Quasi-geostrophic convective turbulence at large Rayleigh number

An asymptotically reduced model for Rayleigh-Bènard convection in a planar geometry is numerically investigated up to reduced Rayleigh numbers (Ra_r = Ek^4/3Ra, where Ek is the Ekman number and Ra is the depth-scaled Rayleigh number) of 280. We carry out a suite of simulations wherein the barotropic (depth averaged) components of the flow are zeroed out at each time-step in order to remove the effects of domain-sized vortices. The results are compared to cases where the barotropic component is not removed. Without the large-scale vortices, a linear scaling between the reduced Reynolds number Re_r = Ek^1/3Re and Ra_r is reported as well as a Ra_r^3/2 scaling for the Nusselt number. In addition, it is found that the Taylor microscale is approximately constant with increasing Ra_r, despite the increase in global Re_r. The kinetic energy spectra are not found to follow a Kolmogorov -5/3 law, which suggests the absence of a traditional inertial range. We interpret these results as evidence that energy in rapidly rotating convection is generated at small (viscous) length scales; kinetic energy cascades to both larger and smaller length scales, the former of which is responsible for the appearance of large scale vortices.