Finite amplitude Kelvin–Helmholtz instability in magnetic fluids

Abstract

A weakly nonlinear theory of Kelvin–Helmholtz instability for magnetic fluids is presented. The method used is that of multiple scales. The equations governing the evolution of the amplitude are derived when the difference U between the velocities of the two fluids is less than or equal to the critical velocity Uc. It is shown that for subcriticial values of U the wave train of constant amplitude is unstable against modulations whereas for the supercritical values the instability is governed by a nonlinear Klein–Gordon equation. From the latter equation, the various stability criteria are obtained.