Stellar mixing

Abstract

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 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 ,a ndμ-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 ) indoubly stable regimes, ∇μ > 0, ∇− ∇ ad 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.