Effect of heat flux on differential rotation in turbulent convection

We studied the effect of the turbulent heat flux on the Reynolds stresses in a rotating turbulent convection. To this end we solved a coupled system of dynamical equations which includes the equations for the Reynolds stresses, the entropy fluctuations and the turbulent heat flux. We used a spectral $\tau$ approximation in order to close the system of dynamical equations. We found that the ratio of the contributions to the Reynolds stresses caused by the turbulent heat flux and the anisotropic eddy viscosity is of the order of $\sim 10 (L_\rho / l_0)^2$, where $l_{0}$ is the maximum scale of turbulent motions and $L_\rho$ is the fluid density variation scale. This effect is crucial for the formation of the differential rotation and should be taken into account in the theories of the differential rotation of the Sun, stars and planets. In particular, we demonstrated that this effect may cause the differential rotation which is comparable with the typical solar differential rotation.