Crespo Del Arco, E.; Maubert, P.; Randriamampianina, A.; Bontoux, P. Spatio-temporal behaviour in a rotating annulus with a source-sink flow. (English) Zbl 0890.76059 J. Fluid Mech. 328, 271-296 (1996). 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. Cited in 3 Documents 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 Keywords:Ekman boundary layers; second transition to quasi-periodic regime; axisymmetric flows; superimposed forced flow; pseudo-spectral numerical method; geostrophic flow; bifurcations; oscillatory regime; break of symmetry; second frequency PDFBibTeX XMLCite \textit{E. Crespo Del Arco} et al., J. Fluid Mech. 328, 271--296 (1996; Zbl 0890.76059) Full Text: DOI References: [1] DOI: 10.1017/S0022112089002399 · doi:10.1017/S0022112089002399 [2] DOI: 10.1007/BF00247741 · Zbl 0395.76045 · doi:10.1007/BF00247741 [3] DOI: 10.1002/fld.1650090405 · Zbl 0665.76107 · doi:10.1002/fld.1650090405 [4] DOI: 10.1017/S0022112084001439 · Zbl 0546.76126 · doi:10.1017/S0022112084001439 [5] DOI: 10.1017/S0022112078000026 · doi:10.1017/S0022112078000026 [6] DOI: 10.1017/S0022112076000980 · doi:10.1017/S0022112076000980 [7] DOI: 10.1016/0045-7825(90)90027-J · Zbl 0722.76061 · doi:10.1016/0045-7825(90)90027-J [8] Chaouche, La Recherche Aèrospatiale 5 pp 1– (1990) [9] DOI: 10.1017/S0022112094002028 · doi:10.1017/S0022112094002028 [10] DOI: 10.1017/S002211207500314X · doi:10.1017/S002211207500314X [11] DOI: 10.1017/S0022112067002289 · doi:10.1017/S0022112067002289 [12] DOI: 10.1017/S0022112070001702 · doi:10.1017/S0022112070001702 [13] DOI: 10.1017/S0022112087002532 · doi:10.1017/S0022112087002532 [14] DOI: 10.1017/S0022112074000450 · Zbl 0314.76076 · doi:10.1017/S0022112074000450 [15] DOI: 10.1002/fld.1650100502 · Zbl 0692.76077 · doi:10.1002/fld.1650100502 [16] DOI: 10.1017/S0022112085001793 · doi:10.1017/S0022112085001793 [17] DOI: 10.1017/S0022112084002834 · Zbl 0582.76114 · doi:10.1017/S0022112084002834 [18] DOI: 10.1017/S002211209000163X · Zbl 0686.76002 · doi:10.1017/S002211209000163X [19] DOI: 10.1017/S002211206800100X · Zbl 0157.57403 · doi:10.1017/S002211206800100X [20] DOI: 10.1016/0021-9991(79)90097-4 · Zbl 0397.65077 · doi:10.1016/0021-9991(79)90097-4 [21] DOI: 10.1017/S0022112090001707 · doi:10.1017/S0022112090001707 [22] DOI: 10.1175/1520-0469(1966)023 2.0.CO;2 · doi:10.1175/1520-0469(1966)023 2.0.CO;2 [23] DOI: 10.1017/S0022112091000782 · Zbl 0728.76115 · doi:10.1017/S0022112091000782 [24] DOI: 10.1017/S0022112063000458 · Zbl 0112.19303 · doi:10.1017/S0022112063000458 [25] DOI: 10.1017/S0022112080000547 · doi:10.1017/S0022112080000547 [26] DOI: 10.1017/S0022112079002093 · doi:10.1017/S0022112079002093 [27] DOI: 10.1017/S0022112080002066 · Zbl 0418.76036 · doi:10.1017/S0022112080002066 [28] Maubert, C. R. Acad. Sci. Paris 315 pp 1593– (1992) [29] DOI: 10.1175/1520-0469(1966)023 2.0.CO;2 · doi:10.1175/1520-0469(1966)023 2.0.CO;2 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.