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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    DATTU, H and SUBBIAH, M 2015. On Reynolds stress and neutral azimuthal modes in the stability problem of swirling flows with radius-dependent density. Sadhana, Vol. 40, Issue. 6, p. 1913.


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


    DATTU, H. and SUBBIAH, M. 2015. A NOTE ON THE STABILITY OF SWIRLING FLOWS WITH RADIUS-DEPENDENT DENSITY WITH RESPECT TO INFINITESIMAL AZIMUTHAL DISTURBANCES. The ANZIAM Journal, Vol. 56, Issue. 03, p. 209.


    Jose, Sharath Roy, Anubhab Bale, Rahul and Govindarajan, Rama 2015. Analytical solutions for algebraic growth of disturbances in a stably stratified shear flow. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science, Vol. 471, Issue. 2181, p. 20150267.


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  • Journal of Fluid Mechanics, Volume 679
  • July 2011, pp. 582-615

Stability of a vortex in radial density stratification: role of wave interactions

  • HARISH N. DIXIT (a1) and RAMA GOVINDARAJAN (a1)
  • DOI: http://dx.doi.org/10.1017/jfm.2011.156
  • Published online: 25 May 2011
Abstract

We study the stability of a vortex in an axisymmetric density distribution. It is shown that a light-cored vortex can be unstable in spite of the ‘stable stratification’ of density. Using a model flow consisting of step jumps in vorticity and density, we show that a wave interaction mediated by shear is the mechanism for the instability. The requirement is for the density gradient to be placed outside the vortex core but within the critical radius of the Kelvin mode. Conversely, a heavy-cored vortex, found in other studies to be unstable in the centrifugal Rayleigh–Taylor sense, is stabilized when the density jump is placed in this region. Asymptotic solutions at small Atwood number At show growth rates scaling as At1/3 close to the critical radius, and At1/2 further away. By considering a family of vorticity and density profiles of progressively increasing smoothness, going from a step to a Gaussian, it is shown that sharp gradients are necessary for the instability of the light-cored vortex, consistent with recent work which found Gaussian profiles to be stable. For sharp gradients, it is argued that wave interaction can be supported due to the presence of quasi-modes. Probably for the first time, a quasi-mode which decays exponentially is shown to interact with a neutral wave to give exponential growth in the combined case. We finally study the nonlinear stages using viscous direct numerical simulations. The initial exponential instability of light-cored vortices is arrested due to a restoring centrifugal buoyancy force, leading to stable non-axisymmetric structures, such as a tripolar state for an azimuthal wavenumber of 2. The study is restricted to two dimensions, and neglects gravity.

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Email address for correspondence: rama@jncasr.ac.in
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