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Symmetries, Dynamics, and Control for the 2D Kolmogorov Flow
Author
Source
Issue
Vol. 2018, Issue 2018 (31 Dec. 2018), pp.1-15, 15 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2018-05-13
Country of Publication
Egypt
No. of Pages
15
Main Subjects
Abstract EN
The symmetries, dynamics, and control problem of the two-dimensional (2D) Kolmogorov flow are addressed.
The 2D Kolmogorov flow is known as the 2D Navier-Stokes (N-S) equations with periodic boundary conditions and with a sinusoidal external force along the x-direction.
First, using the Fourier Galerkin method on the original 2D Navier-Stokes equations, we obtain a seventh-order system of nonlinear ordinary differential equations (ODEs) which approximates the behavior of the Kolmogorov flow.
The dynamics and symmetries of the reduced seventh-order ODE system are analyzed through computer simulations for the Reynolds number range 0 Extensive numerical simulations show that the obtained system is able to display the different behaviors of the Kolmogorov flow. Then, we design Lyapunov based controllers to control the dynamics of the system of ODEs to different attractors (e.g., a fixed point, a periodic orbit, or a chaotic attractor). Finally, numerical simulations are undertaken to validate the theoretical developments.
American Psychological Association (APA)
Smaoui, Nejib. 2018. Symmetries, Dynamics, and Control for the 2D Kolmogorov Flow. Complexity،Vol. 2018, no. 2018, pp.1-15.
https://search.emarefa.net/detail/BIM-1134197
Modern Language Association (MLA)
Smaoui, Nejib. Symmetries, Dynamics, and Control for the 2D Kolmogorov Flow. Complexity No. 2018 (2018), pp.1-15.
https://search.emarefa.net/detail/BIM-1134197
American Medical Association (AMA)
Smaoui, Nejib. Symmetries, Dynamics, and Control for the 2D Kolmogorov Flow. Complexity. 2018. Vol. 2018, no. 2018, pp.1-15.
https://search.emarefa.net/detail/BIM-1134197
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1134197