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Applied Scientific Research

, Volume 48, Issue 3–4, pp 341–351 | Cite as

Numerical analysis of secondary and tertiary states of fluid flow and their stability properties

  • F. H. Busse
Article

Abstract

In fluid systems exhibiting a gradual transition to a turbulent state in dependence on external parameters the increasing complexity of motion is usually caused by sequences of bifurcations in the solution space. Through the consideration of the configuration of highest symmetry compatible with the basic physical problem most bifurcations can be identified by their symmetry breaking properties. Because it can incorporate all available symmetries in the selection of expansion functions, the Galerkin method turns out to be especially useful for the numerical analysis of highly symmetric fluid flow and their instabilities. By allowing for the broken symmetries, the nonlinear evolution of the flow can be followed numerically through several bifurcations. A complete stability analysis with respect to arbitrary infinitesimal disturbances is possible on the basis of Floquet's theory. This method has been applied in cases of Taylor-Couette flow, Rayleigh-Bénard convection, and shear flows with cubic profiles.

Keywords

Fluid Flow Symmetry Breaking Galerkin Method Nonlinear Evolution Gradual Transition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Kluwer Academic Publishers 1991

Authors and Affiliations

  • F. H. Busse
    • 1
  1. 1.Physikalisches InstitutUniversität BayreuthBayreuthGermany

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