Theory of Solar Meridional Circulation at High Latitudes

TL;DR

This paper develops a hydrodynamical model to analyze the Sun's high latitude meridional flows, revealing how turbulent viscosity influences flow node structures and their behavior at high latitudes.

Contribution

It introduces a novel model incorporating Coriolis forces and turbulent diffusion to understand high latitude solar flows, highlighting the role of turbulent viscosity in flow node dynamics.

Findings

Number of flow nodes depends on turbulent viscosity.

Node merging occurs as meridional flow speed increases.

High viscosity leads to fewer or no nodes at high latitudes.

Abstract

We build a hydrodynamical 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 $\geq 60^{\circ}$. 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 $\epsilon=2 \Omega n \pi H^2/\nu$, in which $\Omega$ is the interior rotation rate, n the radial wavenumber of the meridional flow, $H$ the depth of the convection zone and $\nu$ 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 $\nu=10^{12}{\rm cm}^2{\rm s}^{-1}$, 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 $60^{\circ}$ to the pole either by node-merging or by node migration and disappearance.