3D Interface Models for Rayleigh-Taylor Problems

TL;DR

This paper develops novel 3D interface models for Rayleigh-Taylor instability that efficiently capture complex flow features, reproduce experimental results, and reveal stabilization effects in multi-fluid configurations, significantly speeding up simulations.

Contribution

The paper introduces a new asymptotic expansion-based interface modeling approach for 3D RTI, enabling faster computation and detailed analysis of instability features.

Findings

Models reproduce experimental data across regimes

Addition of a third fluid stabilizes the mixing layer growth

Models capture small-scale structures and interface interactions

Abstract

We derive interface models for 3D Rayleigh-Taylor instability (RTI), making use of a novel asymptotic expansion in the non-locality of the fluid flow. These interface models are derived for the purpose of studying universal features associated to RTI such as the Froude number in single-mode RTI, the predicted quadratic growth of the interface amplitude under multi-mode random perturbations, the optimal (viscous) mixing rates induced by the RTI and the self-similarity of horizontally averaged density profiles, and the remarkable stabilization of the mixing layer growth rate which arises for the three-fluid two-interface heavy-light-heavy configuration, in which the addition of a third fluid bulk slows the growth of the mixing layer to a linear rate. Our interface models can capture the formation of small-scale structures induced by severe interface roll-up, reproduce experimental data in a number of different regimes, and study the effects of multiple interface interactions even as the interface separation distance becomes exceedingly small. Compared to traditional numerical schemes used to study such phenomena, our models provide a computational speed-up of at least two orders of magnitude.