A Bound on the Vertical Transport of Heat in the 'ultimate' State of Slippery Convection at Large Prandtl Numbers
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.
X. Wang and J. P. Whitehead, "A Bound on the Vertical Transport of Heat in the 'ultimate' State of Slippery Convection at Large Prandtl Numbers," Journal of Fluid Mechanics, vol. 729, pp. 103 - 122, Cambridge University Press, Jan 2013.
The definitive version is available at https://doi.org/10.1017/jfm.2013.289
Mathematics and Statistics
Keywords and Phrases
Benard Convection; Mantle Convection; Turbulent Convection
International Standard Serial Number (ISSN)
Article - Journal
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01 Jan 2013