Energy transfer in Rayleigh-Taylor instability

The spatial structure and energy budget for Rayleigh-Taylor instability are examined using results from a $512\times 512\times 2040$ point direct numerical simulation. The outer-scale Reynolds number of the flow follows a rough $t^3$ power law and reaches a final value of about 5500. Taylor microscales and Reynolds numbers are plotted to characterize anisotropy in the flow and document progress towards the mixing transition. A mixing parameter is defined which characterizes the relative rates of entrainment and mixing in the flow. The spectrum of each term in the kinetic energy equation is plotted, at regular time intervals, as a function of the inhomogeneous direction and the two-dimensional wave number for the homogeneous directions. The energy spectrum manifests the beginning of an inertial range by the latter stages of the simulation. The production and dissipation spectra become increasingly opposite and separate in wave space as the flow evolves. The transfer spectrum depends strongly on the inhomogeneous direction, with the net transfer being from large to small scales. Energy transfer at the bubble/spike fronts is strictly positive. Extensive cancellation occurs between the pressure and advection terms. The dilatation term produces negligible energy transfer, but its overall effect is to move energy from high to low density regions.