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SUMMARY:Spots Stripes and Turbulence: Pattern-Formation in Shear Flows
DTSTART:20120323T093000
DTEND:20120323T103000
DTSTAMP:20260510T105929Z
UID:4e1868d7387f58b56898dbab057ac24c6b4d0999e58d3b18960182bf
CATEGORIES:Conferences - Seminars
DESCRIPTION:Dr. Tobias Schneider\, Harvard School of Engineering and Appli
 ed Sciences\, USA\nLocally perturbing a parallel shear flow induces a spat
 ially localized patch of turbulence that slowly invades the surrounding la
 minar flow. Though spatio-temporal patterns such as these 'turbulent spots
 ' play a crucial role in transitional flows\, the mechanism which gives ri
 se to the observed localized structures is not well understood. I will pre
 sent the first evidence that a well-developed theory of a localized patter
 n in simpler PDE models carries over to Navier-Stokes flow and allows to c
 apture the observed patterns. Specifically\, I will demonstrate the existe
 nce of a new class of exact equilibrium and traveling wave solutions to th
 e full Navier-Stokes equations. Those solutions share the topology of peri
 odic solutions previously shown to play key roles in the transition to tur
 bulence and turbulent dynamics itself but are localized in space. Solution
 s of different size are organized in a snakes-and-ladders structure striki
 ngly similar to that observed in simpler pattern-forming PDE systems. Thes
 e localized solutions are a step towards extending the emerging dynamical 
 systems view of transitional turbulence to spatially extended flows and un
 covering the mechanisms underlying spatio-temporal turbulent patterns.
LOCATION:BM 5202 https://plan.epfl.ch/?room==BM%205202
STATUS:CONFIRMED
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