Ultimate state of two-dimensional Rayleigh-Bénard convection between free-slip fixed-temperature boundaries

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...

Full description

Saved in:
Bibliographic Details
Published in:Physical review letters 2011-06, Vol.106 (24), p.244501-244501, Article 244501
Main Authors: Whitehead, Jared P, Doering, Charles R
Format: Article
Language:English
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0031-9007
1079-7114
DOI:10.1103/physrevlett.106.244501