Vorticity skewness of finite-amplitude rapidly rotating Rayleigh-Bénard convection*

Rotating Rayleigh-Bénard convection denotes the convection between a warm plate and a cold plate in a rotating environment. It is a classic model for understanding convective vortices in the atmosphere and ocean. The influence of background rotation on fluid inertia breaks the symmetry between cyclones and anticyclones. Such a symmetry breaking could be represented by vorticity skewness, which still lacks a systematic theory. Rapidly rotating convection with stress-free boundaries and unit Prandtl number is a convenient starting point. The investigation starts from the convective onset stage, where the vortices grow stationarily. Asymptotic analysis shows that the volumetric vorticity skewness S is produced by the interaction between the n=0, 1, and n=1, 2 vertical eigenmodes. The n=0 (barotropic) mode positively contributes to S mainly by stretching the vertical relative vorticity, an ageostrophic effect. The n=2 mode makes a minor negative contribution to S by preferentially intensifying the outflow over the inflow, a non-hydrostatic effect. The theory predicts S to be proportional to the global Rossby number defined with the volumetric standard deviation of vorticity, Ro_g. The proportional factor does not depend on the Rayleigh and Ekman numbers, agreeing with direct numerical simulations. Then, the system enters the equilibrium stage. The stretching of vertical vorticity still dominantly contributes to S. At Ro_g ≥0.5, the emergent unsteady flow significantly suppresses the asymmetry between the inflow and outflow strength and weakens its influence on S.