Turbulence Closure for Mixing Length Theories

TL;DR

This paper introduces a rapid, versatile turbulence closure model based on mixing length theory that captures key physical effects and instabilities in stellar environments, with a focus on computational efficiency and broad applicability.

Contribution

The authors develop a novel turbulence closure model incorporating multiple physical effects and instabilities, implemented in an open source code for stellar evolution applications.

Findings

Model captures convective, baroclinic, shear, and MRI instabilities.

Demonstrates non-linear saturation and asymptotic scaling of transport coefficients.

Efficient implementation suitable for stellar evolution simulations.

Abstract

We present an approach to turbulence closure based on mixing length theory with three-dimensional fluctuations against a two-dimensional background. This model is intended to be rapidly computable for implementation in stellar evolution software and to capture a wide range of relevant phenomena with just a single free parameter, namely the mixing length. We incorporate magnetic, rotational, baroclinic and buoyancy effects exactly within the formalism of linear growth theories with nonlinear decay. We treat differential rotation effects perturbatively in the corotating frame using a novel controlled approximation which matches the time evolution of the reference frame to arbitrary order. We then implement this model in an efficient open source code and discuss the resulting turbulent stresses and transport coefficients. We demonstrate that this model exhibits convective, baroclinic and shear instabilities as well as the magnetorotational instability (MRI). It also exhibits non-linear saturation behaviour, and we use this to extract the asymptotic scaling of various transport coefficients in physically interesting limits.