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Gyroscopic pumping of large-scale flows in stellar interiors, and application to Lithium Dip stars

The maintenance of large-scale differential rotation in stellar convective regions by rotationally influenced convective stresses also drives large-scale meridional flows by angular--momentum conservation. This process is an example of ``gyroscopic pumping'', and has recently been studied in detail in the solar context. An important question concerns the extent to which these gyroscopically pumped meridional flows penetrate into nearby stably stratified (radiative) regions, since they could potentially be an important source of non-local mixing. Here we present an extensive study of the gyroscopic pumping mechanism, using a combination of analytical calculations and numerical simulations both in Cartesian geometry and in spherical geometry. The various methods, when compared with one another, provide physical insight into the process itself, as well as increasingly sophisticated means of estimating the gyroscopic pumping rate. As an example of application, we investigate the effects of this large-scale mixing process on the surface abundances of the light elements Li and Be for stars in the mass range 1.3-1.5 solar masses (so-called ``Li-dip stars''). We find that gyroscopic pumping is a very efficient mechanism for circulating material between the surface and the deep interior, so much in fact that it over-estimates Li and Be depletion by orders of magnitude for stars on the hot side of the dip.However, when the diffusion of chemical species back into the surface convection zone is taken into account, a good fit with observed surface abundances of Li and Be as a function of stellar mass in the Hyades cluster can be found for reasonable choices of model parameters.