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The common feature of sheared flows of an ideal fluid and plasma in magneticfield is the Kelvin-Helmholtz instability. This instability is described byidentical equations in mentioned two cases. The wave equation for theeigenmodes in the plasma obtained by the kinetic method in the long-wave limitcoincides with the Rayleigh equation known for an ideal fluid. Velocity profilewith a transition layer of finite width is considered. Odd modes areinvestigated. Localized velocity shear layer is the source of perturbationspropagating beyond the transition layer. The conditions of localization of themodes are studied.

Odd modes of Kelvin-Helmholtz instability in sheared flows of plasmas and fluids