Turbulence Closure for Mixing Length Theories

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.

arXiv comment17 pages, 20 figures, published in MNRAS. Figures 9-19 and C1 and associated text have been updated relative to MNRAS version to reflect minor changes due to corrections to the numerical code. Typographic errors have been corrected in equations 8, 10 and 11 and Figure 1 caption. Figure 3 legend updated to be clearer, and colors have been coordinated between Figures 1-3

References in corpus (20)

• The NumPy array: a structure for efficient numerical computation
• Accretion disc viscosity: how big is alpha?
• Three-Dimensional General Relativistic Radiation Magnetohydrodynamical Simulation of Super-Eddington Accretion, using a new code HARMRAD with M1 Closure
• A Solution Accurate, Efficient and Stable Unsplit Staggered Mesh Scheme for Three Dimensional Magnetohydrodynamics
• Accretion disc dynamo activity in local simulations spanning weak-to-strong net vertical magnetic flux regimes
• Spectra and statistics of velocity and temperature fluctuations in turbulent convection
• On the Saturation of the Magnetorotational Instability via Parasitic Modes
• Local models of stellar convection: Reynolds stresses and turbulent heat transport
• The signature of the magnetorotational instability in the Reynolds and Maxwell stress tensors in accretion discs
• Constraints on AGN accretion disc viscosity derived from continuum variability
• The fundamental difference between shear alpha viscosity and turbulent magnetorotational stresses
• Turbulent transport by diffusive stratified shear flows: from local to global models. Part I: Numerical simulations of a stratified plane Couette flow
• The eddy heat-flux in rotating turbulent convection
• A model of the entropy flux and Reynolds stress in turbulent convection
• The stability of stratified, rotating systems and the generation of vorticity in the Sun
• A comparison of local simulations and reduced models of MRI-induced turbulence
• Theory of differential rotation and meridional circulation
• On the Anisotropic Nature of MRI-Driven Turbulence in Astrophysical Disks
• A two-dimensional mixing length theory of convective transport
• Moment estimates for Lévy Processes

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• An Atlas of Convection in Main-Sequence Stars
• Dynamo Model for North-South Asymmetry of Solar Activity
• Coupled Day-Night Models of Exoplanetary Atmospheres
• Convective Differential Rotation in Stars and Planets I: Theory
• The Dependence of Stellar Activity Cycles on Effective Temperature
• Convective Differential Rotation in Stars and Planets II: Observational and Numerical Tests
• Multiscale Turbulence Synthesis: Validation in 2D Hydrodynamics