  A mean-field theory of differential rotation in a density stratified
turbulent convection has been developed. This theory is based on a combined
effect of the turbulent heat flux and anisotropy of turbulent convection on the
Reynolds stress. A coupled system of dynamical budget equations consisting in
the equations for the Reynolds stress, the entropy fluctuations and the
turbulent heat flux has been solved. To close the system of these equations,
the spectral tau approach which is valid for large Reynolds and Peclet numbers,
has been applied. The adopted model of the background turbulent convection
takes into account an increase of the turbulence anisotropy and a decrease of
the turbulent correlation time with the rotation rate. This theory yields the
radial profile of the differential rotation which is in agreement with that for
the solar differential rotation.
