Diffuse-boundary Rayleigh-Taylor instability

For density profiles, N (y), making a smooth transition from N (-infinity) = 0 to N ( + infinity) = const with dlnN/dy decreasing monotonically with y, it is shown that the Rayleigh-Taylor instability exhibits essentially different behavior above and below a certain critical wave number, k/sub c/. For k > k/sub c/ the growth of the response to an initial perturbation is slower than exponential, approx. t/sup -1/2/ exp(..gamma../sub b/t). For k < k/sub c/ and unstable eigenmode (analogous to that in the sharp boundary case) exists, and purely exponential growth occurs.