known depth averaged velocity field. The depth averaged velocities must be computed with a high accuracy in order to make possible a reasonable determination of the secondary flow. The depth averaged velocities are computed from the shallow water equations. These equations are solved by means of an implicit finite difference method of the ADI-type. The reproduction of the depth averaged flow with the generally used partly explicit ADI-method appeared not to be usabIe for the flow in tidal channels, because of a large diffusion coefficient, required to obtain stability. In this report a fully implicit ADI-method is considered. The simulation of the steady flow in a curved flume with the geometrical proportions of a river is compared to measurements. The reproduction of the depth averaged velocity field is satisfactory. A disturbance connected with the irregular numerical representation of the sidewalls will be much smaller in a tidal channel. The secondary flow, assumed fully developed, is computed, based on this depth averaged velocity, and compared to the measurements. The agreement is reasonable, especially when the narrowness of the flume and the connected severe influence of the disturbances at the sidewalls on the radius of curvature of the flow is considered.