Vortex Dynamics in Rotating Rayleigh-B\'enard Convection

Abstract

We investigate the spatial distribution and dynamics of the vortices in rotating Rayleigh-B\'enard convection in a reduced Rayleigh-number range $1.3{\le}Ra/Ra_{c}{\le}166$. Under slow rotations ($Ra{\gtrsim}10Ra_{c}$), the vortices are randomly distributed. The size-distribution of the Voronoi cells of the vortex centers is well described by the standard $\Gamma$ distribution. In this flow regime the vortices exhibit Brownian-type horizontal motion. The probability density functions of the vortex displacements are, however, non-Gaussian at short time scales. At modest rotating rates ($4Ra_{c}{\le}Ra{\lesssim}10Ra_{c}$) the centrifugal force leads to radial vortex motions, i.e., warm cyclones (cold anticyclones) moving towards (outward from) the rotation axis. The mean-square-displacements of the vortices increase faster than linearly at large time. This super-diffusive behavior can be satisfactorily explained by a Langevin model incorporating the centrifugal force. In the rapidly rotating regime ($1.6Ra_{c}{\le}Ra{\le}4Ra_{c}$) the vortices are densely distributed, with the size-distribution of their Voronoi cells differing significantly from the standard $\Gamma$ distribution. The hydrodynamic interaction of neighboring vortices results in formation of vortex clusters. Inside clusters the correlation of the vortex velocity fluctuations is scale free, with the correlation length being approximately $30\%$ of the cluster length. We examine the influence of cluster forming on the dynamics of individual vortex. Within clusters, cyclones exhibit inverse-centrifugal motion as they submit to the motion of strong anticyclones, while the velocity for outward motion of the anticyclones is increased. Our analysis show that the mobility of isolated vortices, scaled by their vorticity strength, is a simple power function of the Froude number