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

The common feature of sheared flows of an ideal fluid and plasma in magnetic field is the Kelvin-Helmholtz instability. This instability is described by identical equations in mentioned two cases. The wave equation for the eigenmodes in the plasma obtained by the kinetic method in the long-wave limit coincides with the Rayleigh equation known for an ideal fluid. Velocity profile with a transition layer of finite width is considered. Odd modes are investigated. Localized velocity shear layer is the source of perturbations propagating beyond the transition layer. The conditions of localization of the modes are studied.