Rayleigh-Taylor Instability of a Viscous Electrically Conducting Fluid in the Presence of a Horizontal Magnetic Field

Abstract

This paper discusses the initial manner of development of an infinitesimal disturbance of a plane horizontal layer of a viscous, perfectly conducting, incompressible fluid of variable density in the presence of a horizontal magnetic field. It is found that when the coeffient of viscosity μ₀ (which is a function of the vertical co-ordinate z) be such that d²μ₀⁄dz²<0, instability might arise in the form of oscillation with increasing amplitude i. e., overstability. This shows that contrary to the usual role of viscosity as a damping factor, it may sometimes act as a destabilising agent. Furthermore, it is seen that a sufficiently strong magnetic field may stabilise a potentially unstable configuration.