Mausumi Dikpati, Peter A. Gilman
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.
View original:
http://arxiv.org/abs/1112.1107
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