Boundary layer structure in turbulent Rayleigh–Bénard convection

Abstract

AbstractThe structure of the boundary layers in turbulent Rayleigh–Bénard convection is studied by means of three-dimensional direct numerical simulations. We consider convection in a cylindrical cell at aspect ratio one for Rayleigh numbers of $\mathit{Ra}= 3\ensuremath{\times} 1{0}^{9} $ and $3\ensuremath{\times} 1{0}^{10} $ at fixed Prandtl number $\mathit{Pr}= 0. 7$. Similar to the experimental results in the same setup and for the same Prandtl number, the structure of the laminar boundary layers of the velocity and temperature fields is found to deviate from the prediction of Prandtl–Blasius–Pohlhausen theory. Deviations decrease when a dynamical rescaling of the data with an instantaneously defined boundary layer thickness is performed and the analysis plane is aligned with the instantaneous direction of the large-scale circulation in the closed cell. Our numerical results demonstrate that important assumptions of existing classical laminar boundary layer theories for forced and natural convection are violated, such as the strict two-dimensionality of the dynamics or the steadiness of the fluid motion. The boundary layer dynamics consists of two essential local dynamical building blocks, a plume detachment and a post-plume phase. The former is associated with larger variations of the instantaneous thickness of velocity and temperature boundary layer and a fully three-dimensional local flow. The post-plume dynamics is connected with the large-scale circulation in the cell that penetrates the boundary region from above. The mean turbulence profiles taken in localized sections of the boundary layer for each dynamical phase are also compared with solutions of perturbation expansions of the boundary layer equations of forced or natural convection towards mixed convection. Our analysis of both boundary layers shows that the near-wall dynamics combines elements of forced Blasius-type and natural convection.