Atwood effects on nonlocality of the scalar transport closure in three-dimensional Rayleigh-Taylor mixing

TL;DR

This study extends the Macroscopic Forcing Method to 3D variable density Rayleigh-Taylor mixing, revealing increased nonlocality and asymmetry in eddy diffusivity at higher Atwood numbers, with significant temporal effects.

Contribution

It introduces a 3D variable density extension of the MFM to quantify nonlocality in RT mixing across different Atwood numbers, highlighting increased nonlocal effects at higher A.

Findings

Eddy diffusivity moments become asymmetric with increasing A.

Higher-order eddy diffusivity moments grow relative to the leading order.

Stronger temporal nonlocality observed at higher Atwood numbers.

Abstract

The importance of nonlocality is assessed in modeling mean scalar transport for turbulent Rayleigh-Taylor (RT) mixing at different Atwood numbers. Building on the two-dimensional incompressible work of Lavacot et al. (2024, JFM), the present work extends the Macroscopic Forcing Method (MFM) to variable density problems in three-dimensional space to measure moments of the generalized eddy diffusivity kernel in RT mixing for increasing Atwood numbers (A=0.05, 0.3, 0.5, 0.8). It is found that as A increases: 1) the eddy diffusivity moments become asymmetric, and 2) the higher-order eddy diffusivity moments become larger relative to the leading-order diffusivity, indicating that nonlocality becomes more important at higher A. There is a particularly strong temporal nonlocality at higher $A$, suggesting stronger history effects. The implications of these findings for closure modeling for finite-Atwood RT are discussed.