Generating the sun's global meridional circulation from differential rotation and turbulent reynolds stresses

To investigate whether the Sun's global meridional circulation is primarily mechanically or thermally driven, we solve a hydrodynamical model to determine what meridional flow pattern is most likely to occur for the Sun's relatively well-observed differential rotation. We include Coriolis forces and turbulent Reynolds stresses, and hold the inclusion of thermodynamics for a future work.We find that the steady-state solution from thismodel is sensitive to themagnitude of the density decline with radius, yielding a single flow cell with poleward surface flow for density declines of less than about a factor of 4 within the convection zone, but two cells, with a reversed circulation in high latitudes, for all higher density declines, including that for the adiabatically stratified solar convection zone. This two-celled pattern is virtually independent of the magnitude of the decline of the turbulent viscosity with depth within the convection zone. For a solar-like density increase with depth, two cells are found for a wide variety of differential rotations, including that closest to solar observations. We compare our meridional circulation with axisymmetric convective rolls that occur in 3D global convective simulations, which tend to align with rotation axis. For solar-like turbulent viscosity, the meridional flow speeds are much larger than observed, implying that an additional physical mechanism is needed that works against the meridional flow. Candidates include negative buoyancy forces, anisotropic small-scale turbulent diffusion of momentum or heat and latitude-dependent radial heat flux by solar convection influenced by rotation. The role of these additional mechanisms in determining flow speed and in producing latitudinal and radial structures in the meridional circulation will be investigated in a future paper.