Analyzing Bifurcations in the Kolmogorov Flow Equations
Simulations of forced 2-D Navier-Stokes equations are analyzed. The forcing is spatially periodic and temporally steady. Two regimes are analyzed: a bursting regime and a regime that exhibits discrete traveling waves. A Karhunen Loeve 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.
KeywordsSymmetry Group Hopf Bifurcation Invariant Subspace Unstable Manifold Heteroclinic Orbit
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