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Spatio-temporal behaviour in a rotating annulus with a source-sink flow. (English) Zbl 0890.76059

The axisymmetric flows arising in a rotating annulus with a superimposed forced flow are investigated with a pseudo-spectral numerical method. The flow enters the annulus at the inner radius with a radial velocity, then develops into a geostrophic flow azimuthally directed and flanked by two Ekman (nonlinear) boundary layers, and finally exits the outer radius, with a radially directed velocity. When the forced flow is weak, the flow is steady. On increasing the mass flow rate, the flow evolves to a chaotic temporal behaviour through several bifurcations, which perturbs the basic spatial configuration of the flow. The first bifurcation drives the steady state into an oscillatory regime, associated with a break of symmetry with respect to the midheight of the annulus. A second transition to a quasi-periodic regime is characterized by the appearance of a second frequency. Further increases in the flow rate lead to a period-five state, via a locking of both frequencies, and then to a chaotic motion.

MSC:

76M25 Other numerical methods (fluid mechanics) (MSC2010)
76U05 General theory of rotating fluids
76E99 Hydrodynamic stability
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
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