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Scale interactions and anisotropy in Rayleigh–Taylor turbulence

Published online by Cambridge University Press:  16 November 2021

Dongxiao Zhao
Affiliation:
Department of Mechanical Engineering and Laboratory for Laser Energetics, University of Rochester, Rochester, NY 14627, USA UM-SJTU Joint Institute, Shanghai Jiao Tong University, Shanghai 200240, PR China
Riccardo Betti
Affiliation:
Department of Mechanical Engineering and Laboratory for Laser Energetics, University of Rochester, Rochester, NY 14627, USA Department of Physics, University of Rochester, Rochester, NY 14627, USA
Hussein Aluie*
Affiliation:
Department of Mechanical Engineering and Laboratory for Laser Energetics, University of Rochester, Rochester, NY 14627, USA
*
Email address for correspondence: hussein@rochester.edu

Abstract

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

Type
JFM Papers
Copyright
© The Author(s), 2021. Published by Cambridge University Press

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