Rayleigh-Bénard Turbulence: Optimal Patterns and Dynamical Modes*

Rayleigh-Bénard convection (RBC) is a fitting prototype for various engineering systems and natural flows. Focusing on a 2-D RBC model with no-slip walls, we follow the wall-to-wall optimal transport framework of Hassanzadeh, P., Chini, G. and Doering, C., Journal of Fluid Mechanics, 751, pp. 627-662, 2014 and seek divergence-free velocity fields that maximize vertical heat transport. We study a wide range of Rayleigh (Ra) numbers, Ra = 10³-10¹⁰, to quantify the contribution of different components of the optimizing flow fields to the total heat transfer and extrapolate the results to the ultimate (i.e., asymptotically high Ra) RBC regime. We then focus on a long Direct Numerical Simulations (DNS) dataset of 3-D RBC at Ra = 10⁶ and compute the Proper Orthogonal Decomposition (POD) and Dynamic Mode Decomposition (DMD) modes. In exploring both systems, we seek insights into the nature of the RBC turbulence and potential connections between the optimal patterns obtained from the 2-D wall-to-wall framework and the modes of the 3-D flow.