Large-scale vortex formation in three-dimensional rotating Rayleigh-Bénard convection

Numerical experiments are performed on three-dimensional thermal convection between parallel plates in a rotating system with a larger horizontal region than in previous studies. It is confirmed that a large-scale vortex (LSV) with positive vorticity (cyclonic) is formed over a significant part of the region and its horizontal size increases if the horizontal region is extended. The correlation analysis in the vertical direction shows that the small-scale motion has a typical structure of the baroclinic vortex of thermal convection in the rotating system, whereas the large-scale motion is a barotropic vortex that is not associated with thermal convection. A horizontal spectral analysis of the individual terms in the kinetic energy equation reveals that the nonlinear effect of the small-scale vortex motion caused by the buoyancy force induces a large-scale toroidal component, and that the LSV is maintained by the balance between the nonlinear effect and the viscous dissipation of the large-scale motion. The results of this analysis indicate the importance of kinetic energy damping mechanism for the appearance of LSVs. When weak damping operates at larger scales, it is expected that the maximum extent of the vortex appears even if the horizontal region is extended further. On the other hand, the emergence of LSVs will be prevented when strong enough damping is effective at larger scales.