Similarity model for corner roll in turbulent Rayleigh-Benard convection

Abstract

The corner roll (CR) in the Rayleigh-Bénard (RB) convection accounts for the behaviors of heat transport and convection flow at the corner. Streamlines of the three-dimensional direct numerical simulations for $10^8<Ra<5\times 10^9$ show that CR presents well-defined similarity and multi-layer structure. A stream function for CR is developed by homotopy and the structure ensemble dynamics. The model presents the scaling of Reynolds number of corner roll $R{e}_{cr}\sim R{a}^{1/4}$. Scaling of CR scale $r=0.77R{a}^{-0.085}$ indicates strong near-wall shearing induced by wind and provides a probability of the `ultimate regime' at high $Ra$.

5 pages, 6 figures