The Navier-Stokes equation driven by heat conduction is studied. As a proto
type we consider Rayleigh-Benard convection, in the Boussinesq approximatio
n. Under a large aspect ratio assumption, which is the case in Rayleigh-Ben
ard experiments with Prandtl number close to one, we prove the existence of
a global strong solution to the 3D Navier-Stokes equation coupled with a h
eat equation, and the existence of a maximal B-attractor. A rigorous two-sc
ale limit is obtained by homogenization theory. The mean velocity field is
obtained by averaging the two-scale limit over the unit torus in the local
variable.