Abstract
In searching for low-dimensional structures in the driven cavity problem, in this case a fluid flow in a closed cylinder created by a rotating lid, we use a Galerkin approximation to project the infinite NavierStokes equations into a finite dimensional subspace in amplitudes. Then, utilizing bifurcation analysis on the system of ODE’s, we succeeded in establishing the early transition to an oscillatory motion as a supercritical Hopf-bifurcation, and in particular we also estimated the critical Reynolds number within 0.2% of the Reynolds number due to the full numerical system in 40000 degrees of freedom. An excellent result with a low-dimensional model consisting of only 25 degrees of freedom. Finally, we present the spectrum of the full numerical system in the range from stationary to chaotic fluid flow. This spectrum diagram will serve as the basic reference system through out all investigations.
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© 1994 Springer Science+Business Media Dordrecht
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Christensen, E.A., Sorensen, J.N., Brons, M., Christiansen, P.L. (1994). Low-Dimensional Behaviour in the Rotating Driven Cavity Problem. In: Flato, M., Kerner, R., Lichnerowicz, A. (eds) Physics on Manifolds. Mathematical Physics Studies, vol 15. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-1938-2_25
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DOI: https://doi.org/10.1007/978-94-011-1938-2_25
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