The effect of surface roughness on the Lagrangian coherent structures in turbulent Rayleigh-Bénard convection

Abstract

We perform direct numerical simulations of turbulent Rayleigh-Bénard (RB) convection in a closed square cell with roughness plates at Rayleigh number fixed at R a = 10 8 and the Prandtl number fixed at Pr = 1. To gain insight into the effect of surface roughness on material transport in turbulent Rayleigh-Bénard convection, the Lagrangian coherent structures (LCSs) are extracted using the finite-time Lyapunov exponent method in the cases of different roughness heights. First, we find that lobe structures are widely present in RB convection and we elucidate how they play a part in transporting heat from coner-flow rolls to large-scale circulation. Then, we quantify the heat flux along the LCSs, which contributes to 80% of the total flux. This implies that the LCSs play an important role in heat transport regardless of the roughness height. Furthermore, two different mechanisms of heat transport in RB convection induced by roughness heights are explained in the Lagrangian perspective: the decrease in Nu number in the cases of h < h c is caused by the LCSs between the roughness elements which hinders the exchange of material between the fluid in the cavity and the bulk region; whereas, the increase in Nu number in the case of h > h c is produced by the enhanced mixing events of the convection that enhance the contribution of heat transport in the bulk region.