Competition between Traveling Fluid Waves of Left and Right Spiral Vortices and Their Different Amplitude Combinations

Abstract

Stability, bifurcation properties, and the spatiotemporal behavior of different nonlinear combination structures of spiral vortices in the counter rotating Taylor-Couette system are investigated by full numerical simulations and by coupled amplitude equation approximations. Stable cross-spiral structures with continuously varying content of left and right spiral modes are found. They provide a stability transferring connection between the initially stable, axially counter propagating wave states of pure spirals and the axially standing waves of so-called ribbons that become stable slightly further away from onset of vortex flow.

arXiv comment4 pages, 5 figures

References in corpus (1)

• Spiral Vortices and Taylor Vortices in the Annulus between Rotating Cylinders and the Effect of an Axial Flow

Cited by in corpus (11)

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• Invariant states in inclined layer convection. Part 2. Bifurcations and connections between branches of invariant states
• Spirals and ribbons in counter-rotating Taylor-Couette flow: frequencies from mean flows and heteroclinic orbits
• Fully nonlinear mode competitions in magnetised Taylor-Couette flow
• Wave-number dependence of the transitions between traveling and standing vortex waves and their mixed states in the Taylor-Couette system
• Bifurcation of standing waves into a pair of oppositely traveling waves with oscillating amplitudes caused by a three-mode interaction
• Controlling the stability transfer between oppositely traveling waves and standing waves by inversion-symmetry-breaking perturbations