Symmetries and dynamics for 2-D Navier-Stokes flow

Hans Armbruster, B. Nicolaenko, N. Smaoui, Pascal Chossat

Research output: Contribution to journalArticle

35 Citations (Scopus)

Abstract

Simulations of forced 2-D Navier-Stokes equations are analyzed. The forcing is spatially periodic and temporally steady. A Karhunen-Loève analysis is used to identify the structures in phase space that generate the PDE behavior. Their relationship to the invariant subspaces generated by the symmetry group is discussed. It is shown that certain modes that are in the stable eigenspace of the Kolmogorov flow solution play an essential role for the dynamics of the attractor for the 2-D Navier-Stokes equations below a Reynolds number of about 30. In this regime all stable solutions are identified and their relation to the symmetry structure is elucidated. A new type of gluing bifurcation generated by the symmetry is found and analyzed. A mechanism for the generation of bursting behavior is suggested.

Original languageEnglish (US)
Pages (from-to)81-93
Number of pages13
JournalPhysica D: Nonlinear Phenomena
Volume95
Issue number1
StatePublished - 1996

Fingerprint

Stokes flow
Stokes Flow
Navier-Stokes
Navier Stokes equations
Navier-Stokes Equations
Gluing
Symmetry
Navier-Stokes equation
Bursting
Stable Solution
Eigenspace
symmetry
Invariant Subspace
Symmetry Group
Forcing
Reynolds number
Attractor
Phase Space
pulse detonation engines
Bifurcation

Keywords

  • Bifurcations
  • Navier-Stokes equations
  • Symmetry

ASJC Scopus subject areas

  • Applied Mathematics
  • Statistical and Nonlinear Physics

Cite this

Armbruster, H., Nicolaenko, B., Smaoui, N., & Chossat, P. (1996). Symmetries and dynamics for 2-D Navier-Stokes flow. Physica D: Nonlinear Phenomena, 95(1), 81-93.

Symmetries and dynamics for 2-D Navier-Stokes flow. / Armbruster, Hans; Nicolaenko, B.; Smaoui, N.; Chossat, Pascal.

In: Physica D: Nonlinear Phenomena, Vol. 95, No. 1, 1996, p. 81-93.

Research output: Contribution to journalArticle

Armbruster, H, Nicolaenko, B, Smaoui, N & Chossat, P 1996, 'Symmetries and dynamics for 2-D Navier-Stokes flow', Physica D: Nonlinear Phenomena, vol. 95, no. 1, pp. 81-93.
Armbruster, Hans ; Nicolaenko, B. ; Smaoui, N. ; Chossat, Pascal. / Symmetries and dynamics for 2-D Navier-Stokes flow. In: Physica D: Nonlinear Phenomena. 1996 ; Vol. 95, No. 1. pp. 81-93.
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