---
OA_place: publisher
_id: '19684'
abstract:
- lang: eng
  text: "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."
acknowledged_ssus:
- _id: ScienComp
acknowledgement: "The work in this thesis was supported by a grant from the Simons
  Foundation (662960, BH).\r\n"
alternative_title:
- ISTA Thesis
article_processing_charge: No
author:
- first_name: Gökhan
  full_name: Yalniz, Gökhan
  id: 66E74FA2-D8BF-11E9-8249-8DE2E5697425
  last_name: Yalniz
  orcid: 0000-0002-8490-9312
citation:
  ama: 'Yalniz G. Transition to turbulence : Data-, solution-, and pattern-driven
    approaches. 2025. doi:<a href="https://doi.org/10.15479/AT-ISTA-19684">10.15479/AT-ISTA-19684</a>'
  apa: 'Yalniz, G. (2025). <i>Transition to turbulence : Data-, solution-, and pattern-driven
    approaches</i>. Institute of Science and Technology Austria. <a href="https://doi.org/10.15479/AT-ISTA-19684">https://doi.org/10.15479/AT-ISTA-19684</a>'
  chicago: 'Yalniz, Gökhan. “Transition to Turbulence : Data-, Solution-, and Pattern-Driven
    Approaches.” Institute of Science and Technology Austria, 2025. <a href="https://doi.org/10.15479/AT-ISTA-19684">https://doi.org/10.15479/AT-ISTA-19684</a>.'
  ieee: 'G. Yalniz, “Transition to turbulence : Data-, solution-, and pattern-driven
    approaches,” Institute of Science and Technology Austria, 2025.'
  ista: 'Yalniz G. 2025. Transition to turbulence : Data-, solution-, and pattern-driven
    approaches. Institute of Science and Technology Austria.'
  mla: 'Yalniz, Gökhan. <i>Transition to Turbulence : Data-, Solution-, and Pattern-Driven
    Approaches</i>. Institute of Science and Technology Austria, 2025, doi:<a href="https://doi.org/10.15479/AT-ISTA-19684">10.15479/AT-ISTA-19684</a>.'
  short: 'G. Yalniz, Transition to Turbulence : Data-, Solution-, and Pattern-Driven
    Approaches, Institute of Science and Technology Austria, 2025.'
corr_author: '1'
date_created: 2025-05-12T15:12:28Z
date_published: 2025-05-13T00:00:00Z
date_updated: 2026-06-18T19:23:35Z
day: '13'
ddc:
- '514'
- '519'
- '532'
- '004'
degree_awarded: PhD
department:
- _id: GradSch
- _id: BjHo
doi: 10.15479/AT-ISTA-19684
file:
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  date_created: 2025-05-12T15:13:28Z
  date_updated: 2025-05-12T15:13:28Z
  file_id: '19685'
  file_name: Gökhan Yalnız - PhD thesis.pdf
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  content_type: video/mp4
  creator: gyalniz
  date_created: 2025-05-12T15:15:59Z
  date_updated: 2025-05-12T15:43:28Z
  description: '3D visualizations of the turbulent flow (left) and the periodic orbits
    (middle) that are being shadowed along with the local state space projections
    (right) onto the principal components of the respective periodic orbit. Shown
    here are the isosurfaces of velocity (red/blue: ±95% of the instantaneous maximum)
    and vorticity (purple/green: ±65% of the instantaneous maximum) in the x-direction.
    Markers along the projections are in sync with the 3D visualizations. The movie
    corresponds to the initial time interval (up to t = 100) of figure 2.2 (a,b);
    periodic orbits and the state space projections are shown only through the shadowing
    events indicated in figure 2.2 (b).'
  file_id: '19686'
  file_name: Movie 2A.1.mp4
  file_size: 37763743
  relation: supplementary_material
  title: Chapter 2 - Movie 2A.1
- access_level: open_access
  checksum: 0ae5ac7d9896003c0c4207dd746808dc
  content_type: video/mp4
  creator: gyalniz
  date_created: 2025-05-12T15:16:09Z
  date_updated: 2025-05-12T15:43:28Z
  description: 'Turbulent flow (left) in HKW domain and its symmetry reduction (right).
    Shown here are the isosurfaces of streamwise velocity (red/blue: u = 0.5 max/min
    u) and streamwise vorticity (green/purple: ω_x = 0.5 max/min ω_x).'
  file_id: '19687'
  file_name: Movie 3A.1.mp4
  file_size: 3902655
  relation: supplementary_material
  title: Chapter 3 - Movie 3A.1
- access_level: open_access
  checksum: ef8d270e066c1a9c3cb5ae46acf945e6
  content_type: video/mp4
  creator: gyalniz
  date_created: 2025-05-12T15:16:21Z
  date_updated: 2025-05-12T15:43:28Z
  description: 'Turbulent flow (left) in P2K domain and its symmetry reduction (right).
