Low Rossby number convection is studied using an asymptotically reduced
system of equations valid in the limit of strong rotation. The equations
describe four regimes as the Rayleigh number $Ra$ increases: a disordered
cellular regime near threshold, a regime of weakly interacting convective
Taylor columns at larger $Ra$, followed for yet larger $Ra$ by a breakdown
of the convective Taylor columns into a disordered plume regime
characterized by reduced hear transport efficiency, and finally by geostrophic
turbulence. The Nusselt number--Rayleigh number scaling in the "ultimate"
regime geostrophic turbulence is predicted and confirmed using direct
numerical simulations of the reduced equations. These simulations reveal
that the geostrophic turbulence is unstable to the formation of large scale
barotropic vortices, via a process known as spectral condensation. The
details of this process are quantified and its implications explored.
This is joint work with I Grooms (Courant Institute), K Julien, A Rubio, J.B. Weiss
(University of Colorado, Boulder) and G Vasil (Sydney).