  The fully developed turbulent Boussinesq convection is known to form
large-scale rolls, often termed the 'large-scale circulation' (LSC). It is an
interesting question how such a large-scale flow is created, in particular in
systems when the energy input occurs at small scales, when inverse cascade is
required in order to transfer energy into the large-scale modes. Here, the
small-scale driving is introduced through stochastic, randomly distributed heat
source (say radiational). The mean flow equations are derived by means of
simplified renormalization group technique, which can be termed 'weakly
nonlinear renormalization procedure' based on consideration of only the leading
order terms at each step of the recursion procedure, as full renormalization in
the studied anisotropic case turns out unattainable. The effective, anisotropic
viscosity is obtained and it is shown, that the inverse energy cascade occurs
via an effective 'motive force' which takes the form of transient negative,
vertical diffusion.
