Forward and reverse modeling of the three‐dimensional viscous Rayleigh‐Taylor instability

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Abstract
A combined finite‐difference/spectral method is used to model the 3D viscous Rayleigh‐Taylor instability. Numerically calculated growth rate spectra are presented for an initial sinusoidal perturbation of the interface separating two fluids with amplitude 10−3H and 0.2H, where H is the height of the system. At small initial amplitude, growth rate spectra closely follow linear theory, whereas the calculation with higher initial amplitude shows wavelength selection towards 3D perturbations. Numerical simulations and analytical theory are used to evaluate the applicability of previous 2D numerical models, which is shown to depend on (1) the wavelength and amplitude of an initially 2D sinusoidal perturbation and (2) the amplitude of background noise. It is also shown that reverse (backward) modeling is capable of restoring the initial geometry as long as overhangs are not developed. If overhangs are present, the possibility of restoring the initial conditions is largely dependent on the stage of overhang development.