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Inequalities and variational principles in double-diffusive turbulence

Published online by Cambridge University Press:  20 April 2006

Melvin E. Stern
Melvin E. Stern
Affiliation:
Graduate School of Oceanography, University of Rhode Island, Kingston, RI 02881
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Abstract

An inequality pertaining to the energetics of the boundary layer in turbulent pipe flow and turbulent thermal convection is generalized for the double-diffusive convection problem, where a semi-infinite layer of cold, fresh and light water overlies another hot, salty and dense layer. The smallest possible salt/heat-flux ratio equals the ratio of the square roots of the respective diffusivities. The bound is asymptotically realizable according to a variational principle. A bound on the relative fluxes is predicted when another solute is added (‘multiple diffusion’).

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 114 , January 1982 , pp. 105 - 121
Copyright
© 1972 Cambridge University Press

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