Internal Hydraulic Jump in Stratified Counterflow

Abstract

Based on a Boussinesq approximation of the governing momentum equations for an internal hydraulic jump in a two-layer counterflow, two important properties of an equal counterflow are demonstrated analytically. Corresponding to a given supercritical upstream state, there can be either two possible downstream conjugate states within the physically realizable range, or none at all. Further, the energy loss criterion across the jump is always satisfied. Consequently, the uniqueness of the downstream state cannot be determined by energy considerations, as done previously for the internal jump in a coflowing stratified flow. Physical arguments, coupled with some experimental observations indicate strongly that the conjugate state closer to the upstream state is the one that will be physically realized. The concept presented herein has been successfully applied to the study of stability and mixing of buoyant discharges in shallow water.