  Rayleigh-Taylor instability occurs when a heavier fluid overlies a lighter
fluid, and the two seek to exchange positions under the effect of gravity. We
present linearized theory for arbitrary 3D initial disturbances that grow in
time, and calculate the evolution of the interface for early times. A new
spectral method is introduced for the fully 3D non-linear problem in a
Boussinesq fluid, where the interface between the light and heavy fluid is
approximated with a smooth but rapid density change in the fluid. The results
of large-scale numerical calculation are presented in fully 3D geometry,
compared and contrasted with the early-time linearized theory.
