SpringerLink
Forum Springer Astron. Astrophys.
Forum Whats New Search Orders


Astron. Astrophys. 334, 1000-1006 (1998)

Previous Section Next Section Title Page Table of Contents

3. Transport of chemical elements

The transport of chemical species proceeds much like that of angular momentum: the concentration [FORMULA] (in mass) of a given element obeys an advection-diffusion equation similar to (2.2)

[EQUATION]

where we have allowed for different diffusivities in the vertical and horizontal directions.

Splitting the concentration in its horizontal average and fluctuation on the isobar,

[EQUATION]

and assuming that [FORMULA], Chaboyer and Zahn (1992) have shown that

[EQUATION]

Since the inverse of the molecular weight is a linear function of the mass concentrations, we have likewise

[EQUATION]

and therefore, with [FORMULA],

[EQUATION]

Eqs. (3.7) and (3.9) have a stationary solution for long enough time [FORMULA]. For (3.7) it is

[EQUATION]

It can be used to evaluate the vertical flux of this chemical species, with the result that the vertical transport obeys a diffusion equation

[EQUATION]

with the effective diffusivity (Chaboyer & Zahn 1992)

[EQUATION]

For simplicity, we have omitted in (3.11) the source and sink term due to nuclear reactions, as well as the effects of element separation through radiation and gravitational settling.

Previous Section Next Section Title Page Table of Contents

© European Southern Observatory (ESO) 1998

Online publication: June 2, 1998

helpdesk.link@springer.de