Scaling with the Stars: The emergence of marginal stability in low Prandtl number turbulence

TL;DR

This paper investigates low Prandtl number turbulence relevant to stellar and planetary interiors, revealing scale-separated dynamics and the emergence of marginal stability through multiscale analysis and reduced-order modeling.

Contribution

It introduces a multiscale analysis of stratified turbulence and demonstrates how reduced-order models can capture marginal stability in low Prandtl number flows.

Findings

Identification of regimes of behavior in stratified turbulence

Demonstration of marginal stability in reduced-order models

Application of multiscale analysis to geophysical fluid dynamics

Abstract

To improve models of the structure and evolution of stellar and planetary interiors, it is important to quantify transport by strongly stratified turbulence in low Prandtl number fluids. Recent numerical studies have shown evidence for scale-separated dynamics in strongly anisotropic flows. Motivated by these results, in the first part of this report we perform a multiscale analysis of the governing equations and identify regimes of behaviour. In the second part, we apply algorithms for solving slow-fast quasilinear systems to our reduced-order systems for low Prandtl number fluids and demonstrate their approach to and maintenance of marginal stability. This is a Fellow's Report for the 2022 Program of the Geophysical Fluid Dynamics Summer School.