Correlation of internal flow structure with heat transfer efficiency in turbulent Rayleigh-Bénard convection

To understand how internal flow structures manifest themselves in the global heat transfer, we study the correlation between different flow modes and the instantaneous Nusselt number (Nu) in a two-dimensional square Rayleigh-Bénard convection cell. High-resolution and long-time direct numerical simulations are carried out for Rayleigh numbers between 107 and 109 and a Prandtl number of 5.3. The investigated Nusselt numbers include the volume-averaged Nuvol, the wall-averaged Nuwall, the kinetic energy dissipation based Nukinetic, and the thermal energy dissipation based Nuthermal. The Fourier mode decomposition and proper orthogonal decomposition are adopted to extract the coherent flow structure. Our results show that the single-roll mode, the horizontally stacked double-roll mode, and the quadrupolar flow mode are more efficient for heat transfer on average. In contrast, the vertically stacked double-roll mode is inefficient for heat transfer on average. The volume-averaged Nuvol and the kinetic energy dissipation based Nukinetic can better reproduce the correlation of internal flow structures with heat transfer efficiency than that of the wall-averaged Nuwall and the thermal energy dissipation based Nuthermal, even though these four Nusselt numbers give consistent time-averaged mean values. The ensemble-averaged time trace of Nu during flow reversal shows that only the volume-averaged Nuvol can reproduce the overshoot phenomenon that is observed in the previous experimental study. Our results reveal that the proper choice of Nu is critical to obtain a meaningful interpretation.