A numerical investigation of an asymptotically reduced model for
quasi-geostrophic Rayleigh-B\'enard convection is conducted in which the
depth-averaged flows are numerically suppressed by modifying the governing
equations. The Reynolds number and Nusselt number show evidence of approaching
the diffusion-free scalings of Re∼RaE/Pr and Nu∼Pr−1/2Ra3/2E2, respectively, where E is the Ekman number and Pr is the
Prandtl number. For large Ra, the presence of depth-invariant flows, such as
large-scale vortices, yield heat and momentum transport scalings that exceed
those of the diffusion-free scaling laws. The Taylor microscale does not vary
significantly with increasing Ra, whereas the integral length scale grows
weakly. The computed length scales remain O(1) with respect to the linearly
unstable critical wavenumber; we therefore conclude that these scales remain
viscously controlled. We do not find a point-wise Coriolis-Inertia-Archimedean
(CIA) force balance in the turbulent regime; interior dynamics are instead
dominated by horizontal advection (inertia), vortex stretching (Coriolis) and
the vertical pressure gradient. A secondary, sub-dominant balance between the
buoyancy force and the viscous force occurs in the interior and the ratio of
the rms of these two forces is found to approach unity with increasing Ra.
This secondary balance is attributed to the turbulent fluid interior acting as
the dominant control on the heat transport. These findings indicate that a
pointwise CIA balance does not occur in the high Rayleigh number regime of
quasi-geostrophic convection in the plane layer geometry. Instead, simulations
are characterized by what may be termed a \textsl{non-local} CIA balance in
which the buoyancy force is dominant within the thermal boundary layers and is
spatially separated from the interior Coriolis and inertial forces.Comment: 32 pages, 11 figure