TY  - INPR
A1  - Feudel, Fred
A1  - Seehafer, Norbert
T1  - On the bifurcation phenomena in truncations of the 2D Navier-Stokes equations
N2  - 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.
T3  - NLD Preprints - 1 
Y1  - 2007
UR  - https://publishup.uni-potsdam.de/frontdoor/index/index/docId/1219
UR  - https://nbn-resolving.org/urn:nbn:de:kobv:517-opus-13390
ER  -