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

TL;DR

This work analyzes nonlocality in mean scalar transport for turbulent three-dimensional Rayleigh–Taylor mixing across Atwood numbers by extending the Macroscopic Forcing Method to variable-density flows and measuring eddy-diffusivity moments $D^{mn}$. It demonstrates that higher Atwood numbers amplify nonlocality, with higher-order and temporal moments growing in magnitude and memory effects lengthening in time, especially near layer edges. Using Matched Moment Inverse, the study tests how spatial, temporal, and spatio-temporal moments influence flux predictions $F$, revealing that temporal moments significantly improve accuracy at low $A$ and that robustness constraints emerge for higher $A$. The authors propose an Atwood-dependent analytic model for the inverse operator coefficients, enabling improved closures in self-similar space and highlighting the need to incorporate Atwood-driven nonlocality into RANS-like RT closures. Overall, the results support incorporating nonlocal, temporally extended eddy-diffusivity effects into variable-density RT models, with a practical path forward via Atwood-aware inverse operators and reduced-order moment constructions.

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.

Figures (35)

• Figure 1: Contours of density for each $A$ case.
• Figure 2: Contours of Mach number for each $A$ case.
• Figure 3: Self-similarity metrics for each $A$ case: (a) bubble height, (b) mixedness, (c) bubble growth parameter. In (c), thick lines are from Equation \ref{['eq:alpha_b']}, and thin lines are from Equation \ref{['eq:alpha_b_est']}.
• Figure 4: Reynolds numbers over time for each of the $A$ cases. The horizontal lines indicate critical values for each Reynolds number.
• Figure 5: Energy spectra at different Atwood numbers at the last timesteps of the simulations. Different lines are the spectra at different $y$ within the mixing layer. Lighter cyan lines are at higher $y$, and darker lines are at lower $y$. The dashed black lines have $-5/3$ slopes.