Abstract
Low-dimensional representations of the axisymmetric Navier-Stokes equations are generated by a Galerkin projection. Proper orthogonal decomposition (POD) techniques based on snapshots generated from a finite-difference algorithm are used. The Reynolds number range is extended by adding displacement vectors to the Galerkin basis. For the fluid flow enclosed in a cylindrical vessel with rotating end cover, the first transition from steady to oscillatory motion is detected as a supercritical Hopf bifurcation. Comparison with the full numerical solution of the Navier-Stokes equations as well as experimental results show excellent agreement.
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Communicated by Roger Temam
One of the authors (EAC) acknowledges financial support from the Danish Research Academy (Grant S910171), the Danish Technical Research Council (Grant 16-4967-2 OS), the Louis Dreyer Myhrwold's Fund, and the Fisker & Nielsens Fund.
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Christensen, E.A., Sørensen, J.N., Brøns, M. et al. Low-dimensional representations of early transition in rotating fluid flow. Theoret. Comput. Fluid Dynamics 5, 259–267 (1993). https://doi.org/10.1007/BF00271422
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DOI: https://doi.org/10.1007/BF00271422