- A new mean-field theory of turbulent convection is developed based on the idea that only the small-scale region of the spectrum is considered as turbulence, whereas its large-scale part, including both regular and semi-organized motions, is treated as the mean flow. In the shear-free regime, this theory predicts the convective wind instability, which causes the formation of large-scale semi-organized motions in the form of cells. In the presence of wind shear, the theory predicts another type of instability, which causes the formation of large-scale semi-organized structures in the form of rolls and the generation of convective-shear waves propagating perpendicular to the convective rolls. The spatial characteristics of these structures, such as the minimum size of the growing perturbations and the size of perturbations with the maximum growth rate, are determined. This theory might be useful for understanding the origin of large-scale cells and rolls observed in the convective boundary layer and laboratory turbulent convection.