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DTSTAMP:20260424T143516Z
UID:1746779400@ist.ac.at
DTSTART:20250509T103000
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DESCRIPTION:Speaker: Gökhan Yalniz\nhosted by Maksym Serbyn\nAbstract: The
  overarching goal of this thesis is to break down the complexity of turbul
 ent flows in terms of enumerable\, coherent structures and patterns. In a 
 five-paper series\, we adopt a variety of perspectives and techniques to r
 elate the properties of systems of increasing complexity to their underlyi
 ng coherent structures.Initially\, we take a dynamical systems point of vi
 ew\, seeing turbulent flow as a chaotic trajectory bouncing between exact 
 unstable solutions of the underlying equations of motion. Using persistent
  homology\, the main tool of topological data analysis capturing the persi
 stence across scales of topological features in a point cloud\, we introdu
 ce a method that quantifies visits of turbulent trajectories to unstable t
 ime-periodic solutions\, also called periodic orbits. We demonstrate this 
 method first in the Rössler and \\KS{} systems. Using this method in 3D K
 olmogorov flow\, we extract a Markov chain from turbulent data\, where eac
 h node corresponds to the neighbourhood of a periodic orbit. The invariant
  distribution of this Markov chain reproduces expectation values on turbul
 ent data when it is used to weight averages on the respective periodic orb
 its.In more realistic\, wall-bounded settings\, such as plane-Couette flow
  (pcf) driven by the relative motion of the walls\, or plane-Poiseuille fl
 ow (ppf) driven by a pressure gradient\, finding exact solutions is diffic
 ult. We use dynamic mode decomposition (DMD)\, a dimensionality reduction 
 method for sequential data\, to identify and approximate low-dimensional d
 ynamics without knowing any exact solutions. Most spatially-extended syste
 ms are equivariant under translations\, and in such cases spatial drifts d
 ominate DMD\, hindering its use in the search for and modelling of low-dim
 ensional dynamics. We augment DMD with a symmetry reduction method trained
  on turbulent data to stop it from seeing translations as a feature\, impr
 oving its ability to extract dynamical information in translation-equivari
 ant systems. We find segments of turbulent trajectories that linearize wel
 l with their symmetry-reduced DMD spectra\, akin to dynamics near exact so
 lutions. Searching for harmonics in the spectra gives leads for periodic o
 rbits with spatial drifts\, one of which converges to a new solution.In la
 rger domains\, turbulence can localize and coexist with surrounding lamina
 r flow. Our preceding approaches are global\, taking all of a domain into 
 account at once\, and cannot readily treat each localized patch individual
 ly. Working first in a minimal oblique domain that can host a single 1D-lo
 calized turbulent patch\, we find that turbulence in ppf is connected to a
  stable periodic orbit at a flow velocity much lower than when turbulence 
 is first onset. We show that\, well in advance of sustained turbulence\, c
 haos sets in explosively\, and for long time horizons\, time series are co
 nsistent with that of a random process.Finally\, in much larger domains\, 
 we study and compare 2D-localized turbulence that appears as large-scale i
 nclined structures\, called stripes\, in ppf and pcf. While appearing simi
 lar\, we find that stripes in these two settings differ significantly in t
 erms of how they sustain themselves\, and in higher velocities\, how they 
 proliferate.
LOCATION:Office Bldg West / Ground floor / Heinzel Seminar Room (I21.EG.101
 ) \, ISTA
ORGANIZER:
SUMMARY:Gökhan Yalniz: Thesis Defense: Transition to turbulence: Data-\, s
 olution-\, and pattern-driven approaches 
URL:https://talks-calendar.ista.ac.at/events/5670
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