---
res:
  bibo_abstract:
  - "The overarching goal of this thesis is to break down the complexity of turbulent
    flows in terms of enumerable, coherent structures and patterns. In a five-paper
    series, we adopt a variety of perspectives and techniques to relate the properties
    of systems of increasing complexity to their underlying coherent structures. \r\n\r\nInitially,
    we take a dynamical systems point of view, 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 persistence across scales of topological features in a point cloud,
    we introduce a method that quantifies visits of turbulent trajectories to unstable
    time-periodic solutions, also called periodic orbits. We demonstrate this method
    first in the Rössler and Kuramoto–Sivashinsky systems. Using this method in 3D
    Kolmogorov flow, we extract a Markov chain from turbulent data, where each node
    corresponds to the neighbourhood of a periodic orbit. The invariant distribution
    of this Markov chain reproduces expectation values on turbulent data when it is
    used to weight averages on the respective periodic orbits.\r\n\r\nIn more realistic,
    wall-bounded settings, such as plane-Couette flow (pcf) driven by the relative
    motion of the walls, or plane-Poiseuille flow (ppf) driven by a pressure gradient,
    finding exact solutions is difficult. We use dynamic mode decomposition (DMD),
    a dimensionality reduction method for sequential data, to identify and approximate
    low-dimensional dynamics without knowing any exact solutions. Most spatially-extended
    systems are equivariant under translations, and in such cases spatial drifts dominate
    DMD, hindering its use in the search for and modelling of low-dimensional dynamics.
    We augment DMD with a symmetry reduction method trained on turbulent data to stop
    it from seeing translations as a feature, improving its ability to extract dynamical
    information in translation-equivariant systems. We find segments of turbulent
    trajectories that linearize well with their symmetry-reduced DMD spectra, akin
    to dynamics near exact solutions. Searching for harmonics in the spectra gives
    leads for periodic orbits with spatial drifts, one of which converges to a new
    solution.\r\n\r\nIn larger domains, turbulence can localize and coexist with surrounding
    laminar flow. Our preceding approaches are global, taking all of a domain into
    account at once, and cannot readily treat each localized patch individually. Working
    first in a minimal oblique domain that can host a single 1D-localized 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, chaos sets in explosively, and for long
    time horizons, time series are consistent with that of a random process.\r\n\r\nFinally,
    in much larger domains, we study and compare 2D-localized turbulence that appears
    as large-scale inclined structures, called stripes, in ppf and pcf. While appearing
    similar, we find that stripes in these two settings differ significantly in terms
    of how they sustain themselves, and in higher velocities, how they proliferate.@eng"
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Gökhan
      foaf_name: Yalniz, Gökhan
      foaf_surname: Yalniz
      foaf_workInfoHomepage: http://www.librecat.org/personId=66E74FA2-D8BF-11E9-8249-8DE2E5697425
    orcid: 0000-0002-8490-9312
  bibo_doi: 10.15479/AT-ISTA-19684
  dct_date: 2025^xs_gYear
  dct_isPartOf:
  - http://id.crossref.org/issn/2663-337X
  dct_language: eng
  dct_publisher: Institute of Science and Technology Austria@
  dct_title: 'Transition to turbulence : Data-, solution-, and pattern-driven approaches@'
...