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    Swaminathan, Rohith V. Ravichandran, S. Perlekar, Prasad and Govindarajan, Rama 2016. Dynamics of circular arrangements of vorticity in two dimensions. Physical Review E, Vol. 94, Issue. 1,

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    Dixit, Harish N. and Govindarajan, Rama 2013. Effect of density stratification on vortex merger. Physics of Fluids, Vol. 25, Issue. 1, p. 016601.

  • Journal of Fluid Mechanics, Volume 646
  • March 2010, pp. 415-439

Vortex-induced instabilities and accelerated collapse due to inertial effects of density stratification

  • DOI:
  • Published online: 09 February 2010

A vortex placed at a density interface winds it into an ever-tighter spiral. We show that this results in a combination of a centrifugal Rayleigh–Taylor (CRT) instability and a spiral Kelvin–Helmholtz (SKH) type of instability. The SKH instability arises because the density interface is not exactly circular, and dominates at large times. Our analytical study of an inviscid idealized problem illustrates the origin and nature of the instabilities. In particular, the SKH is shown to grow slightly faster than exponentially. The predicted form lends itself for checking by a large computation. From a viscous stability analysis using a finite-cored vortex, it is found that the dominant azimuthal wavenumber is smaller for lower Reynolds number. At higher Reynolds numbers, disturbances subject to the combined CRT and SKH instabilities grow rapidly, on the inertial time scale, while the flow stabilizes at low Reynolds numbers. Our direct numerical simulations are in good agreement with these studies in the initial stages, after which nonlinearities take over. At Atwood numbers of 0.1 or more, and a Reynolds number of 6000 or greater, both stability analysis and simulations show a rapid destabilization. The result is an erosion of the core, and breakdown into a turbulence-like state. In studies at low Atwood numbers, the effect of density on the inertial terms is often ignored, and the density field behaves like a passive scalar in the absence of gravity. The present study shows that such treatment is unjustified in the vicinity of a vortex, even for small changes in density when the density stratification is across a thin layer. The study would have relevance to any high-Péclet-number flow where a vortex is in the vicinity of a density-stratified interface.

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L. Coquart , D. Sipp & L. Jacquin 2005 Mixing induced by Rayleigh–Taylor instability in a vortex. Phys. Fluids 17, 021703.

S. C. Crow 1970 Stability theory for a pair of trailing vortices. AIAA J. 8, 21722179.

R. E. Duff , F. H. Harlow & C. W. Hirt 1962 Effects of diffusion on interface instability between gases. Phys. Fluids 5, 417425.

P. Flohr & J. C. Vassilicos 1997 Accelerated scalar dissipation in a vortex. J. Fluid Mech. 348, 295317.

A. E. Gill 1982 Atmosphere–Ocean Dynamics. Academic Press.

T. Itano 2004 Stability of an elliptic flow with a horizontal axis under stable stratification. Phys. Fluids 16, 11641167.

Ch. Josserand & M. Rossi 2007 The merging of two co-rotating vortices: a numerical study. Eur. J. Mech. B Fluids 26, 779794.

R. R. Kerswell 2002 Elliptical instability. Annu. Rev. Fluid Mech. 34, 83113.

M. R. Khorrami , M. R. Malik & R. L. Ash 1989 Application of spectral collocation techniques to the stability of swirling flows. J. Comput. Phys. 81, 206229.

S. Leibovich 1969 Stability of density stratified rotating flows. AIAA J. 7, 177178.

T. Miyazaki & Y. Fukumoto 1992 Three dimensional instability of strained vortices in a stably stratified fluid. Phys. Fluids A 4, 25152522.

A. H. Neilsen , X. He , J. J. Rasmussen & T. Bohr 1996 Vortex merging and spectral cascade in two-dimensional flows. Phys. Fluids 8, 22632265.

J. Reinaud , L. Joly & P. Chassaing 2000 The baroclinic secondary instability of the two-dimensional shear layer. Phys. Fluids 12, 24892505.

P. M. Saunders 1973 The instability of a baroclinic vortex. J. Phys. Oceanogr. 3, 6165.

E. Villermaux 1998 On the role of viscosity in shear instabilities. Phys. Fluids 10, 368373.

C. S. Yih 1961 Dual role of viscosity in the instability of revolving fluids of variable density. Phys. Fluids 4, 806811.

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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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