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SUMMARY:Richardson number-dependent bounds on buoyancy flux - Caulfield\, 
 CP (Cambridge)
DTSTART:20081212T140000Z
DTEND:20081212T143000Z
UID:TALK15628@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:Parameterizing the mixing of a stratified fluid subject to she
 ar is a fundamental challenge for models of environmental and industrial f
 lows. In particular\, it is of great value to parameterize the efficiency 
 of turbulent mixing\, in the sense of the proportion of the kinetic energy
  converted into potential energy (through irreversible mixing of fluid of 
 different density) compared to the total amount converted to both potentia
 l energy and internal energy (through viscous dissipation). Various compet
 ing models have been presented to relate the mixing efficiency to bulk pro
 perties of the flow\, especially through different Richardson numbers\, wh
 ich quantify the relative importance of buoyancy and shear within the flow
 .\nOne promising approach is to construct rigorous bounds on the long-time
  average of the buoyancy flux (i.e. the mixing rate) within simple model s
 tratified shear flows\, imposing physically reasonable constraints on the 
 model flow fields. In this talk\, we apply this technique to stably strati
 fied Couette flow\, imposing as a constraint the mixing efficiency\, and s
 how that a bound on the long-time average of the buoyancy flux can only be
  found for a certain range of bulk Richardson numbers. For sufficiently st
 rong stratifications\, it appears that no bound exists\, suggesting that i
 t is not possible to find a statistically steady state. We discuss the imp
 lications of this result for various classical stratified shear turbulence
  models. 
LOCATION:Seminar Room 1\, Newton Institute
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