Volume 528, April 2011
|Number of page(s)||9|
|Published online||04 March 2011|
1 NASA, Goddard Institute for Space
York, NY 10025, USA
2 Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY 10027, USA
Received: 17 March 2010
Accepted: 25 August 2010
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 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, ε. In the local and stationary cases, when production equals dissipation, the model equations are all algebraic.
Key words: turbulence / diffusion / convection / hydrodynamics / methods: analytical / stars: rotation
© ESO, 2011
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