Study of the effect of viscosity and homogeneous horizontal magnetic field on Rayleigh-Taylor instability

Rayleigh-Taylor instability of a heavy fluid supported by a lighter one, in the presence of a homogeneous horizontal magnetic field pervading both the fluids is investigated. These fluids are considered to be incompressible, viscous, and infinitely conducting. In the lower region, z < 0, the density is constant as well as in the upper region, z > 0. The dispersion relation that defines the growth rate sigma, is derived as a function of the physical parameters of the system under the condition k(y)/k(x) = pi and numerically analyzed. It is shown that the horizontal magnetic field helps to stabilize the instability. The growth rate depends on the relation between wave number components, where the instability increases with increasing pi and thereby the role of horizontal magnetic field gradually declines.