J. Fluid Mech. (2010), vol. 646, pp. 415–439. c  Cambridge University Press 2010 doi:10.1017/S0022112009992515 415 Vortex-induced instabilities and accelerated collapse due to inertial effects of density stratification HARISH N DIXIT AND RAMA GOVINDARAJAN† Engineering Mechanics Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore 560064, India (Received 1 October 2008; revised 29 September 2009; 30 September 2009; first published online 9 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-P´ eclet-number flow where a vortex is in the vicinity of a density-stratified interface. 1. Introduction Vortical structures are subject to instabilities of various kinds, a common cause for the instability being the existence of other vortical structures in the neighbourhood. The Crow instability (Crow 1970) for a counter-rotating vortex pair of small core is well known. Vortices of finite core, rendered non-axisymmetric (often elliptic) by the strain field of their neighbours, are then unstable to shorter wavelength disturbances (see e.g. Kerswell 2002). Miyazaki & Fukumoto (1992) and Itano (2004) studied the effect of stratification of density perpendicular to the vortex axis on these elliptical instabilities. Both found that stratification suppresses the elliptical † Email address for correspondence: rama@jncasr.ac.in