Using periodic orbits to quantitatively describe and control 3D fluid turbulence.

Project Information

PERTURB

Grant agreement ID: 865677

DOI

10.3030/865677

EC signature date 19 December 2019

Start date 1 January 2021

End date 31 December 2025

Funded under

• EXCELLENT SCIENCE - European Research Council (ERC)

Total cost

€ 1 999 830,00

EU contribution

€ 1 999 830,00

Coordinated by

ECOLE POLYTECHNIQUE FEDERALE DE LAUSANNE
Switzerland

CORDIS provides links to public deliverables and publications of HORIZON projects.

Links to deliverables and publications from FP7 projects, as well as links to some specific result types such as dataset and software, are dynamically retrieved from OpenAIRE .

Publications

Peer reviewed articles (15)

Invariant tori in dissipative hyperchaos

Author(s): J.P. Parker, T.M.Schneider
Published in: Chaos: An Interdisciplinary Journal of Nonlinear Science, Issue Volume 32, Issue 11, 2022, Page(s) 113102, ISSN 1054-1500
Publisher: American Institute of Physics
DOI: 10.1063/5.0119642

Ghost states underlying spatial and temporal patterns: How nonexistent invariant solutions control nonlinear dynamics

Author(s): Zheng Zheng, Pierre Beck, Tian Yang, Omid Ashtari, Jeremy P. Parker, Tobias M. Schneider
Published in: Physical Review E, Issue 112, 2025, Page(s) 024212, ISSN 2470-0045
Publisher: American Physical Society (APS)
DOI: 10.1103/8b86-3plx

Symmetry-reduced low-dimensional representation of large-scale dynamics in the asymptotic suction boundary layer

Author(s): Matthias Engel, Omid Ashtari, Moritz Linkmann
Published in: European Journal of Mechanics - B/Fluids, Issue Volume 102, 2023, Page(s) 80-90, ISSN 0997-7546
Publisher: Elsevier BV
DOI: 10.1016/j.euromechflu.2023.07.007

Data-driven guessing and gluing of unstable periodic orbits

Author(s): Pierre Beck, Jeremy P. Parker, Tobias M. Schneider
Published in: Physical Review E, Issue 112, 2025, Page(s) 024203, ISSN 2470-0045
Publisher: American Physical Society (APS)
DOI: 10.1103/9vjc-g86s

The topology of a chaotic attractor in the Kuramoto–Sivashinsky equation

Author(s): Marie Abadie, Pierre Beck, Jeremy P. Parker, Tobias M. Schneider
Published in: Chaos: An Interdisciplinary Journal of Nonlinear Science, Issue 35, 2025, ISSN 1054-1500
Publisher: American Institute of Physics
DOI: 10.1063/5.0237476

The Lorenz system as a gradient-like system

Author(s): Jeremy P Parker
Published in: Nonlinearity, Issue 37, 2025, Page(s) 095022, ISSN 0951-7715
Publisher: Institute of Physics Publishing
DOI: 10.1088/1361-6544/ad68bb

Variational methods for finding periodic orbits in the incompressible Navier-Stokes equations

Author(s): J.P. Parker; T.M. Schneider
Published in: Journal of Fluid Mechanics, Issue 941, 2022, Page(s) A17, ISSN 0022-1120
Publisher: Cambridge University Press
DOI: 10.1017/jfm.2022.299

Natural convection in a vertical channel. Part 2. Oblique solutions and global bifurcations in a spanwise-extended domain

Author(s): Zheng Zheng, Laurette S. Tuckerman, Tobias M. Schneider
Published in: Journal of Fluid Mechanics, Issue 1000, 2024, Page(s) A29, ISSN 0022-1120
Publisher: Cambridge University Press
DOI: 10.1017/jfm.2024.840

Search for unstable relative periodic orbits in channel flow using symmetry-reduced dynamic mode decomposition

Author(s): Matthias Engel, Omid Ashtari, Tobias M. Schneider, Moritz Linkmann
Published in: Journal of Fluid Mechanics, Issue 1013, 2025, Page(s) A45, ISSN 0022-1120
Publisher: Cambridge University Press
DOI: 10.1017/jfm.2025.10255

Koopman analysis of the periodic Korteweg–de Vries equation

Author(s): Jeremy P Parker, Claire Valva
Published in: Chaos: An Interdisciplinary Journal of Nonlinear Science, Issue Volume 33, Issue 4, 2023, Page(s) 043102, ISSN 1054-1500
Publisher: American Institute of Physics
DOI: 10.1063/5.0137088

Predicting chaotic statistics with unstable invariant tori

Author(s): Jeremy P Parker, Omid Ashtari, Tobias M Schneider
Published in: Chaos: An Interdisciplinary Journal of Nonlinear Science, Issue Volume 33, Issue 8, 2023, Page(s) 083111, ISSN 1054-1500
Publisher: American Institute of Physics
DOI: 10.1063/5.0143689

Jacobian-free variational method for computing connecting orbits in nonlinear dynamical systems

Author(s): Omid Ashtari, Tobias M Schneider
Published in: Chaos: An Interdisciplinary Journal of Nonlinear Science, Issue Volume 33, Issue 7, 2023, Page(s) 073134, ISSN 1054-1500
Publisher: American Institute of Physics
DOI: 10.1063/5.0143923

Natural convection in a vertical channel. Part 1. Wavenumber interaction and Eckhaus instability in a narrow domain

Author(s): Zheng Zheng, Laurette S. Tuckerman, Tobias M. Schneider
Published in: Journal of Fluid Mechanics, Issue 1000, 2024, Page(s) A28, ISSN 0022-1120
Publisher: Cambridge University Press
DOI: 10.1017/jfm.2024.842

Constructing periodic orbits of high-dimensional chaotic systems by an adjoint-based variational method

Author(s): Sajjad Azimi, Omid Ashtari, Tobias M. Schneider
Published in: Phys. Rev. E, Issue 24700045, 2022, Page(s) 014217, ISSN 2470-0045
Publisher: American Physical Society
DOI: 10.1103/physreve.105.014217

Identifying invariant solutions of wall-bounded three-dimensional shear flows using robust adjoint-based variational techniques

Author(s): O. Ashtari; T.M. Schneider
Published in: Journal of Fluid Mechanics, Issue 977, 2023, Page(s) A7, ISSN 0022-1120
Publisher: Cambridge University Press
DOI: 10.1017/jfm.2023.927