### Ultimate state of two-dimensional Rayleigh-Bénard convection

Doering, CR *(University of Michigan)*

Monday 23 July 2012, 11:00-11:40

Seminar Room 1, Newton Institute

#### 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.