Abstract
In searching for low-dimensional structures in the rotating driven cavity problem we use a Galerkin approximation to project the infinite Navier-Stokes equations into a finite dimensional subspace spanned by a number of basic modes. The resulting system of ODE’s, where the variables are the amplitudes of the basic modes, is analysed using bifurcation theory. By this technique we established, with only 25 modes, the early transition to an oscillatory motion as a supercritical Hopf-bifurcation, and in particular we estimated the critical Reynolds number within 0.2% of the Reynolds number due to the full numerical system in 40000 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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Christiansen, E.A., Sørensen, J.N., Brøns, M., Christiansen, P.L. (1993). Low-Dimensional Behaviour in the Rotating Driven Cavity Problem. In: Christiansen, P.L., Eilbeck, J.C., Parmentier, R.D. (eds) Future Directions of Nonlinear Dynamics in Physical and Biological Systems. NATO ASI Series, vol 312. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-1609-9_6
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DOI: https://doi.org/10.1007/978-1-4899-1609-9_6
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