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Astron. Astrophys. 321, 465-476 (1997)

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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.

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© European Southern Observatory (ESO) 1997

Online publication: June 30, 1998
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