Mathematical analysis of long-wave breaking on open channels with bottom friction

In this paper we study the breaking of long waves propagating along an open channel with linear friction on the bottom. The equations governing the wa ve propagation consist of a pair of first-order nonlinear hyperbolic partia l differential equations (PDEs). We first transformed the PDEs into a pair of ordinary differential equations (ODEs) along the characteristic directio ns by means of a pair of Riemann invariants. By analyzing the ODEs, we foun d that the breaking of waves can be identified by the singularity of the de rivative of the Riemann invariants. Thus, we derived an analytical solution for the derivative of the Riemann invariants. Then, a breaking criterion a nd an analytical formula for the estimation of breaking time were developed and validated through numerical experiments. It is also shown in the paper that the present model includes the previous model neglecting bottom frict ion as a special case. (C) 1999 Elsevier Science Ltd. All rights reserved.