Statistics of mixing in three-dimensional Rayleigh--Taylor turbulence at low Atwood number and Prandtl number one

TL;DR

This study uses high-resolution simulations to analyze the statistical properties of three-dimensional Rayleigh--Taylor turbulence at low Atwood number and Prandtl number one, revealing universal scaling behaviors similar to classical turbulence.

Contribution

It extends mean-field analysis to include intermittency effects in RT turbulence, demonstrating universality in turbulence scaling across different flow geometries.

Findings

Scaling exponents match those of classical Navier--Stokes turbulence.

Intermittency affects velocity and temperature fluctuation statistics.

Results support universality of turbulence regardless of injection mechanism.

Abstract

Three-dimensional miscible Rayleigh--Taylor (RT) turbulence at small Atwood number and at Prandtl number one is investigated by means of high resolution direct numerical simulations of the Boussinesq equations. RT turbulence is a paradigmatic time-dependent turbulent system in which the integral scale grows in time following the evolution of the mixing region. In order to fully characterize the statistical properties of the flow, both temporal and spatial behavior of relevant statistical indicators have been analyzed. Scaling of both global quantities ({\it e.g.}, Rayleigh, Nusselt and Reynolds numbers) and scale dependent observables built in terms of velocity and temperature fluctuations are considered. We extend the mean-field analysis for velocity and temperature fluctuations to take into account intermittency, both in time and space domains. We show that the resulting scaling exponents are compatible with those of classical Navier--Stokes turbulence advecting a passive scalar at comparable Reynolds number. Our results support the scenario of universality of turbulence with respect to both the injection mechanism and the geometry of the flow.