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Barotropic rotation and radiative equilibrium are mutually incompatible instars. The issue is often addressed by allowing for a meridional circulation,but this is not devoid of theoretical complications. Models of rotation in theSun which maintain strict radiative equilibrium, making use of the observationthat the Sun is not in a state of barotropic rotation, have recently beensuggested. To investigate the dynamical behaviour of these solutions, we studythe local stability of stratified, weakly magnetized, differentially rotatingfluids to non-axisymmetric perturbations. Finite heat conductivity, kinematicviscosity, and resistivity are present. The evolution of local embeddedperturbations is governed by a set of coupled, ordinary differential equationswith time-dependent coefficients. Two baroclinic models of rotation for theupper radiative zone and tachocline are studied: (i) an interpolation based onhelioseismology data, (ii) a theoretical solution directly compatible withradiative equilibrium. The growth of the local Goldreich-Schubert-Frickeinstability appears to be suppressed, largely because of the viscosity. Anextensive exploration of wavenumber space is carried out, with and without amagnetic field. Although we easily find classical local instabilities when theyought formally to be present, for the Sun the analysis reveals neither unstablesolutions, nor even solutions featuring a large transient growth. We have notruled out larger scale or nonlinear instabilities, nor have we rigorouslyproven local stability. But rotational configurations in close agreement withobservations, generally thought to be vulnerable to the classic localGoldreich-Schubert-Fricke instability, do appear to be locally stable underrather general circumstances.

The radiative zone of the Sun and the tachocline: stability of baroclinic patterns of differential rotation