ON THE PENETRATION OF MERIDIONAL CIRCULATION BELOW THE SOLAR CONVECTION ZONE. II. MODELS WITH CONVECTION ZONE, THE TAYLOR-PROUDMAN CONSTRAINT, AND APPLICATIONS TO OTHER STARS

The solar convection zone exhibits a strong level of differential rotation, whereby the rotation period of the polar regions is about 25%-30% longer than the equatorial regions. The Coriolis force associated with these zonal flows perpetually "pumps" the convection zone fluid, and maintains a quasi-steady circulation, poleward near the surface. What is the influence of this meridional circulation on the underlying radiative zone, and in particular, does it provide a significant source of mixing between the two regions? In Paper I, we began to study this question by assuming a fixed meridional flow pattern in the convection zone and calculating its penetration depth into the radiative zone. We found that the amount of mixing caused depends very sensitively on the assumed flow structure near the radiative-convective interface. We continue this hydrodynamic study here by including a simple model for the convection zone "pump", and calculating in a self-consistent manner the meridional flows generated in the whole Sun. We find that the global circulation timescale depends in a crucial way on two factors: the overall stratification of the radiative zone as measured by the square root of the Prandtl number times the ratio of the Brunt-Vaisala frequency to the rotation rate, and, for weakly stratified systems, the presence or absence of stresses within the radiative zone capable of breaking the Taylor-Proudman constraint. We conclude by discussing the consequences of our findings for the solar interior and argue that a potentially important mechanism for mixing in young main-sequence stars has so far been neglected.