Symmetries, Dynamics, and Control for the 2D Kolmogorov Flow

Symmetries, Dynamics, and Control for the 2D Kolmogorov Flow

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 Gale...

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Veröffentlicht in:Complexity (New York, N.Y.) N.Y.), 2018-01, Vol.2018 (2018), p.1-15
1. Verfasser: Smaoui, Nejib
Format: Artikel
Sprache:eng
Schlagworte:
Analysis
Applied mathematics
Attractors (mathematics)
Boundary conditions
Computational fluid dynamics
Computer simulation
Design
Differential equations
Dynamical systems
Fluid flow
Fluids
Galerkin method
Interdisciplinary aspects
Mathematical analysis
Navier-Stokes equations
Nonlinear differential equations
Nonlinear equations
Numerical analysis
Reynolds number
Simulation
Stokes law (fluid mechanics)
Two dimensional flow
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Beschreibung
Zusammenfassung: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
ISSN:1076-2787
1099-0526
DOI:10.1155/2018/4602485