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A novel flow state consisting of two oppositely travelling waves (TWs) withoscillating amplitudes has been found in the counterrotating Taylor-Couettesystem by full numerical simulations. This structure bifurcates out of axiallystanding waves that are nonlinear superpositions of left and right handedspiral vortex waves with equal time-independent amplitudes. Beyond a criticaldriving the two spiral TW modes start to oscillate in counterphase due to aHopf bifurcation. The trigger for this bifurcation is provided by a nonlinearlyexcited mode of different symmetry than the spiral TWs. A three-mode coupledamplitude equation model is presented that captures this bifurcation scenario.The mode-coupling between two symmetry degenerate critical modes and anonlinearly excited one that is contained in the model can be expected to occurin other structure forming systems as well.

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