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Carnegie Mellon NSF logoCenter for Nonlinear Analysis
Charlie Doering
Afilliation: Mathematics, Physics, and Complex Systems, University of Michigan

Title: Ultimate State of Two-Dimensional Rayleigh-Bénard Convection Between Free-Slip Fixed-Temperature Boundaries

Abstract: Rigorous upper limits on the vertical heat transport in two dimensional Rayleigh-B\'enard convection between stress-free isothermal boundaries are derived from the Boussinesq approximation of the Navier-Stokes equations. The Nusselt number $Nu$ is bounded in terms of the Rayleigh number $Ra$ according to $Nu \leq 0.2292 \, Ra^{5/12}$ uniformly in the Prandtl number $Pr$. This scaling challenges some theoretical arguments regarding the asymptotic high Rayleigh number heat transport by turbulent convection. (Joint work with Jared Whitehead.)