NUMERICAL-ANALYSIS OF SECONDARY AND TERTIARY STATES OF FLUID-FLOW AND THEIR STABILITY PROPERTIES

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-Benard convection, and shear flows with cubic profiles.