Mathematical Problems in Engineering
Volume 2009 (2009), Article ID 526945, 16 pages
doi:10.1155/2009/526945
Review Article

Flow Around a Slender Circular Cylinder: A Case Study on Distributed Hopf Bifurcation

J. A. P. Aranha, K. P. Burr, I. C. Barbeiro, I. Korkischko, and J. R. Meneghini

Nucleus of Dynamics and Fluids (NDF), Mechanical Engineering, University of Sao Paulo, Sao Paulo, Brazil

Received 17 December 2008; Accepted 6 January 2009

Academic Editor: José Roberto Castilho Piqueira

Copyright © 2009 J. A. P. Aranha et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper presents a short overview of the flow around a slender circular cylinder, the purpose being to place it within the frame of the distributed Hopf bifurcation problems described by the Ginzburg-Landau equation (GLE). In particular, the chaotic behavior superposed to a well tuned harmonic oscillation observed in the range Re > 270, with Re being the Reynolds number, is related to the defect-chaos regime of the GLE. Apparently new results, related to a Kolmogorov like length scale and the rms of the response amplitude, are derived in this defect-chaos regime and further related to the experimental rms of the lift coefficient measured in the range Re > 270.