Abstract
Journal of Fluid Mechanics, 885:R4 (2020) We prove a new rigorous upper bound on the vertical heat transport for Bénard-Marangoni convection of a two- or three-dimensional fluid layer with infinite Prandtl number. Precisely, for Marangoni numberMa ≫ 1the Nusselt numberNuis bounded asymptotically byNu ≲ Ma^(2/7)(\ln Ma)^(-1/7) . Key to our proof are a background temperature field with a hyperbolic profile near the fluid's surface, and new estimates for the coupling between temperature and vertical velocity.