  We examine the linear behavior of three-dimensional Lagrangian displacements
in a stratified, shearing background. The isentropic and iso-rotation surfaces
of the equilibrium flow are assumed to be axisymmetric, but otherwise fully
two-dimensional. Three-dimensional magnetic fields are included in the
perturbation equations; however the equilibrium is assumed to be well-described
by purely hydrodynamic forces. The model, in principle very general, is used to
study the behavior of fluid displacements in an environment resembling the
solar convection zone. Some very suggestive results emerge. All but
high-latitude displacements align themselves with the observed surfaces of
constant angular velocity. The tendency for the angular velocity to remain
constant with depth in the bulk of the convective zone, together with other
critical features of the rotation profile, emerge from little more than a
visual inspection of the governing equation. In the absence of a background
axial angular velocity gradient, displacements exhibit no poleward bias,
suggesting that solar convection "plays-off" of prexisting shear rather than
creates it. We argue that baroclinic vorticity of precisely the right order is
generated at the radiative/convective zone boundary due to centrifugal
distortion of equipotential surfaces that is not precisely followed by
isothermal surfaces. If so, many features of the Sun's internal rotation become
more clear, including: i) the general appearance of the tachocline; ii) the
extension of differential rotation well into the radiative zone; iii) the
abrupt change of morphology of convective zone isorotation surfaces; and iv)
the inability of current numerical simulations to reproduce the solar rotation
profile without imposed entropy boundary conditions.
