## Publication Abstracts

### Canuto 2011

**528**, A77, doi:10.1051/0004-6361/201014448.

In this paper, salt-fingers (also called thermohaline convection) and semi-convection are treated under the name of double-diffusion (DD). We present and discuss the solutions of the RSM (Reynolds stress models) equations that provide the momentum, heat, μ fluxes, and their corresponding diffusivities denoted by K_{m,h,μ}. Such fluxes are given by a set of linear, algebraic equations that depend on the following variables: mean velocity gradient (differential rotation), temperature gradients (for both stable and unstable regimes), and μ-gradients (DD). Some key results are as follows. Salt-fingers. When shear is strong and DD is inefficient, heat and μ diffusivities are identical. Second, when shear is weak K_{μ} > K_{h} and the difference can be sizeable O(10) meaning that heat and μ diffusivities must therefore be treated as different. Third, for strong-to-moderate shears and for R_{μ} less than 0.8, both heat and μ diffusivities are practically independent of _{μ}. Fourth, the latter result favors parameterizations of the type K_{h,μ} ∼ CR_{μ}^{u} suggested by some authors. Our results, however, show that C is not a constant but a linear function of the Reynolds number Re = ε(νN^{2})^{-1} defined in terms of the kinematic viscosity ν, the Brunt-Väisälä frequency N, and the rate of energy input into the system, ε. Fifth, we suggest that ε is an essential ingredient that has been missing in all diffusivity models, but which ought to be present because without a source of energy, turbulence dies out and so does the turbulent mixing (for example, the turbulent kinetic energy is proportional to the power 2/3 of ε). Moreover, since different stellar environments have different ε, its presence is necessary for differentiating mixing regimes in different stars. Semi-convection. In this case the destabilizing effect is the T-gradient, and when shear is weak, K_{h} > K_{μ}. Since the model is symmetric under the change R_{μ} to R_{μ}^{-1}, most of the results obtained in the previous case can be translated to this case.

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#### BibTeX Citation

@article{ca06320r, author={Canuto, V. M.}, title={Stellar mixing: II. Double diffusion processes}, year={2011}, journal={Astron. Astrophys.}, volume={528}, pages={A77}, doi={10.1051/0004-6361/201014448}, }

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#### RIS Citation

TY - JOUR ID - ca06320r AU - Canuto, V. M. PY - 2011 TI - Stellar mixing: II. Double diffusion processes JA - Astron. Astrophys. VL - 528 SP - A77 DO - 10.1051/0004-6361/201014448 ER -

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