[{"OA_place":"publisher","oa_version":"Published Version","day":"13","oa":1,"publication_identifier":{"issn":["2663-337X"]},"article_processing_charge":"No","citation":{"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.","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>","short":"G. Yalniz, Transition to Turbulence : Data-, Solution-, and Pattern-Driven Approaches, Institute of Science and Technology Austria, 2025.","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>","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>."},"date_updated":"2026-06-18T19:23:35Z","department":[{"_id":"GradSch"},{"_id":"BjHo"}],"year":"2025","related_material":{"record":[{"relation":"part_of_dissertation","status":"public","id":"9558"},{"relation":"part_of_dissertation","status":"public","id":"12105"},{"relation":"part_of_dissertation","status":"public","id":"13274"},{"id":"14466","status":"public","relation":"part_of_dissertation"},{"relation":"part_of_dissertation","id":"7563","status":"public"}]},"abstract":[{"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.","lang":"eng"}],"acknowledgement":"The work in this thesis was supported by a grant from the Simons Foundation (662960, BH).\r\n","_id":"19684","date_created":"2025-05-12T15:12:28Z","supervisor":[{"id":"3A374330-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-2057-2754","first_name":"Björn","full_name":"Hof, Björn","last_name":"Hof"}],"alternative_title":["ISTA Thesis"],"file":[{"file_size":20058169,"date_updated":"2025-05-12T15:13:28Z","file_name":"Gökhan Yalnız - PhD thesis.pdf","file_id":"19685","access_level":"open_access","checksum":"0e452642b79f13633f1595bde71a67e3","relation":"main_file","success":1,"content_type":"application/pdf","date_created":"2025-05-12T15:13:28Z","creator":"gyalniz"},{"date_created":"2025-05-12T15:15:59Z","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).","creator":"gyalniz","file_id":"19686","title":"Chapter 2 - Movie 2A.1","access_level":"open_access","date_updated":"2025-05-12T15:43:28Z","file_size":37763743,"file_name":"Movie 2A.1.mp4","relation":"supplementary_material","content_type":"video/mp4","checksum":"921099d76adab2df784ce12ce41cfb22"},{"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).","creator":"gyalniz","date_created":"2025-05-12T15:16:09Z","content_type":"video/mp4","relation":"supplementary_material","checksum":"0ae5ac7d9896003c0c4207dd746808dc","title":"Chapter 3 - Movie 3A.1","access_level":"open_access","file_id":"19687","file_name":"Movie 3A.1.mp4","date_updated":"2025-05-12T15:43:28Z","file_size":3902655},{"creator":"gyalniz","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).","date_created":"2025-05-12T15:16:21Z","checksum":"ef8d270e066c1a9c3cb5ae46acf945e6","relation":"supplementary_material","content_type":"video/mp4","date_updated":"2025-05-12T15:43:28Z","file_size":7043169,"file_name":"Movie 3A.2.mp4","file_id":"19688","access_level":"open_access","title":"Chapter 3 - Movie 3A.2"},{"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).","creator":"gyalniz","date_created":"2025-05-12T15:16:36Z","relation":"supplementary_material","content_type":"video/mp4","checksum":"7ed871f428100d6827ac9b0e8ca8e985","file_id":"19689","access_level":"open_access","title":"Chapter 3 - Movie 3A.3","date_updated":"2025-05-12T15:43:28Z","file_size":7748659,"file_name":"Movie 3A.3.mp4"},{"title":"Chapter 3 - Movie 3A.4","access_level":"open_access","file_id":"19690","file_name":"Movie 3A.4.mp4","file_size":5873052,"date_updated":"2025-05-12T15:43:28Z","content_type":"video/mp4","relation":"supplementary_material","checksum":"dd5a252e1da00c8f303588e22e2baeef","date_created":"2025-05-12T15:16:50Z","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).","creator":"gyalniz"},{"checksum":"5ac58b86810698db28cbfc28f351ff70","relation":"supplementary_material","content_type":"video/mp4","date_updated":"2025-05-12T15:43:28Z","file_size":9209327,"file_name":"Movie 4A.1.mp4","file_id":"19691","title":"Chapter 4 - Movie 4A.1","access_level":"open_access","creator":"gyalniz","description":"Movie demonstrating the quasi-steady Reynolds number descent from turbulence to a periodic orbit.","date_created":"2025-05-12T15:17:11Z"},{"date_created":"2025-05-12T15:17:43Z","creator":"gyalniz","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_name":"Movie 5A.1.mp4","file_size":5893993,"date_updated":"2025-05-12T15:43:28Z","title":"Chapter 5 - Movie 5A.1","access_level":"open_access","file_id":"19692","checksum":"ac877f1e1ef39439911bf37cb1793b8e","content_type":"video/mp4","relation":"supplementary_material"},{"date_created":"2025-05-12T15:17:49Z","creator":"gyalniz","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.","date_updated":"2025-05-12T15:43:28Z","file_size":3990352,"file_name":"Movie 5A.2.mp4","file_id":"19693","title":"Chapter 5 - Movie 5A.2","access_level":"open_access","checksum":"fd17eabb70129ceaa414e40924d1d2fe","relation":"supplementary_material","content_type":"video/mp4"},{"content_type":"video/mp4","relation":"supplementary_material","checksum":"32f904497ab0bbee38f0788d96b91454","access_level":"open_access","title":"Chapter 5 - Movie 5A.3","file_id":"19694","file_name":"Movie 5A.3.mp4","file_size":5171009,"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.","creator":"gyalniz","date_created":"2025-05-12T15:17:58Z"},{"relation":"source_file","content_type":"application/x-zip-compressed","checksum":"f313261b9bb12dfb943fead8318954c6","file_id":"19695","access_level":"closed","date_updated":"2025-05-12T15:43:28Z","file_size":18991996,"file_name":"Gökhan Yalnız - PhD thesis.zip","creator":"gyalniz","date_created":"2025-05-12T15:27:10Z"}],"file_date_updated":"2025-05-12T15:43:28Z","doi":"10.15479/AT-ISTA-19684","project":[{"_id":"238598C6-32DE-11EA-91FC-C7463DDC885E","name":"Revisiting the Turbulence Problem Using Statistical Mechanics","grant_number":"662960"}],"month":"05","has_accepted_license":"1","corr_author":"1","user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","type":"dissertation","degree_awarded":"PhD","publisher":"Institute of Science and Technology Austria","date_published":"2025-05-13T00:00:00Z","author":[{"last_name":"Yalniz","full_name":"Yalniz, Gökhan","first_name":"Gökhan","orcid":"0000-0002-8490-9312","id":"66E74FA2-D8BF-11E9-8249-8DE2E5697425"}],"title":"Transition to turbulence : Data-, solution-, and pattern-driven approaches","language":[{"iso":"eng"}],"publication_status":"published","page":"155","ddc":["514","519","532","004"],"acknowledged_ssus":[{"_id":"ScienComp"}],"status":"public"}]