*Astron. Astrophys. 321, 465-476 (1997)*
## 5. Conclusions
The main results of this paper are summarized in the abstract and
will not be repeated here. Let us however make a few comments on the
need of further improvements of the theory.
First let us recall that the inhibiting nature of the
*µ*-gradient is linked to its presence in the Richardson
criterion. Would there be no Richardson criterion, there would be no
*µ*-gradient inhibiting effect. However we are not allowed
to neglect the Richardson criterion. Indeed the Richardson criterion
tells us when there is sufficient energy in the shear to allow mixing.
If we must keep the Richardson criterion, we can however wonder if its
formulation is not too schematic. In particular, its derivation does
not account for the other already existing milder sources of
turbulence such as semiconvection and horizontal turbulence (cf. Zahn
1992), which may be present even when Richardson criterion says there
is no turbulence. This pre-existing mild turbulence would make invalid
some of the usual assumptions as for example the assumption of full
homogeneity at any level and also the usual assumption that the
turbulent eddies keep their original composition. Thus we come to the
conclusion that the progress of stellar modeling may only go through a
better hydrodynamical description of turbulence.
© European Southern Observatory (ESO) 1997
Online publication: June 30, 1998
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