  A new mean-field theory of turbulent convection is developed. This theory
predicts the convective wind instability in a shear-free turbulent convection
which causes formation of large-scale semi-organized fluid motions in the form
of cells or rolls. Spatial characteristics of these motions, such as the
minimum size of the growing perturbations and the size of perturbations with
the maximum growth rate, are determined. This study predicts also the existence
of the convective shear instability in a sheared turbulent convection which
results in generation of convective shear waves with a nonzero hydrodynamic
helicity. Increase of shear promotes excitation of the convective shear
instability. Applications of the obtained results to the atmospheric turbulent
convection and the laboratory experiments on turbulent convection are
discussed. This theory can be applied also for the describing a mesogranular
turbulent convection in astrophysics.
