The Effect of a Vertical Magnetic Field on Rayleigh-Taylor Instability.

Abstract

Two semi-infinite incompressible fluids of equal kinematic and magnetic viscosities, v, but differing density, Pi, P2, lie at rest in a uniform gravitational field perpendicular to the plane interface between them A uniform vertical magnetic field pervades the system The growth rate, n, of the instabilities which develop when the denser fluid (P2) overlies the lighter fluid (pi) is deduced as a function of k, the horizontal wave number. It is shown that, if the magnetic field is sufficiently strong (more precisely, if the Alfven velocities, V2, V2, are large compared with [p12]'/3, where g is the acceleration due to gravity) n is almost constant for a large range of k; namely, for g/V2 « k V/ . In this range, n g/V2 - g/Vi The magnetic field does not significantly affect the growth rate for either small or large wavelengths.