On vortex rings impacting a sharply-stratified interface

Abstract

This thesis presents an investigation into the dynamics of vortex rings impacting a sharply-stratified density interface. This problem has a long history and is important for understanding how individual eddies in stratified turbulence mix the density field. We tackle this problem using a combination of experimental, numerical and modelling techniques to understand the flow instability and subsequent mixing induced by the impinging vortex ring. Our findings demonstrate that there exists a critical Richardson number, corresponding to a mixing transition, beyond which the mixing efficiency is constant.

Using a novel Stereo Particle Image Velocimetry (Stereo-PIV) technique, we analyze a series of vortex ring experiments. By amalgamating an ensemble of these experiments, we measure the full, time-resolved, three-dimensional velocity field of the vortex-ring interaction. These measurements capture the instability that is produced on the baroclinically generated vorticity field. This instability is identified as a Crow-like instability. At low Richardson numbers, the timescale of the interface rebound is faster than that of the instability. As a result, there exists a critical Richardson number below which the Crow-like instability will not have sufficient time to grow to large amplitude.

By generating a large number of vortex-ring interactions, we measure the incremental change to the stratification. After an initialization period, there is strong evidence to suggest that the mixing due to each vortex ring becomes constant over a moderate range of Richardson numbers. We suggest that the mixing efficiency of the vortex rings does drop at low Richardson numbers (below unity) in agreement with the analysis of the Stereo-PIV measurements. A model of the system accurately predicts the dependence of the mixing rate on the Richardson number.

Based upon our study of the vortex-ring system, we construct a one-dimensional turbulence model that includes the energy advection from the vortex rings. This model is validated with both physical experiments and numerical simulations of repeated vortex-ring generations. The constant mixing efficiency regime is recovered in all three methodologies.

Through examining the detailed dynamics of the flow, this work suggests that there exists a critical Richardson number corresponding to a transition between mixing regimes, and that this critical Richardson number is a result of the growth of a Crow-like instability. We have highlighted how to improve current mixing-models to capture this physics. New avenues of future research are currently underway to study the mixing produced by a stratified mixing-box experiment in light of these new developments.