The dynamical origin of large-scale flows in systems driven by concentrated
Archimedean forces is considered. A two-dimensional model of plumes, such
as those observed in thermal convection at large Rayleigh and Prandtl numbe
rs, is introduced. From this model, we deduce the onset of mean flow as an
instability of a convective state consisting of parallel vertical flow supp
orted by buoyancy forces. The form of the linear equation governing the ins
tability is derived and two modes of instability are discussed, one of whic
h leads to the onset of steady Eulerian mean flow in the system. We are thu
s able to link the origin of mean flow precisely to the profiles of the unp
erturbed plumes. The form of the nonlinear partial differential equation go
verning the Eulerian mean flow, including nonlinear effects, is derived in
one special case. The extension to three dimensions is outlined. (C) 2000 A
merican Institute of Physics. [S1054-1500(00)01101-0].