Abstract
Results are presented for the steady motion of finite cored uniform vortices in an incompressible perfect fluid. The cases of single vortices, vortex pairs, single rows and the staggered double row are considered. The stability of the flows to two-dimensional disturbances is examined. In particular, it is shown that finite area stabilises the Karman vortex street for a finite band of aspect ratio values about the Karman value of 0.281.
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
S. Goldstein 1965 Modern Developments in Fluid Mechanics. Dover.
T. Matsui and M. Okude 1982 Vortex pairing in a Karman vortex street. (To appear).
J.P. Christiansen 1973 Numerical simulation of hydrodynamics by the method of point vortices. J. Comp. Phys., 13, 363–379.
K. Kuwahara and H. Takami 1973 Numerical studies of two-dimensional vortex motion by a system of point vortices. J. Phys. Soc. Japan 34, 247–253.
O. Held and V.M. Del Prete 1978 Convergence of vortex methods for Euler’s equations. Math. Comp., 32, 791–809.
H. Lamb 1932 Hydrodynamics. Sixth Ed. Cambridge Univ. Press.
G.S. Deem and N.J. Zabusky 1978 Vortex waves; stationary V states, interactions, recurrence and breaking. Phys. Rev. Lett., 40, 859–862.
N.J. Zabusky 1981 Recent developments in contour dynamics for the Euler equations. Proc. I V Int. Conf. on Collective Phenomena. New York Academy of Sciences.
J. Burbea and M. Landau 1982 The Kelvin waves in vortex dynamics and their stability. J. Comp. Phys. (to appear).
D.W. Moore and P.G. Saffman 1971 Structure of a line vortex in an imposed strain. Aircraft Wake Turbulence (Eds. J.H. Olsen, A. Goldburg and M. Rogers) p.339–354. Plenum Press.
S. Kida 1981 Motion of an elliptic vortex in a uniform shear flow. J. Phys. Soc. Japan 50, 3517–3520.
P.G. Saffman 1979 The approach of a vortex pair to a plane surface in inviscid fluid. J. Fluid Mech., 92, 497–503.
S. Kida 1982 Stabilizing effects of finite core on Karman vortex street. (Unpublished manuscript.)
G.R. Baker, P.G. Saffman and J.S. Sheffield 1976 Structure of a linear array of hollow vortices of finite cross section. J. Fluid Mech., 74, 469–476.
V.I. Arnold 1980 Mathematical Methods of Classical Mechanics. Springer Verlag.
A.C. Robinson and P.G. Saffman 1982 Three-dimensional stability of vortex arrays. (Unpublished manuscript.)
C.-Y. Tsai and S.E. Widnall 1976 The stability of short waves on a straight vortex filament in a weak externally imposed strain field. J. Fluid Mech., 73, 721–733.
D.W. Moore and P.G. Saffman 1975 The instability of a straight vortex filament in a strain field. Proc. Roy. Soc. A 346, 413–425.
R.T. Pierrehumbert and S.E. Widnall 1982 The two-and three-dimensional instabilities of a spatially periodic shear layer. J. Fluid Mech., 114, 59–82.
R.T. Pierrehumbert 1980 A family of steady translating vortex pairs with distributed vorticity. J. Fluid Mech., 99, 129–144.
P.G. Saffman and R. Szeto 1980 Equilibrium shapes of a pair of equal uniform vortices. Physics of Fluids 23, 2339–2342.
H.C. Pocklington 1895 The configuration of a pair of equal and opposite hollow straight vortices, of finite cross-section, moving steadily through fluid. Proc. Camb. Phil. Soc., 8, 178–187.
P.G. Saffman and R. Szeto 1981 Structure of a linear array of uniform vortices. Stud. App. Math., 65, 223–248.
R.T. Pierrehumbert and S.E. Widnall 1981 The structure of organized vortices in a free shear layer. J. Fluid Mech., 102, 301–313.
A. Roshko 1976 Structure of turbulent shear flows: a new look. AIAA Journal 14, 1349–1357.
P.G. Saffman 1981 Vortex interactions and coherent structures. Transition and Turbulence (Ed. R.E. Meyer) p.149–166. Academic Press.
T.H. Havelock 1931 The stability of motion of rectilinear vortices in ring formation. Phil. Mag. (7) 11, 617–633.
P.G. Saffman and J.C. Schatzman 1982 Stability of a vortex street of finite vortices. J. Fluid Mech., 117, 171–185.
D.R. Underlineman, P.F. Brinich and M.E. Goldstein 1976 Vortex shedding from a blunt trailing edge with equal and unequal external mean velocities. J. Fluid Mech., 75, 721–735.
J.P. Christiansen and N.J. Zabusky 1973 Instability, coalescence and fission of finite-area vortex structures. J. Fluid Mech., 61, 219–243.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1982 Springer Fachmedien Wiesbaden
About this chapter
Cite this chapter
Saffman, P.G. (1982). Structure and Stability of Streets of Finite Vortices. In: Hornung, H.G., Müller, EA. (eds) Vortex Motion. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-663-13883-9_10
Download citation
DOI: https://doi.org/10.1007/978-3-663-13883-9_10
Publisher Name: Vieweg+Teubner Verlag, Wiesbaden
Print ISBN: 978-3-528-08536-0
Online ISBN: 978-3-663-13883-9
eBook Packages: Springer Book Archive