    Shown here are the isosurfaces of streamwise velocity (red/blue: u = 0.5 max/min
    u) and streamwise vorticity (green/purple: ω_x = 0.5 max/min ω_x).'
  file_id: '19688'
  file_name: Movie 3A.2.mp4
  file_size: 7043169
  relation: supplementary_material
  title: Chapter 3 - Movie 3A.2
- access_level: open_access
  checksum: 7ed871f428100d6827ac9b0e8ca8e985
  content_type: video/mp4
  creator: gyalniz
  date_created: 2025-05-12T15:16:36Z
  date_updated: 2025-05-12T15:43:28Z
  description: 'Relative periodic orbit RPO_79.4 (left) of the plane-Couette flow
    (HKW domain) and its symmetry reduction (right). Shown here are the isosurfaces
    of streamwise velocity (red/blue: u = 0.5 max/min u) and streamwise vorticity
    (green/purple: ω_x = 0.5 max/min ω_x).'
  file_id: '19689'
  file_name: Movie 3A.3.mp4
  file_size: 7748659
  relation: supplementary_material
  title: Chapter 3 - Movie 3A.3
- access_level: open_access
  checksum: dd5a252e1da00c8f303588e22e2baeef
  content_type: video/mp4
  creator: gyalniz
  date_created: 2025-05-12T15:16:50Z
  date_updated: 2025-05-12T15:43:28Z
  description: 'Symmetry-reduced flow (left), its SRDMD approximation (middle), and
    state space projection (right) showing the spiral-out episode in P2K domain (figure
    3.6 (b) and figure 3.8 (b)). Shown here are the isosurfaces of streamwise velocity
    (red/blue: u = 0.5 max/min u) and streamwise vorticity (green/purple: ω_x = 0.5
    max/min ω_x).'
  file_id: '19690'
  file_name: Movie 3A.4.mp4
  file_size: 5873052
  relation: supplementary_material
  title: Chapter 3 - Movie 3A.4
- access_level: open_access
  checksum: 5ac58b86810698db28cbfc28f351ff70
  content_type: video/mp4
  creator: gyalniz
  date_created: 2025-05-12T15:17:11Z
  date_updated: 2025-05-12T15:43:28Z
  description: Movie demonstrating the quasi-steady Reynolds number descent from turbulence
    to a periodic orbit.
  file_id: '19691'
  file_name: Movie 4A.1.mp4
  file_size: 9209327
  relation: supplementary_material
  title: Chapter 4 - Movie 4A.1
- access_level: open_access
  checksum: ac877f1e1ef39439911bf37cb1793b8e
  content_type: video/mp4
  creator: gyalniz
  date_created: 2025-05-12T15:17:43Z
  date_updated: 2025-05-12T15:43:28Z
  description: Streamwise velocity fluctuations (from laminar) of plane-Couette flow
    (Re^C =335) at the y = 0 wall-normal plane in coordinates stationary with respect
    to the bulk velocity. Here, x is the streamwise direction (the wall at y = 1 moves
    to the right) and z is the spanwise direction. Time is in advectime time units.
    Shown is the full (L_x = L_z = 400) domain.
  file_id: '19692'
  file_name: Movie 5A.1.mp4
  file_size: 5893993
  relation: supplementary_material
  title: Chapter 5 - Movie 5A.1
- access_level: open_access
  checksum: fd17eabb70129ceaa414e40924d1d2fe
  content_type: video/mp4
  creator: gyalniz
  date_created: 2025-05-12T15:17:49Z
  date_updated: 2025-05-12T15:43:28Z
  description: Streamwise velocity fluctuations (from laminar) of plane-Poiseuille
    flow (Re^P =660) at the y = 0.5 wall-normal plane in coordinates stationary with
    respect to the bulk velocity. Here, x is the streamwise direction (the mean negative
    pressure gradient is to the right) and z is the spanwise direction. Time is in
    advectime time units. Shown is the full (L_x = L_z = 400) domain.
  file_id: '19693'
  file_name: Movie 5A.2.mp4
  file_size: 3990352
  relation: supplementary_material
  title: Chapter 5 - Movie 5A.2
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  content_type: video/mp4
  creator: gyalniz
  date_created: 2025-05-12T15:17:58Z
  date_updated: 2025-05-12T15:43:28Z
  description: Streamwise velocity fluctuations (from laminar) of plane-Poiseuille
    flow (Re^P=660) at the y = 0.5 wall-normal plane in coordinates stationary with
    respect to the average velocity of the downstream tip of the stripe. Here, x is
    the streamwise direction (the mean negative pressure gradient is to the right)
    and z is the spanwise direction. Time is in advectime time units. Shown is a zoom-in
    of the full (L_x = L_z) domain.
  file_id: '19694'
  file_name: Movie 5A.3.mp4
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  title: Chapter 5 - Movie 5A.3
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file_date_updated: 2025-05-12T15:43:28Z
has_accepted_license: '1'
language:
- iso: eng
month: '05'
oa: 1
oa_version: Published Version
page: '155'
project:
- _id: 238598C6-32DE-11EA-91FC-C7463DDC885E
  grant_number: '662960'
  name: Revisiting the Turbulence Problem Using Statistical Mechanics
publication_identifier:
  issn:
  - 2663-337X
publication_status: published
publisher: Institute of Science and Technology Austria
related_material:
  record:
  - id: '9558'
    relation: part_of_dissertation
    status: public
  - id: '12105'
    relation: part_of_dissertation
    status: public
  - id: '13274'
    relation: part_of_dissertation
    status: public
  - id: '14466'
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  - id: '7563'
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status: public
supervisor:
- first_name: Björn
  full_name: Hof, Björn
  id: 3A374330-F248-11E8-B48F-1D18A9856A87
  last_name: Hof
  orcid: 0000-0003-2057-2754
title: 'Transition to turbulence : Data-, solution-, and pattern-driven approaches'
type: dissertation
user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd
year: '2025'
...