Comparing models with DNS of stratified turbulence at low Prandtl number

Quantifying transport by strongly stratified turbulence in stellar and planetary interiors is paramount to the development of accurate stellar evolution models. Recent theoretical work by Chini et al. (2022) and Shah et al. (in prep, see also abstract in this meeting) using multiscale asymptotic modeling has helped create a map of parameter space delimiting various regimes where specific force balances are expected. Each regime is predicted to give rise to distinct scaling laws for the characteristic vertical eddy scale, vertical velocity, and buoyancy fluctuation, as functions of the input parameters (the Reynolds number, the Prandtl number, and the Froude number). In this work, we compare their model with various existing and new datasets obtained using DNS. The DNS are forced with a constant-in-time horizontal body force in the streamwise direction that varies sinusoidally in the spanwise direction, but is invariant in the direction of gravity. A constant stratification is imposed, and all fluctuations around the background state are assumed to be otherwise triply-periodic in the domain. All simulations are run until a statistically stationary state is achieved. The Prandtl number is low (Pr ≤ 0.1), consistent with our interest in stellar and planetary fluid flows. We find that the DNS generally agree with the model predictions of Shah et al., with the caveat that it is not possible to achieve high enough Reynolds numbers to probe all possible regimes.