Continuous hydraulic jumps in laminar channel flow

Abstract

On the basis of the generalized Saint-Venant equations, hydraulic jumps in laminar open channel flow are obtained as continuous shock structures. They arise as stable stationary solutions of the governing equations and are particularly well suited for a dynamical systems analysis, where they manifest themselves as near-parabolic trajectories in phase space. We derive an analytic approximate expression for the jump length as a function of the Froude and effective Reynolds numbers, reflecting the fact that-along with inertia-gravity and viscous diffusion both contribute to the balance of forces that shape the jump. The stability of the jumps is confirmed by means of a numerical experiment and an analysis of the propagation and attenuation of small perturbations.