Ultimate State of Two-Dimensional Rayleigh-Bénard Convection between Free-Slip Fixed-Temperature Boundaries

Jared P. Whitehead, Charles R. Doering
2011 Physical Review Letters  
Rigorous upper limits on the vertical heat transport in two dimensional Rayleigh-Benard 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 ≤ 0.2295 Ra^5/12 uniformly in the Prandtl number Pr. This Nusselt number scaling challenges some theoretical arguments regarding the asymptotic high Rayleigh number heat transport by turbulent
more » ... rt by turbulent convection.
doi:10.1103/physrevlett.106.244501 pmid:21770573 fatcat:ifr76kqbijgtlh7fqgybfe6l3q