Two-point spectral model for variable-density homogeneous turbulence

TL;DR

This paper develops and tests a two-point spectral closure model for buoyancy-driven variable-density turbulence, accurately capturing spectral distributions and mixing mechanisms across different Atwood numbers.

Contribution

The study introduces a spectral model with optimized coefficients that effectively reproduces turbulence statistics and reveals key mixing mechanisms, advancing modeling of variable-density flows.

Findings

Model accurately predicts spectral distributions at various Atwood numbers.

Four coefficients are sufficient for reasonable results.

Model captures the impact of different parameters on turbulence evolution.

Abstract

We present a study of buoyancy-driven variable-density homogeneous turbulence, using a two-point spectral closure model. We compute the time-evolution of the spectral distribution in wavenumber $k$ of the correlation of density and specific-volume $b(k)$, the mass flux $\bm{a}(k)$, and the turbulent kinetic energy $E(k)$, using a set of coupled equations. Under the modeling assumptions, each dynamical variable has two coefficients governing spectral transfer among modes. In addition, the mass flux $\bm{a}(k)$ has two coefficients governing the drag between the two fluids. Using a prescribed initial condition for $b(k)$ and starting from a quiescent flow, we first evaluate the relative importance of the different coefficients used to model this system, and their impact on the statistical quantities. We next assess the accuracy of the model, relative to Direct Numerical simulation of the complete hydrodynamical equations, using $b$, ${\bm a}$ and $E$ as metrics. We show that the model is able to capture the spectral distribution and global means of all three statistical quantities at both low and high Atwood number for a set of optimized coefficients. The optimization procedure also permits us to discern a minimal set of four coefficients which are sufficient to yield reasonable results while pointing to the mechanisms that dominate the mixing process in this problem.