zbMATH — the first resource for mathematics

From the double vortex street behind a cylinder to the wake of a sphere. (English) Zbl 1045.76521
Summary: We review the main results concerning the first instabilities, characterised by the breaking of spatio–temporal symmetries, occurring in the wake of bluff bodies, as the flow speed is increased. Phenomenological wake models are compared to experiments for the geometry of a circular cylinder and of a sphere. The transition from a cylindrical to spherical configuration is also illustrated in various ways, such as the transverse coupling of two sphere wakes and a reduction in length or a wavy deformation of a circular cylinder. Finally, we report preliminary results concerning the fluid–structure interactions in the case of a longitudinally tethered sphere.

76D25 Wakes and jets
76-05 Experimental work for problems pertaining to fluid mechanics
Full Text: DOI
[1] Bénard, H., Formation de centres de giration à l’arrière d’un obstacle en mouvement, C. R. acad. sci. Paris, 147, 839-842, (1908)
[2] von Kármán, T., Über den mechanismus des widerstandes, den ein bewegter Körper in einer flüssigkeit erfährt, Göttingen nachr. math.-phys. kl., 509-519, (1911) · JFM 42.0800.01
[3] Bearman, P.W., Vortex shedding from oscillating bluff bodies, Annu. rev. fluid mech., 16, 195-222, (1984) · Zbl 0605.76045
[4] ()
[5] Leweke, T.; Bearman, P.W.; Williamson, C.H.K., Bluff body wakes and vortex induced vibrations, J. fluids structures, 15, 3/4, (2001)
[6] Williamson, C.H.K., Vortex dynamics in the cylinder wake, Annu. rev. fluid mech., 28, 477-539, (1996)
[7] Zdravkovich, M., Flow around circular cylinders, (2002), Oxford Science · Zbl 0882.76004
[8] Bers, A., Space – time evolution of plasma instabilities – absolute and convective, (), 451-517
[9] Huerre, P.; Monkewitz, P.A., Local and global instabilities in spatially developing flows, Annu. rev. fluid mech., 22, 473-537, (1990) · Zbl 0734.76021
[10] Hopf, E., Abzweigung einer periodischen Lösung von einer stationären Lösung eines differentialsystems, (), 94, 163-193, (1942), English translation:
[11] Landau, L.D., On the problem of turbulence, (), 44, 387-391, (1944), English translation:
[12] Williamson, C.H.K., Defining a universal and continuous strouhal – reynolds number relationship for the laminar vortex shedding of a circular cylinder, Phys. fluids, 31, 2742-2744, (1988)
[13] Williamson, C.H.K., Oblique and parallel modes of vortex shedding in the wake of a circular cylinder at low Reynolds numbers, J. fluid mech., 206, 579-627, (1989)
[14] Hammache, M.; Gharib, M., An experimental study of the parallel and oblique vortex shedding from circular cylinders, J. fluid mech., 232, 567-590, (1991)
[15] Eisenlohr, H.; Eckelmann, H., Vortex splitting and its consequences in the vortex street wake of cylinders at low Reynolds numbers, Phys. fluids A, 1, 189-192, (1989)
[16] Leweke, T.; Provansal, M., The flow behind rings: bluff body wakes without end effects, J. fluid mech., 288, 265-310, (1995)
[17] Provansal, M.; Mathis, C.; Boyer, L., Bénard – von Kármán instability: transient and forced regimes, J. fluid mech., 182, 1-22, (1987) · Zbl 0641.76046
[18] Schumm, M.; Berger, E.; Monkewitz, P.A., Self-excited oscillations in the wake of two-dimensional bluff bodies and their control, J. fluid mech., 271, 17-53, (1994)
[19] Wesfreid, J.E.; Goujon-Durand, S.; Zielinska, B.J.A., Global mode behaviour of the streamwise velocity in wakes, J. phys. II Paris, 6, 1343-1357, (1995)
[20] Villermaux, E., On the strouhal – reynolds dependence in the Bénard-Kármán problem, ()
[21] W. van Saarloos, Front propagation into unstable states, Phys. Rev. (2003), submitted for publication · Zbl 1042.74029
[22] Albarède, P.; Provansal, M., Quasi-periodic cylinder wakes and the ginzburg – landau mode, J. fluid mech., 291, 191-222, (1995) · Zbl 0850.76152
[23] P. Albarède, Self-organisation in the 3D wakes of bluff bodies, Ph.D. Dissertation, Université de Provence, Marseille, France, 1991
