THEORY OF SOLAR MERIDIONAL CIRCULATION AT HIGH LATITUDES

We build a hydrodynamic model for computing and understanding the Sun's large-scale high-latitude flows, including Coriolis forces, turbulent diffusion of momentum, and gyroscopic pumping. Side boundaries of the spherical "polar cap," our computational domain, are located at latitudes >= 60 degrees. Implementing observed low-latitude flows as side boundary conditions, we solve the flow equations for a Cartesian analog of the polar cap. The key parameter that determines whether there are nodes in the high-latitude meridional flow is epsilon = 2 Omega n pi H-2/nu, where Omega is the interior rotation rate, n is the radial wavenumber of the meridional flow, H is the depth of the convection zone, and nu is the turbulent viscosity. The smaller the epsilon (larger turbulent viscosity), the fewer the number of nodes in high latitudes. For all latitudes within the polar cap, we find three nodes for nu = 10(12) cm(2) s(-1), two for 10(13), and one or none for 10(15) or higher. For nu near 10(14) our model exhibits "node merging": as the meridional flow speed is increased, two nodes cancel each other, leaving no nodes. On the other hand, for fixed flow speed at the boundary, as nu is increased the poleward-most node migrates to the pole and disappears, ultimately for high enough nu leaving no nodes. These results suggest that primary poleward surface meridional flow can extend from 60 degrees to the pole either by node merging or by node migration and disappearance.