ACCURACY OF KINEMATIC WAVE AND DIFFUSION WAVE APPROXIMATIONS FOR TIME-INDEPENDENT FLOW WITH MOMENTUM EXCHANGE INCLUDED

Abstract

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.