• convection;
  • hydrodynamics;
  • Sun: helioseismology;
  • Sun: rotation


We examine the linear behaviour of three-dimensional Lagrangian displacements in a stratified, shearing background. The isentropic and isorotation 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 behaviour 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 pre-existing 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.