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.

Annihilative Fractals Formed in Rayleigh-Taylor Instability

“…In most experiments and models, disturbance with only one wave mode has been observed at the boundary [6][7][8][9]. Recently, a model with nonlinear surface tension was calculated whose disturbance has several wave modes [10]. In our experiments of RT instability, however, a fractal pattern without the characteristic length appears at the surface, as shown in Figs.…”

A new upper bound for the largest growth rate of linear Rayleigh–Taylor instability

“…We mention that, in the classical Rayleigh-Taylor (RT) experiments [8,12], the phenomenon of that the instability growth is limited by surface tension during the linear stage, where the growth is exponential in time, has been shown. Obviously, the convergence behavior (2.2) mathematically verifies the phenomenon.…”

On effect of surface tension in the Rayleigh–Taylor problem of stratified viscoelastic fluids

“…In classical Rayleigh-Taylor (RT) experiments [8,10], it has been shown that the phenomenon of that surface tension during the linear stage can restrain the instability growth, and the growth is exponential in time. Obviously, this phenomenon can be verified mathematically by the convergence behavior (3.2).…”