[24] Leweke, T.; Provansal, M.; Miller, G.D.; Williamson, C.H.K., Cell formation in cylinder wakes at low Reynolds numbers, Phys. rev. lett., 78, 1259-1262, (1997)
[25] Gaster, M., Vortex shedding from slender cones at low Reynolds numbers, J. fluid mech., 38, 565-576, (1969)
[26] Facchinetti, M.L.; de Langre, E.; Biolley, F., Vortex shedding modeling using diffusive van der Pol oscillators, C. R. Mécanique, 330, 451-456, (2002) · Zbl 1084.76021
[27] Schouveiler, L.; Provansal, M., Self-sustained oscillations in the wake of a sphere, Phys. fluids, 14, 3846-3854, (2002) · Zbl 1185.76323
[28] Thompson, M.C.; Leweke, T.; Provansal, M., Kinematics and dynamics of sphere wake transition, J. fluids structures, 15, 575-585, (2001)
[29] Ghidersa, B.; Dušek, J., Breaking of axisymmetry and onset of unsteadiness in the wake of a sphere, J. fluid mech., 423, 33-69, (2000) · Zbl 0977.76028
[30] Ormières, D.; Provansal, M., Transition to turbulence in the wake of a sphere, Phys. rev. lett., 83, 80-83, (1999)
[31] Tomboulides, A.G.; Orszag, S.A., Numerical investigation of transitional and weak turbulent flow past a sphere, J. fluid mech., 416, 45-73, (2000) · Zbl 1156.76419
[32] Natarajan, R.; Acrivos, A., The instability of the steady flow past spheres and disks, J. fluid mech., 254, 323-344, (1993) · Zbl 0780.76027
[33] Johnson, T.A.; Patel, V.C., Flow past a sphere up to a Reynolds number of 300, J. fluid mech., 378, 19-70, (1999)
[34] Peschard, I.; Le Gal, P.; Takeda, Y., On the spatio – temporal structure of cylinder wakes, Exp. fluids, 26, 188-196, (1999)
[35] Schouveiler, L.; Brydon, A.; Leweke, T.; Thompson, M.C., Interactions of the wakes of two spheres placed side by side, Eur. J. mech. B fluids, 22, (2003), this volume · Zbl 1045.76509
[36] Sakamoto, H.; Haniu, H., A study on vortex shedding frequency from spheres in a uniform flow, Trans. ASME J. fluids engrg., 112, 386-392, (1990)
[37] Sakamoto, H.; Haniu, H., The formation mechanism and shedding frequency of vortices from a sphere in uniform shear flow, J. fluid mech., 287, 151-171, (1995)
[38] Schouveiler, L.; Provansal, M., Periodic wakes of low aspect ratio cylinders with free hemispherical ends, J. fluids structures, 15, 565-573, (2001)
[39] Schouveiler, L.; Provansal, M.; Leweke, T., Etude des sillages périodiques d’une ou de deux sphères et de cylindres droits ou ondulés à bouts libres, (), 223-228
[40] Owen, J.C.; Szewczyk, A.A.; Bearman, P.W., Suppression of Kármán vortex shedding, Phys. fluids, 12, S9, (2000)
[41] Sheard, G.J.; Thompson, M.C.; Hourigan, K., From spheres to circular cylinders: the stability and flow structures of bluff ring wakes, J. fluid mech., 492, 147-180, (2003) · Zbl 1063.76539
[42] Berger, E.; Wille, R., Periodic flow phenomena, Annu. rev. fluid mech., 4, 313-340, (1972)
[43] Gharib, M.; Derango, P., A liquid film (soap film) tunnel to study two-dimensional laminar and turbulent shear flows, Physica D, 37, 406-416, (1989)
[44] Couder, Y.; Chomaz, J.M.; Rabaud, M., On the hydrodynamics of soap films, Physica D, 37, 384-405, (1989)
[45] Jauvtis, N.; Govardhan, R.; Williamson, C.H.K., Multiple modes of vortex-induced vibration of a sphere, J. fluids structures, 15, 555-563, (2001)
[46] Khalak, A.; Williamson, C.H.K., Fluid forces and dynamics of a hydroelastic structure with very low mass and damping, J. fluids structures, 11, 973-982, (1997)
[47] Provansal, M.; Leweke, T.; Schouveiler, L.; Guébert, N., 3D oscillations and vortex induced vibrations of a tethered sphere in a flow parallel to the thread, ()
[48] Wu, M.; Gharib, M., Experimental studies on the shape and path of small air bubbles rising in Clean water, Phys. fluids, 14, L49-L52, (2002) · Zbl 1059.85002
[49] Mougin, G.; Magnaudet, J., Path instability of a rising bubble, Phys. rev. lett., 88, 014502, (2002)
[50] M.L. Facchinetti, E. de Langre, F. Biolley, On wake oscillator models for 2-D vortex-induced vibrations, J. Fluids Structures (2003), submitted for publication
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.