A mechanism for differential rotation based on angular momentum transport by compressible convection

It is shown that compressible convective motions in a density-stratified rotating fluid give rise to non-diffusive fluxes of the angular momentum (Λ-effect), thus leading to differential rotation. This also occurs for the case of extremely small convection anisotropy. Attention is focused on this case of quasi-isotropic convection and the Λ-effect of quasi-isotropic convection is derived. The corresponding fluxes of the angular momentum, as well as the resulting deviation of the rotation from homogeneity, are shown to be proportional to the second spatial derivative of the fluid density squared. The solution of the Reynolds equation is found for a particular density profile. Isorotational surfaces corresponding to different values of the Rossby number, Ro, are considered. The angular velocity increases with depth and towards the equator when Ro≾0.3 which corresponds to the middle and lower parts of the solar convection zone. The results obtained are compared with observations. A possible physical picture of the differential rotation set up by compressible convection is suggested.