On Zero-Inertia and Kinematic Waves

Small perturbation analysis of the linearized open-channel flow equations leads to the conclusion that zero-inertia waves propagate in the downstream direction only with a speed equal to that of kinematic waves. In addition, such an analysis indicates that kinematic waves travel with no attentuation in amplitude. In this work, it is shown both by theory and nonlinear numerical experiments that zero-inertia waves propagate both in the downstream and upstream direction. In fact, the zero-inertia wave characteristics are horizontal lines, and the problem requires two-point boundary data, which extends the applicability of zero-inertia models to cases of great practical interest. It is also shown the nonlinear kinematic-wave characteristics are inclined relative to each other and that they may intersect to create a kinematic shock. This shock is always present in wave motion on a dry bed and leads to significant subsidence of the depth and discharge in the flow behind it, a behavior which is not due to amplitude attentuation, as in the case of dynamic waves. Merely it is due to a consequence of the presence of the kinematic-shock front.