Stellar mixing

I. Formalism^⋆

¹ NASA, Goddard Institute for Space Studies, New York, NY 10025, USA
² Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY 10027, USA
e-mail: vmc13@columbia.edu

Received: 17 March 2010
Accepted: 25 August 2010

Abstract

In this paper we use the Reynolds stress models (RSM) to derive algebraic expressions for the following variables: a) heat fluxes; b) μ fluxes; and c) momentum fluxes. These relations, which are fully 3D, include:

1) stable and unstable stratification, represented by the Brunt-Väisäla frequency, ;

2) double diffusion, salt-fingers, and semi-convection, represented by the density ratio R_μ = ∇_μ(∇ − ∇_ad)^-1;

3) shear (differential rotation), represented by the mean squared shear Σ² or by the Richardson number, Ri =    N²Σ^-2;

4) radiative losses represented by a Peclet number, Pe;

5) a complete analytical solution of the 1D version of the model. In general, the model requires the solution of two differential equations for the eddy kinetic energy K and its rate of dissipation, ε. In the local and stationary cases, when production equals dissipation, the model equations are all algebraic.