Hydraulic Jump in One-dimensional Flow

TL;DR

This paper investigates the hydraulic jump in one-dimensional viscous flow, establishing a scaling relation, analyzing the role of viscosity, and providing experimental validation, with insights into flow dynamics and analogies to acoustic phenomena.

Contribution

It introduces a new scaling relation for the jump position, highlights the significance of viscosity, and links flow perturbations to acoustic white hole metrics, supported by experiments.

Findings

Viscosity causes the hydraulic jump to be a first-order transition.

A linear height profile is observed before the jump.

Experimental data supports the theoretical model.

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.