Volume 528, April 2011
|Number of page(s)||7|
|Published online||04 March 2011|
III. The case of a passive tracer⋆
NASA, Goddard Institute for Space Studies,
2 Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY 10027, USA
Accepted: 25 August 2010
In Papers I–II, we derived the expressions for the turbulent diffusivities of momentum, temperature T, and mean molecular weight μ. Since the scalar T-μ fields are active tracers (by influencing the density and thus the velocity field), whereas passive tracers such as 7Li are carried along by the flow without influencing it, it would be unjustified to use the diffusivities of the T-μ fields to represent the diffusivity of passive tracers. In this paper, we present the first derivation of a passive tracer diffusivity. Some key results are: a) In the general 3D case, the passive tracer diffusivity is a tensor given in algebraic form; b) the diffusivity tensor depends on shear, vorticity, T, and μ-gradients, thus including double diffusion and differential rotation; c) in the 1D version of the model, the passive tracer diffusivity is a scalar denoted by Kc; d) in doubly stable regimes, ∇μ > 0, ∇ − ∇ad < 0, Kc is nearly the same as those of the T-μ fields; e) in semi-convection regimes, ∇μ > 0, ∇ − ∇ad > 0, Kc is larger than that of the μ-field; f) in salt fingers regimes ∇μ < 0,∇ − ∇ad < 0, Kc is smaller than that of the μ-field; and finally, g) in the only case we know of a direct measurement of a passive tracer diffusivity, the oceanographic North Atlantic Tracer Release Experiment (NATRE), the model reproduces the data quite closely.
Key words: diffusion / instabilities / turbulence / stars: interiors / convection / methods: analytical
© ESO, 2011
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