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

Laurent Joly, Jean N. Reinaud

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

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/b(0) 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.

Original languageEnglish
Pages (from-to)133-151
Number of pages19
JournalJournal of Fluid Mechanics
Volume582
DOIs
Publication statusPublished - 10 Jul 2007

Keywords

  • NAVIER-STOKES EQUATIONS
  • VORTEX INTERACTIONS
  • 2 DIMENSIONS
  • DYNAMICS

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