Diffusive mixing by shears in rotating stars.

Details Diffusive mixing by shears in rotating stars. Diffusive mixing by shears in rotating stars.

Sep 1996

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1996a%26a...313..140m&link_type=abstract

Astronomy and Astrophysics, v.313, p.140-144

Astronomy and Astrophysics

Astrophysics

36

Stars: Evolution, Interiors, Rotation, Diffusion

Scientific paper

We show that the Richardson criterion, even in its improved form found recently, is insufficient by itself to describe the occurrence of shear instabilities in rotating stars. The coupling between the shears and their effects on the T-gradient must be accounted for. When this is done, we obtain a new more complete criterion, in which the shear properties essentially depend on one critical dimensionless number θ. We must distinguish the cases of radiative and semiconvective zones. For a radiative zone, the stability criterion becomes (1)/(4) ((dU)/(dz))^2^<(gφ∇mu_)/(H_p_). If this condition is not realized, we show that there is always a range of scales in the turbulent spectrum where shear instabilities occur. The corresponding diffusion coefficient, depending only on θ, is given. In a semiconvective zone, the stability criterion, with respect to shears, is (1)/(4) ((dU)/(dz))^2^<(gφ∇mu_)/(H_p_)-(1)/(1+2sqrt(6)) (gδ)/(H_p_) (∇_rad_-∇_ad_). We also derive the appropriate diffusion coefficient when the above criterion is not satisfied. Different ranges of turbulent scales may also exist, depending on θ. Interestingly enough, we may notice that the above criterion is also that expressing the transition from shear to semiconvective instabilities.

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