A Prediction for the Optimal Stratification for Turbulent Mixing

TANG, W. and CAULFIELD, C. P. and KERSWELL, R. R. (2009) A Prediction for the Optimal Stratification for Turbulent Mixing. Journal of Fluid Mechanics, 634 (-1). pp. 487-497. DOI https://doi.org/10.1017/S0022112009990711

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By identifying the stratification which leads to maximal buoyancy flux in a stably-stratified plane Couette flow, we make a prediction of what bulk stratification (as a function of the shear) is optimal for turbulent mixing. A previous attempt to do this (Caulfield, Tang & Plasting, J. Fluid Mech., vol. 498, 2004, p. 315) failed due to an unexpected degeneracy in the variational problem. Here, we overcome this issue by parameterizing the variational problem implicitly with the overall mixing efficiency which is then optimized across to return a rigorous upper bound on the buoyancy flux. We find that the bulk Richardson number quickly approaches 1/6 in the asymptotic limit of high shear with the associated mixing efficiency tending to 1/3. The predicted mean profiles associated with the bound appear to have a layered structure, with the gradient Richardson number being low both in the interior, and in boundary layers near the walls, with a global maximum, also equal to 1/6, occurring at the edge of the boundary layers.

Item Type: Article
Uncontrolled Keywords: BPI; 09AREP;
Subjects: 99 - Other
Divisions: 99 - Other
Journal or Publication Title: Journal of Fluid Mechanics
Volume: 634
Page Range: pp. 487-497
Identification Number: https://doi.org/10.1017/S0022112009990711
Depositing User: Sarah Humbert
Date Deposited: 08 Jul 2010 14:04
Last Modified: 23 Jul 2013 09:57
URI: http://eprints.esc.cam.ac.uk/id/eprint/1452

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