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SUMMARY:Bounds on mixing efficiency and Richardson number in stably strati
 fied turbulent shear flow - Colm-cille Caulfield\, BPI &amp\; DAMTP
DTSTART:20080926T134500Z
DTEND:20080926T144500Z
UID:TALK13782@talks.cam.ac.uk
CONTACT:Dr C. P.  Caulfield
DESCRIPTION:The Miles-Howard theorem is a classical result\, which has bee
 n extremely influential in the study of stratified shear flow. The theorem
  states that if the local Richardson number (i.e. the ratio of the buoyanc
 y frequency to the square of the velocity shear) throughout a laminar invi
 scid stratified shear flow is everywhere greater than a quarter\, the flow
  is stable to two-dimensional infinitesimal normal mode perturbations.  Th
 ough heuristic energy arguments are commonly presented\, and similar crite
 ria based around bulk Richardson numbers (i.e. the ratio of the overall re
 duced gravity times the layer depth to the square of the velocity differen
 ce) are widely used  to parameterize the mixing behaviour in fully nonline
 ar turbulent flows\, rigorous theoretical results  for flow stabilization 
 by strong stratification have been elusive. We derive such a nonlinear res
 ult for a model flow (stratified Couette flow\, where the top and bottom b
 oundaries are set at constant relative velocity\, and constant\, staticall
 y stable densities) by generating rigorous bounds on the long-time average
  of the buoyancy flux\, subject to the requirement that the ratio between 
 the buoyancy flux and the forcing (i.e. the "mixing efficiency") is an (ar
 bitrary) constant\, demonstrating that a statistically steady state is onl
 y possible for sufficiently small values of the bulk Richardson number. Co
 nversely\, for a given (sufficiently small) Richardson number\, we show th
 at the mixing efficiency has a strict lower bound within this model flow. 
LOCATION:Open Plan Area\, BP Institute\, Madingley Rise CB3 0EZ
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