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Neutral modes of a two-dimensional vortex and their link to persistent cat's eyes
Turner, M. R.
Gilbert, Andrew D.
Bassom, Andrew P.
University of Exeter; University of Western Australia
Physics of Fluids
American Institute of Physics
This paper considers the relaxation of a smooth two-dimensional vortex to axisymmetry after the application of an instantaneous, weak external strain field. In this limit the disturbance decays exponentially in time at a rate that is linked to a pole of the associated linear inviscid problem (known as a Landau pole). As a model of a typical vortex distribution that can give rise to cat's eyes, here distributions are examined that have a basic Gaussian shape but whose profiles have been artificially flattened about some radius rc. A numerical study of the Landau poles for this family of vortices shows that as rc is varied so the decay rate of the disturbance moves smoothly between poles as the decay rates of two Landau poles cross. Cat's eyes that occur in the nonlinear evolution of a vortex lead to an axisymmetric azimuthally averaged profile with an annulus of approximately uniform vorticity, rather like the artificially flattened profiles investigated. Based on the stability of such profiles it is found that finite thickness cat's eyes can persist (i.e., the mean profile has a neutral mode) at two distinct radii, and in the limit of a thin flattened region the result that vanishingly thin cat's eyes only persist at a single radius is recovered. The decay of nonaxisymmetric perturbations to these flattened profiles for larger times is investigated and a comparison made with the result for a Gaussian profile.
Copyright © 2008 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in Physics of Fluids 20 (2008) and may be found at http://link.aip.org/link/?PHFLE6/20/027101/1
20 (2), article 027101