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°. 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 ε = 2ΩnπH ²/ν, where Ω is the interior rotation rate, n is the radial wavenumber of the meridional flow, H is the depth of the convection zone, and ν is the turbulent viscosity. The smaller the ε (larger turbulent viscosity), the fewer the number of nodes in high latitudes. For all latitudes within the polar cap, we find three nodes for ν = 10¹² cm² s^-1, two for 10 ¹³, and one or none for 10¹⁵ or higher. For ν near 10¹⁴ 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 ν is increased the poleward-most node migrates to the pole and disappears, ultimately for high enough ν leaving no nodes. These results suggest that primary poleward surface meridional flow can extend from 60° to the pole either by node merging or by node migration and disappearance.