  It has been previously shown (Phys. Rev. E 66, 066305, 2002) that a
non-rotating turbulent convection with nonuniform large-scale flows contributes
to the turbulent heat flux. As a result, the turbulent heat flux depends
explicitly not only on the gradients of the large-scale temperature, but it
also depends on the gradients of the large-scale velocity. This is because the
nonuniform large-scale flows produce anisotropic velocity fluctuations which
modify the turbulent heat flux. This effect causes an excitation of a
convective-wind instability and formation of large-scale semi-organised
coherent structures (large-scale convective cells). We perform mean-field
numerical simulations of shear-free convection which take into account the
modification of the turbulent heat flux by nonuniform large-scale flows. The
redistribution of the turbulent heat flux by the nonuniform large-scale motions
in turbulent convection plays a crucial role in the formation of the
large-scale semi-organised coherent structures. This effect results in a strong
reduction of the critical effective Rayleigh number (based on the eddy
viscosity and turbulent temperature diffusivity) required for the formation of
the large-scale convective cells. The convective-wind instability is excited
when the scale separation ratio between the height of the convective layer and
the integral turbulence scale is large. The level of the mean kinetic energy at
saturation increases with the scale separation ratio. Inside the large-scale
convective cells, there are local regions with the positive vertical gradient
of the potential temperature which implies that these regions are stably
stratified.
