Stellar mixing

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, N2 = - gH_p-1 (nabla -nabla _ad)(1-R_μ); 2) double diffusion, salt-fingers, and semi-convection, represented by the density ratio Rμ = ∇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, ɛ. In the local and stationary cases, when production equals dissipation, the model equations are all algebraic. This work is dedicated to Aura Sofia Canuto.