Mixing by shear instabilities in differentially rotating inhomogeneous stars with application to accreting white dwarf models for novae

The problem of how shear instabilities redistribute matter and angular momentum accreted by a star from a disk is considered. Necessary conditions for stability of the star to nonaxisymmmetric perturbations are derived by use of the short wavelength approximation. By considering growth rates, it is shown that freshly accreted material rapidly takes up a quasi-spherical distribution due to dynamical instabilities. However, mixing inward toward the stellar interior occurs on a thermal time scale or longer. The application of these results to accreting white dwarf models of classical novae are discussed.