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 rot ating fluid for which the alpha-effect has been recently (paper I) det ermined. The anisotropy of the turbulence is mainly due to density str atification and the turbulence is horizontal in the bulk of the convec tion zone. The resulting LAMBDA-effect is very non-trivial: there are big differences between the slow and rapid rotation cases. Only a posi tive radial flux of angular momentum with a simple latitudinal variati on exists for the former case. The corresponding angular velocity dist ribution shows near-independence of latitude and a distinct super-rota tion in radius. For rapid rotation we find radial and latitudinal flux es 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 zon e. The pole-equator difference of OMEGA at the bottom of convection zo ne 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 mag nitude of the differential rotation saturates at about 50 % for very s mall Rossby numbers.