Bifurcation of standing waves into a pair of oppositely traveling waves with oscillating amplitudes caused by a three-mode interaction

Abstract

A novel flow state consisting of two oppositely travelling waves (TWs) with oscillating amplitudes has been found in the counterrotating Taylor-Couette system by full numerical simulations. This structure bifurcates out of axially standing waves that are nonlinear superpositions of left and right handed spiral vortex waves with equal time-independent amplitudes. Beyond a critical driving the two spiral TW modes start to oscillate in counterphase due to a Hopf bifurcation. The trigger for this bifurcation is provided by a nonlinearly excited mode of different symmetry than the spiral TWs. A three-mode coupled amplitude equation model is presented that captures this bifurcation scenario. The mode-coupling between two symmetry degenerate critical modes and a nonlinearly excited one that is contained in the model can be expected to occur in other structure forming systems as well.

arXiv comment4 pages, 5 figures

References in corpus (3)

• Spiral Vortices and Taylor Vortices in the Annulus between Rotating Cylinders and the Effect of an Axial Flow
• Competition between Traveling Fluid Waves of Left and Right Spiral Vortices and Their Different Amplitude Combinations
• Wave-number dependence of the transitions between traveling and standing vortex waves and their mixed states in the Taylor-Couette system

Cited by in corpus (2)

• End-wall effects on the transition between Taylor vortices and spiral vortices
• Spirals and ribbons in counter-rotating Taylor-Couette flow: frequencies from mean flows and heteroclinic orbits