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Parabolic resonances and instabilities.

Vered Rom-Kedar1

  • 1Department of Applied Mathematics and Computer Science, The Weizmann Institute of Science, P.O. Box 26, Rehovot 76100, Israel.

Chaos (Woodbury, N.Y.)
|March 1, 1997
PubMed
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A new type of chaotic behavior is discovered in perturbed Hamiltonian systems, leading to instabilities and long trapping times. This phenomenon, termed parabolic resonance, has implications for atmospheric particle transport.

Area of Science:

  • Physics
  • Applied Mathematics
  • Atmospheric Science

Background:

  • Integrable Hamiltonian systems with parabolic fixed points can exhibit complex dynamics when perturbed.
  • Parabolic resonance is a co-dimension one phenomenon in near-integrable systems.

Purpose of the Study:

  • To investigate the occurrence and characteristics of parabolic resonance in two-degrees-of-freedom Hamiltonian systems.
  • To explore the chaotic behavior associated with parabolic resonance and its implications.

Main Methods:

  • Perturbation theory for Hamiltonian systems.
  • Numerical simulations to observe dynamics near parabolic resonances.
  • Analysis of a model from atmospheric studies.

Main Results:

Related Experiment Videos

  • Parabolic resonance is a generic phenomenon in perturbed near-integrable Hamiltonian systems.
  • Chaotic motion near parabolic resonance shows directional instabilities and long trapping times.
  • Flat parabolic resonance in an atmospheric model facilitates equatorial-to-high latitude particle transport.

Conclusions:

  • Parabolic resonance is a significant dynamical feature in Hamiltonian systems.
  • The identified mechanism explains particle transport in atmospheric models.
  • Further study of modified atmospheric models reveals persistent traces of flat instabilities.