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The merger of two-dimensional radially stratified high-Froude-number vortices

Published online by Cambridge University Press:  14 June 2007

LAURENT JOLY  and
JEAN N. REINAUD
LAURENT JOLY
Affiliation:
ENSICA, 1 Place Émile Blouin, 31056 Toulouse, France
JEAN N. REINAUD
Affiliation:
Mathematical Institute, University of St Andrews, KY16 9SS, St Andrews, UK
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Abstract

We investigate the influence of density inhomogeneities on the merger of two corotating two-dimensional vortices at infinite Froude number. In this situation, buoyancy effects are negligible, yet density variations still affect the flow by pure inertial effects through the baroclinic torque. We first re-address the effects of a finite Reynolds number on the interaction between two identical Gaussian vortices. Then, by means of direct numerical simulations, we show that vortices transporting light fluid in a heavier counterpart merge from further distances than vortices in a uniform density medium. On the other hand, heavy vortices only merge from small separation distances. We measure the critical distance a/b0 of the vortex radii to their initial separation distance. It departs from the homogeneous threshold of 0.22 in response to increasing density contrasts between the vortices and their surroundings. An analysis of the contribution of the baroclinic vorticity to the dynamics of the flow is detailed and explains the observed behaviour. This analysis is completed by a simple model based on point vortices that mimics the flow. It is concluded that vortices carrying light fluid are more likely to generate large-scale structures than heavy ones in an inhomogeneous fluid.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 582 , 10 July 2007 , pp. 133 - 151
Copyright
Copyright © Cambridge University Press 2007

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