Statistical analysis of multimode weakly nonlinear Rayleigh-Taylor instability in the presence of surface tension

Abstract

A weakly nonlinear model is proposed for the Rayleigh-Taylor instability in the presence of surface tension. The dynamics of a multimode perturbation of the interface between two incompressible, inviscid, irrotational, and immiscible fluids is analyzed. The quadratic and cubic nonlinear effects are taken into account. They include the nonlinear corrections to the exponential growths of the fundamental modulations. The role of the initial modulation spectrum is discussed. A saturation criterion in terms of the product of a local rms and a particular wave number is exhibited. It gives theoretical foundations for numerical conjectures and allows one to analyze the effects of fundamental parameters of the problem such as the dimension or the Atwood number.