Evolution of Multi-mode Rayleigh-Taylor Instability Towards Self-Similar Turbulent Mixing

The evolution of the multimode Rayleigh-Taylor instability of nearly incompressible fluids, with density ratio r = 2, is investigated by means of two-dimensional hydrodynamic simulations. The study focuses on the effect of the initial perturbation on the evolution towards turbulent mixing. It is shown that, for sufficiently large times, a self-similar mixing regime occurs, in which typical spatial scales (such as the size of the mixed layer) evolve proportionally to g(t - t0)2, where g is the gravity, t the time, and t0 is a characteristic time depending on the initial conditions. A model for the prediction of t0 is then presented, which is in agreement with the simulations.