Hydraulic Jump in One-dimensional Flow

Abstract

In the presence of viscosity the hydraulic jump in one dimension is seen to be a first-order transition. A scaling relation for the position of the jump has been determined by applying an averaging technique on the stationary hydrodynamic equations. This gives a linear height profile before the jump, as well as a clear dependence of the magnitude of the jump on the outer boundary condition. The importance of viscosity in the jump formation has been convincingly established, and its physical basis has been understood by a time-dependent analysis of the flow equations. In doing so, a very close correspondence has been revealed between a perturbation equation for the flow rate and the metric of an acoustic white hole. We finally provide experimental support for our heuristically developed theory.