"Ultimate state" of two-dimensional Rayleigh-Benard convection
Charles Doering, University of Michigan
Abstract: Rayleigh-Bénard convection is the buoyancy-driven flow of a fluid heated from below and cooled from above. Heat transport by convection an important physical process for applications in engineering, atmosphere and ocean science, and astrophysics, and it serves as a fundamental paradigm of modern nonlinear dynamics, pattern formation, chaos, and turbulence. Determining the bulk transport properties of high Rayleigh number convection turbulent convection remains a grand challenge for experiment, simulation, theory, and analysis. In this talk, after a general survey of the theory and applications of Rayleigh-Bénard convection we describe recent results for mathematically rigorous upper limits on the vertical heat transport in two dimensional Rayleigh-Bénard convection between stress-free isothermal boundaries derived from the Boussinesq approximation of the Navier-Stokes equations. These bounds challenge some popular theoretical arguments regarding the asymptotic high
Rayleigh number heat transport scaling.