Singular perturbation problems
turbulence via chaos techniques
Springer Online Journal Archives 1860-2000
Abstract Flow-induced oscillations of rigid cylinders exposed to fully developed turbulent flow can be described by a fourth order autonomous system. Among the pertinent constants, the mass ratio is the control parameter governing the transition from limit cycle oscillations to chaotic vibrations. Particular attention is paid to the stability of the limit cycles: it has been found that they lose their stability at the point of appearance of quasi-periodic motion. The documentation of this transition is performed in terms of Lyapunov exponents, phase plots, Fourier spectra, bifurcation diagrams, and Poincaré maps. As opposed to the calculation of the Lyapunov exponents where remarkable numerical difficulties were encountered, the investigation of the remaining quantities shows clearly the passage of cylinder motions from limit cycle oscillations to more and more irregular vibrations, leading finally to chaos.
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