Scale interactions and anisotropy in Rayleigh-Taylor turbulence

TL;DR

This paper investigates energy transfer mechanisms in Rayleigh-Taylor turbulence, revealing differences between 2D and 3D flows, and clarifying the roles of baropycnal and deformation work in energy cascades.

Contribution

It introduces a coarse-graining method to analyze scale interactions in RT turbulence without Fourier transforms, highlighting distinct energy transfer processes in 2D and 3D.

Findings

In 3D, kinetic energy cascades to smaller scales via deformation work.

In 2D, energy re-channels to larger scales, enhancing mixing layer growth.

Large-scale flow isotropization occurs in 2D due to upscale energy transfer.

Abstract

We study energy scale-transfer in Rayleigh-Taylor (RT) flows by coarse-graining in physical space without Fourier transforms, allowing scale analysis along vertical direction. Two processes are responsible for kinetic energy flux across scales: baropycnal work $\Lambda$, due to large-scale pressure gradients acting on small-scales of density and velocity, and deformation work $\Pi$, due to multi-scale velocity. Our coarse-graining analysis shows how these fluxes exhibit self-similar evolution that is quadratic-in-time, similar to RT mixing layer. We find that $\Lambda$ is a conduit for potential energy, transferring energy non-locally from the largest scales to smaller scales in the inertial range where $\Pi$ takes over. In 3D, $\Pi$ continues a persistent cascade to smaller scales, whereas in 2D $\Pi$ re-channels the energy back to larger scales despite the lack of vorticity conservation in 2D variable density flows. This gives rise to a positive feedback loop in 2D-RT (absent in 3D) in which mixing layer growth and the associated potential energy release are enhanced relative to 3D, explaining the oft-observed larger $\alpha$ values in 2D simulations. Despite higher bulk kinetic energy levels in 2D, small inertial scales are weaker than in 3D. Moreover, the net upscale cascade in 2D tends to isotropize the large-scale flow, in stark contrast to 3D. Our findings indicate the absence of net upscale energy transfer in 3D-RT as is often claimed; growth of large-scale bubbles and spikes is not due to "mergers" but solely due to baropycnal work $\Lambda$.