Signature of Optimal Coherent Structures in Turbulent 2D Rayleigh Benard Convection

Steady solutions that maximize the heat transport in 2D Rayleigh Bénard convection (RBC) with no-slip horizontal walls have been studied in detail in Waleffe, Boonkasame & Smith (2015) and Sondak, Smith & Waleffe (2015). The close agreement of Nu-Ra scaling of the optimal solutions with data from 3D simulations and experiments suggests a link between the optimal coherent structures and turbulent 3D RBC. We explore this connection by searching for signatures of the optimal solutions in 2D turbulent RBC. Spatial correlations between the optimal structures and turbulent fields are computed at a variety of Pr and Ra in high aspect ratio domains. Our results show highly correlated (> 0.8) structures that resemble the optimal structure appear frequently throughout the turbulent flow field. The similarities in these structures are especially pronounced in the boundary layer. We compare momentum and thermal boundary layer scaling between the optimal and turbulent solutions and find that they are in very good agreement. As a precursor to stability analysis of the optimal solutions, the effect of mean flow on the agreement between statistics of the optimal and turbulent solutions is diagnosed using additional turbulent simulations that exclude mean flows by imposing mirror symmetry.