Modelling of Low-Dimensional, Incompressible, Viscous, Rotating Fluid Flow
This presentation introduces a low-dimensional model for an incompressible, viscous, rotating fluid flow in a cylindrical vessel. The low-dimensional model is formed by projecting the transport equations on some subspace, spanned by known solutions to the discretized Navier-Stokes equations. Using the software package PATH, a program that analyses finite non-linear ODE-systems, such as our low-dimensional model, we find the bifurcation path with the Reynolds number as modelparameter. Thus, the transition from a stationary to a periodic solution in physical space is recognized as a super-critical Hopf-bifurcation in low-dimensional space.
Further aspects are to determine the bifurcations in space for all aspect ratios, and even further to give the dynamical concepts of a given fluid flow system.
KeywordsReynolds Number Periodic Solution Transport Equation Critical Reynolds Number Cylindrical Vessel
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