The kinematics of stratified mixing through internal wavebreaking

Abstract

The evolution of an internal wavebreaking event in a continuous stable stratification is examined using schlieren colour imagery combined with streak photography. For standing but strongly interacting wavemodes forced to breaking, the Richardson number defined by local gradients of density and velocity is critically low only in the immediate vicinity of the breaking region where convective overturning also occurs. Breaking and vertical mixing results from the rapid development of three-dimensional interleaving density microstructure within a confined volume which persists and gravitates to modify weakly the surrounding density distribution. Continual mixing through internal motion is seen as a widespread repetition of such events.Based on the observations, a general description of the process is proposed and applied in two types of simple kinematical model to provide an estimate of ‘mixing efficiency’, the ratio of potential energy gained through stratification weakening to kinetic energy expended in motions on the scales of the mixing event. These models do not rely on an assumed similarity between momentum and buoyancy transfer. They yield, for complete homogenization of small discrete volumes, an efficiency of ¼ in a linear stratification. Mixing across a density interface is predicted to have a lower efficiency, and lower efficiency is expected where homogenization is incomplete.