spiral waves of wavenumber m = 5, 4 and 3 are in good agreement with previous experimental results. The present transition scenario of the spiral wavenumber with increasing Reynolds number for 0.33 b = is the same as that of Egbers and Rath (1995 Acta Mech. 111 125-40), while for 0.50 b = , it is only partially similar to those of Wulf et al (1999 Phys. Fluids 11 1359 and Egbers and Rath (1995 Acta Mech. 111 125-40).
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