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CATEGORIES:Seminars for the Institute for Energy and Environm
ental Flows (formerly BP Institute)
SUMMARY:Bounds on mixing efficiency and Richardson number
in stably stratified turbulent shear flow - Colm-c
ille Caulfield\, BPI &\; DAMTP
DTSTART;TZID=Europe/London:20080926T144500
DTEND;TZID=Europe/London:20080926T154500
UID:TALK13782AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/13782
DESCRIPTION:The Miles-Howard theorem is a classical result\, w
hich has been extremely influential in the study o
f stratified shear flow. The theorem states that i
f the local Richardson number (i.e. the ratio of t
he buoyancy frequency to the square of the velocit
y shear) throughout a laminar inviscid stratified
shear flow is everywhere greater than a quarter\,
the flow is stable to two-dimensional infinitesima
l normal mode perturbations. Though heuristic ene
rgy arguments are commonly presented\, and similar
criteria based around bulk Richardson numbers (i.
e. the ratio of the overall reduced gravity times
the layer depth to the square of the velocity diff
erence) are widely used to parameterize the mixin
g behaviour in fully nonlinear turbulent flows\, r
igorous theoretical results for flow stabilizatio
n by strong stratification have been elusive. We d
erive such a nonlinear result for a model flow (st
ratified Couette flow\, where the top and bottom b
oundaries are set at constant relative velocity\,
and constant\, statically stable densities) by gen
erating rigorous bounds on the long-time average o
f the buoyancy flux\, subject to the requirement t
hat the ratio between the buoyancy flux and the fo
rcing (i.e. the "mixing efficiency") is an (arbitr
ary) constant\, demonstrating that a statistically
steady state is only possible for sufficiently sm
all values of the bulk Richardson number. Converse
ly\, for a given (sufficiently small) Richardson n
umber\, we show that the mixing efficiency has a s
trict lower bound within this model flow.
LOCATION:Open Plan Area\, BP Institute\, Madingley Rise CB3
0EZ
CONTACT:Dr C. P. Caulfield
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