Stellar mixing

Abstract

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 R μ . Fourth, the latter result favors parameterizations of the type K h,μ ∼ CR 0 μ 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 −1 μ , most of the results obtained in the previous case can be translated to this case.

The Dawes Review 2: Nucleosynthesis and Stellar Yields of Low- and Intermediate-Mass Single Stars

“…The green lines show expected velocities in the convective regions, while the brown lines show the dramatically reduced velocities expected for thermohaline or semi-convective mixing. For a general hydrodynamic formulation that includes both thermohaline mixing and semi-convection we refer the reader to Spiegel (1972) and Grossman et al (1993), and the series of papers by Canuto (Canuto 2011a, 2011b, 2011c, 2011d, 2011e).

Figure 11. These diagrams show the main stability criteria for stellar models, the expected kind of mixing, and typical velocities.

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Key issues review: numerical studies of turbulence in stars

“…Extensive theoretical, numerical and experimental information from the geosciences has been analysed by Canuto 2012aCanuto , 2012bCanuto , 2012cCanuto , 2012d, for application to the problem of stellar convection and mixing.…”

Stellar evolution models with overshooting based on 3-equation non-local theories

“…The dissipation rate equation Eq. ( 9) has hence remained part of the Reynolds stress model of Canuto (2011a), whether for dealing with double-diffusive convection (Canuto 2011b) or overshooting (Canuto 2011c). The latter paper provides a detailed discussion of the computation of , which considers Eq.…”