A viscous magnetohydrodynamic Kelvin–Helmholtz instability in the interface of two fluid layers: Part I. Basic mechanism

Abstract

This study investigates the combined effect of density, velocity and magnetic field gradients on the Kelvin–Helmholtz instability of two viscous fluid layers. For the linear phase of instability that refers to the early stage of development of Kelvin–Helmholtz instability, the linear growth rate and frequency are presented. With respect to our selected variables and the Atwood number, the behaviour of growth rate and frequency are analysed. It is found that, the behaviour of frequency is not affected by the magnetic field and viscous term. The velocity gradient with the small Atwood numbers tends to stabilize KHI flows, while the velocity gradient with the large Atwood numbers has destabilizing effect on KHI. The growth rate reduces with the constant magnetic field and viscous term, while it enhances with magnetic field gradient.