LAMBDA-EFFECT AND DIFFERENTIAL ROTATION IN STELLAR CONVECTION ZONES

We derive the non-diffusive part of the Reynolds stress tensor (the ''LAMBDA-effect'') for the same model of inhomogeneous turbulence of rotating fluid for which the alpha-effect has been recently (paper I) determined. The anisotropy of the turbulence is mainly due to density stratification and the turbulence is horizontal in the bulk of the convection zone. The resulting LAMBDA-effect is very non-trivial: there are big differences between the slow and rapid rotation cases. Only a positive radial flux of angular momentum with a simple latitudinal variation exists for the former case. The corresponding angular velocity distribution shows near-independence of latitude and a distinct super-rotation in radius. For rapid rotation we find radial and latitudinal fluxes with more complicated profiles in latitude. The resulting rotation law is close to that provided by helioseismology. At mid-latitudes the rotation rate OMEGA is almost uniform trough the whole convection zone. The pole-equator difference of OMEGA at the bottom of convection zone is smaller than at the top. Probably almost all of the known single main-sequence cool stars belong to the ''rapid rotator'' class. When the angular velocity increase beyond the solar value, the relative magnitude of the differential rotation saturates at about 50 % for very small Rossby numbers.