Scaling laws prediction from a solvable model of turbulent thermal convection

A solvable turbulent model is used to predict both the structure of the bou ndary layer and the scaling laws in thermal convection. The transport of he at depends on the interplay between the thermal, viscous and integral scale s of turbulence, and thus, on both the Prandtl number and the Reynolds numb ers. Depending on their values, a wide variety of possible regimes is found , including the classical 2/7 and 1/3 law, and a new 4/13 = 0.308 law for t he Nusselt power law variation with the Rayleigh number.