TOD

Abstract

Determining the transport properties of high Rayleigh number convection turbulent convection remains a grand challenge for experiment, simulation, theory, and analysis. In this talk, after a brief review 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 nature of the asymptotic high Rayleigh number ‘ultimate regime’ of turbulent convection. This is joint work with Jared Whitehead.