Shear zone instability of a 2d periodic Euler flow

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It has been known for over 150 years that a shear flow can become unstable due to microscopic perturbations. The instability manifests itself in waves on water surface, in clouds, in sun’s corona, and in the famous Jupiter’s Red Spot. The traditional approach to study the linear stability of a flow is through the analysis of Euler’s equations of fluid motion. In this paper we present an alternative approach which relies on the mapping of Euler’s equations on an infinite system of interacting vortices. Using this approach we are able to predict the limits of stability of a shear layer of finite width confined to a cylindrical surface. We also predict the wavelength of the most unstable mode and compare it with the results of molecular dynamics simulations.