Letter: Similarity model for corner roll in turbulent Rayleigh-Bénard convection

The corner roll (CR) in the Rayleigh-Bénard convection accounts for the behaviors of convection flow and heat transport in the corner. The three-dimensional direct numerical simulations for 108 < Ra < 5 × 109 show that CR presents a well-defined similarity and multi-layer structure. The CR can be described by a stream function derived from the homotopy and the structure ensemble dynamics. The scale of CR has a negative scaling r = 0.770Ra−0.085. A new scaling theory for CR suggests the scalings for Recr ∼ Ra0.248 and Nucr ∼ Ra1/3 very close to the simulated ones.