Analysis and PDE Seminar: Models for Rayleigh-Taylor mixing and interface turnover

Seminar | April 3 | 4:10-5 p.m. | 740 Evans Hall

 Steve Shkoller, UC Davis

 Department of Mathematics

The instability of a heavy fluid layer supported by a light one is generally known as Rayleigh-Taylor (RT) instability. It can occur under gravity and, equivalently, under an acceleration of the fluid system in the direction toward the denser fluid. Whenever the pressure is higher in the lighter fluid, the differential acceleration causes the two fluids to mix.

The Euler equations serve as the basic mathematical model for RT instability and mixing between two fluids. This highly unstable system of conservation laws is both difficult to analyze (as it is ill-posed in the absence of surface tension and viscosity) and simulate; DNS of RT can be prohibitively expensive. In this talk, I will describe a novel framework to derive a hierarchy of asymptotic models that can be used to predict the location and shape of the RT interface as well as the mixing of the two fluids.

The models are derived in two very different asymptotic regimes. The first regime assumes that the fluid interface is a graph with size restrictions on the slope of the interface. The model PDE inherits the RT stability condition from the Euler equations, and in the stable regime, it is both locally and globally well-posed with precise asymptotic behavior that predicts nonlinear saturation for bubble growth. In the second asymptotic regime the interface can turnover, and there are no size restrictions on the amplitude or slope of the interface.

I will describe these models and show numerical simulations and comparisons with well-known RT experiments and simulations. I will then show results of fluid mixing, and discuss current work, advancing both modeling strategies. This is joint work with Rafa Granero.