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Turbulence closure for mixing length theories

Accepted version
Peer-reviewed

Type

Article

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Authors

Jermyn, AS 
Lesaffre, P 
Tout, CA 
Chitre, SM 

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.

Description

Keywords

convection, stars: evolution, stars: interiors, stars: rotation

Journal Title

Monthly Notices of the Royal Astronomical Society

Conference Name

Journal ISSN

0035-8711
1365-2966

Volume Title

476

Publisher

Oxford University Press (OUP)
Sponsorship
Science and Technology Facilities Council (ST/L003910/1)