Rayleigh-Taylor instability with a sheared flow boundary layer

S. Chandrasekhar, in his book, Hydrodynamic and Hydromagnetic Stability (New York: Dover, 1961), derives the stability criteria for a semi-infinite uniform density incompressible inviscid fluid with uniform horizontal velocity supported in a gravitational field by one of higher density and opposite velocity. A transitional layer of inviscid fluid with a density equal to the average of the upper and lower fluids, and a horizontal velocity that varies linearly with depth from that of the upper fluid at the top to that of the lower fluid at the bottom is assumed. This analysis of the Kevin-Helmholtz (K-H) instability may be transformed into a model of the effect of such a velocity sheared boundary layer on the Rayleigh-Taylor (R-T) instability of modes with wave numbers in the direction of the sheared velocity by reversing the sign of the top-bottom density differential. Orthogonal modes are unaffected by the shear in the linear limit and are, therefore, R-T unstable unless an independent mechanism for their stabilization is present, such as a magnetic field orthogonal to the sheared velocity. The combined R-T/K-H stability analysis is, therefore, expected to be most applicable for magnetically accelerated media such as a Z pinch with an axial velocity sheared outer layer orthogonal to the outer azimuthal magnetic field which drives the implosion.