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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Underlying large-scale structures in transitional
pipe flow - Mellibovsky\, F (Universitat Politcnic
a de Catalunya)
DTSTART;TZID=Europe/London:20080910T165000
DTEND;TZID=Europe/London:20080910T171000
UID:TALK13365AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/13365
DESCRIPTION:Pipe flow undergoes transition to turbulence despi
te the linear stability of its basic laminar solut
ion. Finite amplitude solutions in the form of tra
velling waves (H. Faisst and B. Eckhardt\, Phys. R
ev. Lett. 91(22)\, 224502 (2003))\, coexisting wit
h the basic flow\, have been identified in the las
t few years. While they have been proved to play a
certain role in the turbulent dynamics (B. Hof et
al.\, Science 305\, 1594 (2004))\, their involvem
ent in the transition process seems to be simply u
ngrounded. Furthermore\, some recent experimental
results point at a transitory nature of turbulence
(B. Hof et al.\, Nature 443(7107)\, 59--62 (2006)
)\, thus questioning the mere existence of a well
defined critical threshold. The region of phase sp
ace dominated by turbulent dynamics would then be
constituted by a surging amount of bifurcating com
plex solutions as the Reynolds Number is increased
\, acting as an attractor most of the time\, but a
lways retaining some probability that any trajecto
ry finds its way back to laminarity. However trans
ient may turbulence be\, the notion of a threshold
separating initial conditions that lead to transi
tion from others that end up decaying still applie
s. It suffices to define the threshold as the poin
t where the perturbation lifetime seems to diverge
\, possibly not to infinity if turbulence is a tra
nsient phenomenon\, but still abruptly. Then\, the
threshold regains interest\, and the question can
be asked of how a solution wandering about critic
ality (T. Schneider et al.\, Phys. Rev. Lett. 99(3
)\, 034502 (2007)) would look like. Starting from
different initial conditions\, and through accurat
e refinements\, trajectories on the edge between t
urbulence and laminarity can then be analysed to e
lucidate which properties of a solution determine
whether it belongs to the laminar or the turbulent
basin of attraction. We analyse these trajectorie
s to try and understand transition. Using an adapt
ed Newton method we systematically search for trav
elling wave solutions underlying the dynamics of t
hese critical trajectories.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:Mustapha Amrani
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