Journal
JOURNAL OF FLUID MECHANICS
Volume 634, Issue -, Pages 487-497Publisher
CAMBRIDGE UNIV PRESS
DOI: 10.1017/S0022112009990711
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Funding
- National Science Foundation [ATM-0222104]
- EU [MIRG-CT-2005-016563]
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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.
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