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

TL;DR

This paper investigates odd eigenmodes of Kelvin-Helmholtz instability in sheared plasma and fluid flows, revealing their localization properties and common underlying equations.

Contribution

It identifies and analyzes odd modes of Kelvin-Helmholtz instability in both plasma and fluid flows, highlighting their similar mathematical descriptions.

Findings

Odd modes are localized near shear layers.

The wave equations for plasma and fluid cases are identical.

Conditions for mode localization are established.

Abstract

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.