Steven A. Balbus, Henrik Latter, Nigel Weiss
The isorotation contours of the solar convective zone (SCZ) show three
distinct morphologies, corresponding to two boundary layers (inner and outer),
and the bulk of the interior. Previous work has shown that the thermal wind
equation together with informal arguments on the nature of convection in a
rotating fluid could be used to deduce the shape of the isorotation surfaces in
the bulk of the SCZ with great fidelity, and that the tachocline contours could
also be described by relatively simple phenomenology. In this paper, we show
that the form of these surfaces can be understood more broadly as a
mathematical consequence of the thermal wind equation and a narrow convective
shell. The analysis does not yield the angular velocity function directly, an
additional surface boundary condition is required. But much can already be
deduced without constructing the entire rotation profile. The mathematics may
be combined with dynamical arguments put forth in previous works to the mutual
benefit of each. An important element of our approach is to regard the constant
angular velocity surfaces as an independent coordinate variable for what is
termed the "residual entropy," a quantity that plays a key role in the equation
of thermal wind balance. The difference between the dynamics of the bulk of the
SCZ and the tachocline is due to a different functional form of the residual
entropy in each region. We develop a unified theory for the rotational behavior
of both the SCZ and the tachocline, using the solutions for the characteristics
of the thermal wind equation. These characteristics are identical to the
isorotation contours in the bulk of the SCZ, but the two deviate in the
tachocline. The outer layer may be treated, at least descriptively, by similar
mathematical techniques, but this region probably does not obey thermal wind
balance.
View original:
http://arxiv.org/abs/1111.3809
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