Scale invariant bounds for mixing in the Rayleigh-Taylor instability

Abstract

We study the Rayleigh-Taylor instability for two miscible, incompressible, inviscid fluids. Scale-invariant estimates for the size of the mixing zone and coarsening of internal structures in the fully nonlinear regime are established following techniques introduced for the Saffman-Taylor instability in [OttoMenon, 2004]. These bounds provide optimal scaling laws and reveal the strong role of dissipation in slowing down mixing.