Abstract
We present inviscid and viscous models for the formation and propagation of single, and co-axial pairs of, vortex rings. Inviscid flows are based on both thin rings, and thick rings treated by a contour dynamics approach, whilst viscous flows are determined from numerical solutions of the Navier-Stokes equations. A kaleidoscope of different flow behaviours for these axisymmetric flows is presented.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Saffman P.G., Vortex Dynamics. Cambridge University Press, Cambridge (1992)
Disselhorst J.H.M. and Van Wijngaarden L., Flow in the exit of open pipes during acousticresonance. J. Fluid Mech. 99 (1980) 293–319
Weidman P.D. and Riley N., Vortex ring pairs: Numerical simulation and experiment. J. FluidMech. 257(1993)311–337
Riley N., On the behaviour of pairs of vortex rings. Quart. J. Mech. Appl. Math. 46 (1993)521–539
Riley N. and Stevens D.P., A note on leapfrogging vortex rings. Fluid Dyn. Res. 11 (1993)235–244
Wakelin S.L. and Riley N., Vortex ring interactions II. Inviscid models. Quart. J. Mech. Appl.Math. 49 (1996) 287–309
Wakelin S.L. and Riley N., On the formation and propagation of vortex rings and pairs ofvortex rings. J. Fluid Mech. 332 (1997) 121–139
Heeg R.S. and Riley N., Simulations of the formation of an axisymmetric vortex ring. J. Fluid Mech. 339 (1997) 119–211
Lamb H., Hydrodynamics. Cambridge University Press, Cambridge (1932)
Abramowitz M. and Stegun LA., Handbook of Mathematical Functions. Dover, New York (1972)
Shariff K., Leonard A. and Ferziger J.H., Dynamics of a class of vortex rings. NASAM-102257 (1989)
Roache P.J., Computational Fluid Dynamics. Hermosa (1972) p. 154
Norbury J., A family of steady vortex rings. J. Fluid Mech 57 (1973) 417–431
Oshima Y., Head-on collision of two vortex rings. J. Phys Soc. Jap. 44 (1978) 328–331
Didden N., On the formation of vortex rings: Rolling-up and production of circulation. Z.angew Math. Phys. 30 (1979) 101–116
Nitsche M. and Krasny R., A numerical study of vortex ring formation at the edge of a circulartube. J. Fluid Mech. 276 (1994) 139–161
Pullin D.I., Vortex ring formation at tube and orifice openings. Phys. Fluids 22 (1979) 401–403
Saffman P.G., The velocity of viscous vortex rings. Stud. Appl. Math. 49 (1970) 371–380
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1998 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Riley, N. (1998). The Fascination of Vortex Rings. In: Biesheuvel, A., van Heijst, G.F. (eds) In Fascination of Fluid Dynamics. Fluid Mechanics and its Applications, vol 45. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4986-0_11
Download citation
DOI: https://doi.org/10.1007/978-94-011-4986-0_11
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-6092-9
Online ISBN: 978-94-011-4986-0
eBook Packages: Springer Book Archive