"A Bound on the Vertical Transport of Heat in the 'ultimate' State of S" by Xiaoming Wang and Jared P. Whitehead
 

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

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