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arXiv · 0708.4357

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

A. Pinter·M. Lücke·Ch. Hoffmann
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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.

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A. Pinter, M. Lücke, Ch. Hoffmann. 2008-07-24. Bifurcation of standing waves into a pair of oppositely traveling waves with oscillating amplitudes caused by a three-mode interaction. https://doi.org/10.1103/physreve.78.015304

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