  Formation of large-scale coherent structures in a turbulent convection via
excitation of large-scale instability is studied. The redistribution of the
turbulent heat flux due to non-uniform large-scale motions plays a crucial role
in the formation of the coherent large-scale structures in the turbulent
convection. The modification of the turbulent heat flux results in strong
reduction of the critical Rayleigh number (based on the eddy viscosity and
turbulent temperature diffusivity) required for the excitation of the
large-scale instability. The mean-field equations which describe the
large-scale instability, are solved numerically. We determine the key
parameters that affect formation of the large-scale coherent structures in the
turbulent convection. In particular, the degree of thermal anisotropy and the
lateral background heat flux strongly modify the growth rates of the
large-scale instability, the frequencies of the generated convective-shear
waves and change the thresholds required for the excitation of the large-scale
instability. This study elucidates the origins of the large-scale circulations
and rolls in the atmospheric convective boundary layers and the meso-granular
structures in the solar convection.
