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SUMMARY:Underlying large-scale structures in transitional pipe flow - Mell
 ibovsky\, F (Universitat Politcnica de Catalunya)
DTSTART:20080910T155000Z
DTEND:20080910T161000Z
UID:TALK13365@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:Pipe flow undergoes transition to turbulence despite the linea
 r stability of its basic laminar solution. Finite amplitude solutions in t
 he form of travelling waves (H. Faisst and B. Eckhardt\, Phys. Rev. Lett. 
 91(22)\, 224502 (2003))\, coexisting with the basic flow\, have been ident
 ified in the last 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 involvement in the transition process seems to be simply ungroun
 ded. 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 space dominated by turbulent dynamics would then be co
 nstituted by a surging amount of bifurcating complex solutions as the Reyn
 olds Number is increased\, acting as an attractor most of the time\, but a
 lways retaining some probability that any trajectory finds its way back to
  laminarity. However transient may turbulence be\, the notion of a thresho
 ld separating initial conditions that lead to transition from others that 
 end up decaying still applies. It suffices to define the threshold as the 
 point where the perturbation lifetime seems to diverge\, possibly not to i
 nfinity if turbulence is a transient phenomenon\, but still abruptly. Then
 \, the threshold regains interest\, and the question can be asked of how a
  solution wandering about criticality (T. Schneider et al.\, Phys. Rev. Le
 tt. 99(3)\, 034502 (2007)) would look like. Starting from different initia
 l conditions\, and through accurate refinements\, trajectories on the edge
  between turbulence and laminarity can then be analysed to elucidate which
  properties of a solution determine whether it belongs to the laminar or t
 he turbulent basin of attraction. We analyse these trajectories to try and
  understand transition. Using an adapted Newton method we systematically s
 earch for travelling wave solutions underlying the dynamics of these criti
 cal trajectories.
LOCATION:Seminar Room 1\, Newton Institute
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