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-Bénard 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≤0.2891Ra(5/12) uniformly in the Prandtl number Pr. This scaling challenges some theoretical arguments regarding asymptotic high Rayleigh number heat transport by turbulent convection.
authors.affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109-1034, USA. jaredwh@umich.edu
authors.forename: Jared P
authors.initials: JP
authors.lastname: Whitehead
authors.forename: Charles R
authors.initials: CR
authors.lastname: Doering