Modelling of Low-Dimensional, Incompressible, Viscous, Rotating Fluid Flow

  • E. A. Christensen
  • J. N. Sørensen
  • M. Brøns
  • P. L. Christiansen
Conference paper
Part of the Research Reports in Physics book series (RESREPORTS)


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.


Reynolds Number Periodic Solution Transport Equation Critical Reynolds Number Cylindrical Vessel 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • E. A. Christensen
    • 1
  • J. N. Sørensen
    • 2
  • M. Brøns
    • 3
  • P. L. Christiansen
    • 1
  1. 1.Laboratory of Applied Mathematical PhysicsThe Technical University of DenmarkLyngbyDenmark
  2. 2.Department of Fluid MechanicsThe Technical University of DenmarkLyngbyDenmark
  3. 3.Mathematical InstituteThe Technical University of DenmarkLyngbyDenmark

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