Model of a slowly rotating solar convection zone

Numerical solutions are evaluated of the equations governing the large-scale motions of rotating stellar convection zones, as derived by Durney and Spruit (DS). With the solar convection zone in mind, these equations were solved by a perturbation method with the uniformly rotating convection zone as the unperturbed state (approximated by a polytrope). The horizontal dimensions of the dominant convective eddy were assumed to be equal (l/sub theta/ = l/sub phi/) and the ratio l/sub theta//l/sub r/ ( = s) a constant independent of polar angle theta and radial distance r (phi is longitude; we recall that the ratios l/sub r//l/sub theta/, l/sub r//l/sub phi/, together with the mixing length, are the basic arbitrary parameters in the equations derived by DS). The collocation method was used to transform the set of partial differential equations in r and theta, into a set of ordinary differential equations in r which were then solved for a variety of boundary conditions. The solutions were evaluated for increasingly larger values of the angular velocity Ω0. For values of Ω0 smaller than the solar angular velocity the energy carried by the meridional motions was large enough to stabilize the turbulent convection, and solutions to the equations ceased to exist (we neglected in this paper the energy carried by radiation). Large pole-equator differences in flux were present in the lower part of the convection zone; at the surface, however, these pole-equator differences in flux were negligible