Similarity model for corner roll in turbulent Rayleigh-Benard convection

TL;DR

This paper develops a similarity model for the corner roll in turbulent Rayleigh-Bénard convection, revealing its structure, scaling laws, and implications for heat transport and the ultimate regime at high Rayleigh numbers.

Contribution

It introduces a new similarity and multi-layer structure model for corner rolls, including a Reynolds number scaling and a CR scale relation based on high-fidelity simulations.

Findings

Reynolds number scales as Ra^{1/4}

CR scale decreases as Ra^{-0.085}

Model indicates conditions for the ultimate regime

Abstract

The corner roll (CR) in the Rayleigh-B\'{e}nard (RB) convection accounts for the behaviors of heat transport and convection flow at the corner. Streamlines of the three-dimensional direct numerical simulations for $10^8<Ra<5\times10^9$ 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 $Re_{cr}\sim Ra^{1/4}$. Scaling of CR scale $r = 0.77 Ra^{-0.085}$ indicates strong near-wall shearing induced by wind and provides a probability of the `ultimate regime' at high $Ra$.