On the bifurcation phenomena in truncations of the 2D Navier-Stokes equations

  • We have studied bifurcation phenomena for the incompressable Navier-Stokes equations in two space dimensions with periodic boundary conditions. Fourier representations of velocity and pressure have been used to transform the original partial differential equations into systems of ordinary differential equations (ODE), to which then numerical methods for the qualitative analysis of systems of ODE have been applied, supplemented by the simulative calculation of solutions for selected initial conditions. Invariant sets, notably steady states, have been traced for varying Reynolds number or strength of the imposed forcing, respectively. A complete bifurcation sequence leading to chaos is described in detail, including the calculation of the Lyapunov exponents that characterize the resulting chaotic branch in the bifurcation diagram.

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Metadaten
Author details:Fred Feudel, Norbert SeehaferORCiD
URN:urn:nbn:de:kobv:517-opus-13390
Publication series (Volume number):NLD Preprints (1)
Publication type:Preprint
Language:English
Publication year:1994
Publishing institution:Universität Potsdam
Release date:2007/05/16
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie
Zentrale und wissenschaftliche Einrichtungen / Interdisziplinäres Zentrum für Dynamik komplexer Systeme
DDC classification:5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik
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