Onset of wavy vortices in Taylor-Couette flow with imperfect reflection symmetry

Abstract

We reveal experimentally a mechanism that alters the critical behavior of a Hopf bifurcation substantially due to the presence of imperfections of the reflection symmetry in a hydrodynamic system. The onset of rotating waves in Taylor vortex flow, which is widely considered as a "classical" example for a Hopf bifurcation in hydrodynamics, is investigated primarily by transient response experiments. While wavy vortex flow is not influenced by such (unavoidable) experimental imperfections, the critical behavior of the axially subharmonic rotating wave with wavy outflow boundaries, also called the small-jet mode, is qualitatively altered. Experimental evidence is provided that the modified critical behavior at the Hopf bifurcation is associated with imperfections of the reflection symmetry of the Taylor-Couette setup. The experimental results on Hopf bifurcation are discussed in the context of a cusp-Hopf bifurcation model recently proposed by Harlim and Langford [Int. J. Bifurcation Chaos Appl. Sci. Eng. 17, 2547 (2007)] and compared to experimental results on imperfect pitchfork bifurcation in small-aspect ratio Taylor-Couette flow.