Role of Large-Scale Structures in the Correlation Between Temperature and Wall-Normal Velocity in Rayleigh-Bénard Convection*

Turbulent Rayleigh-Bénard convection is critical in scientific and engineering contexts, especially concerning the scaling of the Nusselt number (Nu) at high Rayleigh numbers (Ra). Direct numerical simulation (DNS) is a primary method for studying this phenomenon but achieving very high Ra with DNS is expensive. To address this, we conducted DNS with Ra up to 4×10⁸, a Prandtl number (Pr) of 1, and a domain aspect ratio of 15. Our spectral analysis of wall-normal velocity and temperature covariance revealed that large-scale structures significantly influence these dynamics but have minimal impact on Nu scaling since these structures remain away from the wall and are not transferred to smaller scales. This suggests that small-domain DNS may inadequately represent large-scale structures for Nu scaling studies. Nevertheless, our findings indicate that using small domains has a limited impact on Nu, despite differences in the dynamics of the covariance. Given that dominant scale transfer from large to small scales was not observed, further investigation is needed to validate these results.