Hostname: page-component-848d4c4894-cjp7w Total loading time: 0 Render date: 2024-06-30T18:58:57.987Z Has data issue: false hasContentIssue false
  • English
  • Français

Modulated point-vortex couples on a beta-plane: dynamics and chaotic advection

Published online by Cambridge University Press:  14 June 2007

I. J. BENCZIK ,
T. TÉL  and
Z. KÖLLÖ
I. J. BENCZIK
Affiliation:
Max Planck Institute for the Physics of Complex Systems, Dresden, Germany
T. TÉL
Affiliation:
Institute for Theoretical Physics, Eötvös University, PO Box 32, H-1518 Budapest, Hungary
Z. KÖLLÖ
Affiliation:
Institute for Theoretical Physics, Eötvös University, PO Box 32, H-1518 Budapest, Hungary
Get access Rights & Permissions [Opens in a new window]

Abstract

The dynamics of modulated point-vortex couples on a β-plane is investigated for arbitrary ratios of the vortex strength. The motion is analysed in terms of an angle- and a location-dependent potential and the structural changes in their shape. The location-dependent potential is best suited for understanding different types of vortex orbits. It is shown to be two-valued in a range of parameters, a feature which leads to the appearance of orbits with spikes, in spite of the integrability of the problem. The advection dynamics in this modulated two-vortex problem is chaotic. We find a transition from closed to open chaotic advection, implying that the transport properties of the flow might be drastically altered by changing some parameters or the initial conditions. The open case, characterized by permanent entrainment and detrainment of particles around the vortices, is interpreted in terms of an invariant chaotic saddle of the Lagrangian dynamics, while the dynamics of the closed case, with a permanently trapped area of the fluid, is governed by a chaotic region and interwoven KAM tori. The transition from open to closed chaotic advection is quantified by monitoring the escape rate of advected particles as a function of the vortex energy.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 582 , 10 July 2007 , pp. 1 - 22
Copyright
Copyright © Cambridge University Press 2007

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Aref, H. 1984 J. Fluid Mech. 143, 1.CrossRefGoogle Scholar
Aref, H. 2002 Phys. Fluids 14, 1315.CrossRefGoogle Scholar
Benczik, I. J., Toroczkai, Z. & Tél, T. 2003 Phys. Rev. E 67, 036303.Google Scholar
Dvorkin, Y. & Paldor, N. J. 1999 Atmos Sci. 56, 1229.2.0.CO;2>CrossRefGoogle Scholar
Hobson, D. D. 1991 Phys. Fluids A 3, 3027.CrossRefGoogle Scholar
Jamaloodeen, M. I. & Newton, P. 2006 Proc. R. Soc. Lond. A 462, 3277–3299.Google Scholar
Jung, C., Tél, T. & Ziemniak, E. 1993 Chaos 3, 555.CrossRefGoogle ScholarPubMed
Kloosterziel, R. C., Carnevale, G. F. & Philippe, D. 1993 Dyn. Atmos. Oceans 19, 65.CrossRefGoogle Scholar
Kuznetsov, L. & Zaslavsky, G. M. 1998 Phys. Rev. E 58, 7330.CrossRefGoogle Scholar
Kuznetsov, L. & Zaslavsky, G. M. 2000 Phys. Rev. E 61, 3772.Google Scholar
Landau, L. D. & Lifshitz, E. N. 1985 Classical Mechanics. Pergamon.Google Scholar
Leoncini, X., Kuznetsov, L. & Zaslavsky, G. M. 2001 Phys. Rev. E 63, 036224.Google Scholar
Makino, M., Kamimura, T. & Taniuti, T. 1981 J. Phys. Soc. Japan 50, 980.CrossRefGoogle Scholar
Newton, P. 2001 The N-vortex Problem: Analytical Techniques. Springer.CrossRefGoogle Scholar
Newton, P. & Shokraneh, H. 2006 Proc. R. Soc. Lond. A 462, 149.Google Scholar
Ottino, J. M. 1989 The Kinematics of Mixing: Stretching, Chaos & Transport. Cambridge University Press.Google Scholar
Paldor, N. 2007 In Lagrangian Analysis and Prediction of Coastal and Ocean Dynamics (ed. Griffa, A, Kirwan, A. D., Marino, A. J., Özgökimen, T. & Rossby, T.), pp. 119–135. Cambridge University Press.CrossRefGoogle Scholar
Paldor, N. & Boss, E. 1992 J. Atmos. Sci.. 49, 2306.2.0.CO;2>CrossRefGoogle Scholar
Paldor, N. & Killworth, P. D. 1988 J. Atmos. Sci. 45, 4013.2.0.CO;2>CrossRefGoogle Scholar
Pedlosky, J. 1979 Geophysical Fluid Dynamics. Springer.CrossRefGoogle Scholar
Péntek, Á., Tél, T. & Toroczkai, Z. 1995 J. Phys. A 28, 2191.Google Scholar
Rom-Kedar, V., Dvorkin, Y. & Paldor, N. 1997 Physica D 106, 389.Google Scholar
Rom-Kedar, V., Leonard, A. & Wiggins, S. 1990 J. Fluid Mech. 214, 347.CrossRefGoogle Scholar
Sommerer, J. C., Ku, H.-C. & Gilreath, H. E. 1996 Phys. Rev. Lett. 77, 5055.Google Scholar
Tél, T. & Gruiz, M. 2006 Chaotic Dynamics. Cambridge University Press.CrossRefGoogle Scholar
Velasco Fuentes, O. U. & van Heijst, G. J. F. 1994 J. Fluid Mech. 259, 79.CrossRefGoogle Scholar
Velasco Fuentes, O. U. & van Heijst, G. J. F. 1995 Phys. Fluids 7, 2735.CrossRefGoogle Scholar
Velasco Fuentes, O. U., van Heijst, G. J. F. & Cremers, B. E. 1995 J. Fluid Mech. 291, 139.CrossRefGoogle Scholar
Velasco Fuentes, O.U. & Velázques Mũnoz, F. A. 2003 Phys. Fluids 15, 1021.CrossRefGoogle Scholar
Zabusky, N. J. & McWilliams, J. C. 1982 Phys. Fluids 25, 2175.CrossRefGoogle Scholar