Double-reflection symmetry of thermal convection for Rayleigh number up to 1010

Abstract

The Rayleigh–Bénard convection system exhibits certain known symmetries at low Rayleigh numbers that are broken as the Rayleigh number increases. In this study, we investigate the statistical symmetry of Rayleigh–Bénard convection at moderately high Rayleigh numbers through direct numerical simulations. The simulations are conducted for a fluid confined within two-dimensional walls, with an aspect ratio of unity and a fixed Prandtl number. Although elliptical large-scale circulations break both left-right and top-down reflection symmetries, we observe the emergence of a restored double-reflection symmetry. This symmetry is evident in the velocity and temperature fields, as well as in the variations of mean velocity and temperature profiles along the streamwise direction and the characteristics of the kinetic and thermal boundary layers. For Rayleigh numbers ranging between 107 and 1010, our results demonstrate a remarkable data collapse under this double-reflection transformation.