Circulation Statistics in Rayleigh-Bénard Convection

Abstract

Important statistical properties of velocity circulation in homogeneous isotropic turbulence (HIT) have been unveiled in recent years, raising the question of whether they persist, or are modified, in other classes of turbulent flows. Motivated by the dominant role of small-scale structures in the circulation fluctuations of HIT, we investigate their relevance in direct numerical simulations of Rayleigh-Bénard convection at a Rayleigh number of $10^9$ and Prandtl number of $O(1)$. Within the thermal boundary layer (TBL), the distribution of elementary vortices is found to be strongly correlated with the temperature field, while the statistics of their core aspect ratios is significantly altered. Additionally, the probability distribution functions of circulation, computed for planar contours which are parallel to the walls, display salient features closely akin to those observed in HIT, with the {\it Area Rule} (a connection between circulation statistics and minimal surfaces) remaining particularly well satisfied -- except for a possible transitional region at a distance of a few TBL thicknesses. Away from the TBL, as expected, the overall statistical behavior of these structures likewise resembles that of HIT, where the intermittent spatial distribution of small vortex tubes is instead determined by the energy dissipation field.