Invariants, symmetries and scaling of Rayleigh-Taylor turbulent mixing

TL;DR

This paper extends Kolmogorov theory to analyze invariants, scaling, and spectra in Rayleigh-Taylor turbulent mixing, revealing unique scale dependencies and flow order, with implications for understanding turbulence structure.

Contribution

It introduces a symmetry-based framework for analyzing invariants and scaling laws in Rayleigh-Taylor turbulence, highlighting differences from classical isotropic turbulence.

Findings

Non-dissipative momentum transfer across scales.

Distinct power-law spectra from Kolmogorov turbulence.

Rayleigh-Taylor mixing exhibits more order than isotropic turbulence.

Abstract

We extend the ideas of Kolmogorov theory on symmetries of turbulent dynamics to analyze invariants, scaling and spectra of unsteady turbulent mixing induced by the Rayleigh-Taylor instability. Time- and scale-invariance of the rate of momentum loss leads to non-dissipative momentum transfer between the scales, to and power-law scale-dependencies of the velocity and Reynolds number and spectra distinct from Kolmogorov, and sets the viscous and dissipation scales. Turbulent mixing exhibits more order compared to isotropic turbulence. Mechanisms of flow regularization are discussed.