# Mathematics Colloquia and Seminars

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### Modeling Rayleigh-Taylor mixing and interface turn-over

**Mathematical Physics & Probability**

Speaker: | Steve Shkoller, UC Davis |

Related Webpage: | https://www.math.ucdavis.edu/~shkoller/ |

Location: | 1147 MSB |

Start time: | Wed, Nov 9 2016, 4:30PM |

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; in particular, RT is an interface fingering instability, which occurs when a perturbed interface, between two fluids of different density, is subjected to a normal pressure gradient.

The Euler equations of inviscid hydrodynamics 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 difficult to computationally simulate at the small spatial scales of RT mixing. As such, our objective is to develop model equations, which can be used to predict the RT mixing layer and growth rate.

In this talk, I will describe two new models for the RT instability, derived in two very different asymptotic regimes. Numerical simulations show excellent agreement with both experiment and Direct Numerical Simulation for the prediction of RT mixing layer growth.