Journal of Nonlinear Science

, Volume 4, Issue 1, pp 355–374 | Cite as

Predicting eddy detachment for an equivalent barotropic thin jet

  • E. A. Ralph
  • L. Pratt


The time-dependent meandering of thin ocean jets in reduced gravity models has recently been shown to obey a natural coordinate version of the standard modified Korteweg-deVries (mKdV) equation. The detachment of eddies from such a jet begins when different segments of the jet path come into contact, causing the initially simply connected jet to “pinch” together. It is shown that this pinching process is effected primarily by breather solutions to the mKdV equation. For a given initial condition the solution will evolve into a dispersive wave train plus a finite number of breathers, the connectivity of which is determined by a steepness parameter λ. Using the scattering transform for the mKdV equation the value(s) of λ can be calculated in a straightforward manner, and the detachment (or lack thereof) of meanders can be forecast to a high degree of confidence by calculating λ. Examples with simple meander disturbances show a remarkable degree of stability and resistance to detachment.

Key words

breather inverse scattering transform modified Korteweg-deVries equation 


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Copyright information

© Springer-Verlag New York Inc 1994

Authors and Affiliations

  • E. A. Ralph
    • 1
  • L. Pratt
    • 1
  1. 1.Woods Hole Oceanographic InstitutionWoods HoleUSA

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