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Three-dimensional visualization of the interaction of a vortex ring with a stratified interface

Published online by Cambridge University Press:  10 May 2017

Jason Olsthoorn Open the ORCID record for Jason Olsthoorn [Opens in a new window]  and
Stuart B. Dalziel
Jason Olsthoorn*
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Centre for Mathematical Sciences, Wilberforce Road, Cambridge, CB3 0WA, UK
Stuart B. Dalziel
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Centre for Mathematical Sciences, Wilberforce Road, Cambridge, CB3 0WA, UK
*
†Email address for correspondence: jason.olsthoorn@cantab.net
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Abstract

The study of vortex-ring-induced stratified mixing has long played a key role in understanding externally forced stratified turbulent mixing. While several studies have investigated the dynamical evolution of such a system, this study presents an experimental investigation of the mechanical evolution of these vortex rings, including the stratification-modified three-dimensional instability. The aim of this paper is to understand how vortex rings induce mixing of the density field. We begin with a discussion of the Reynolds and Richardson number dependence of the vortex-ring interaction using two-dimensional particle image velocimetry measurements. Then, through the use of modern imaging techniques, we reconstruct from an experiment the full three-dimensional time-resolved velocity field of a vortex ring interacting with a stratified interface. This work agrees with many of the previous two-dimensional experimental studies, while providing insight into the three-dimensional instabilities of the system. Observations indicate that the three-dimensional instability has a similar wavenumber to that found for the unstratified vortex-ring instability at later times. We determine that the time scale associated with this instability growth has an inverse Richardson number dependence. Thus, the time scale associated with the instability is different from the time scale of interface recovery, possibly explaining the significant drop in mixing efficiency at low Richardson numbers. The structure of the underlying instability is a simple displacement mode of the vorticity field.

JFM classification

Geophysical and Geological Flows: Stratified flows Vortex Flows: Vortex instability
Type
Papers
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Journal of Fluid Mechanics , Volume 820 , 10 June 2017 , pp. 549 - 579
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© 2017 Cambridge University Press 

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