Stellar mixing

V. M. Canuto
2011 Astronomy and Astrophysics  
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 7 Li 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
more » ... st 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 K c ; d) in doubly stable regimes, ∇ μ > 0, ∇ − ∇ ad < 0, K c is nearly the same as those of the T -μ fields; e) in semi-convection regimes, ∇ μ > 0, ∇ − ∇ ad > 0, K c is larger than that of the μ-field; f) in salt fingers regimes ∇ μ < 0, ∇ − ∇ ad < 0, K c 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.
doi:10.1051/0004-6361/201015372 fatcat:rm3swx6tdjcpxnxeydzkiszdwa