Abstract

An upper bound on the rate of vertical heat transport is established in three dimensions for stress-free velocity boundary conditions on horizontally periodic plates. a variation of the background method is implemented that allows negative values of the quadratic form to yield 'small' (O.1=Pr/) corrections to the subsequent bound. for large (but finite) Prandtl numbers this bound is an improvement over the 'ultimate' Ra1=2 scaling and, in the limit of infinite Pr, agrees with the bound of Ra5=12 recently derived in that limit for stress-free boundaries. © 2013 Cambridge University Press.

Department(s)

Mathematics and Statistics

Keywords and Phrases

Benard Convection; Mantle Convection; Turbulent Convection

International Standard Serial Number (ISSN)

1469-7645; 0022-1120

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2023 Cambridge University Press, All rights reserved.

Publication Date

01 Jan 2013

Share

 
COinS