A reduced model for nonlinear dispersive waves in a rotating environment

Paul A. Milewski, Esteban G. Tabak

Research output: Contribution to journalArticlepeer-review


The simplest model for geophysical flows is one layer of a constant density fluid with a free surface, where the fluid motions occur on a scale in which the Coriolis force is significant. In the linear shallow water limit, there are non-dispersive Kelvin waves, localized near a boundary or near the equator, and a large family of dispersive waves. We study weakly nonlinear and finite depth corrections to these waves, and derive a reduced system of equations governing the flow. For this system we find approximate solitary Kelvin waves, both for waves traveling along a boundary and along the equator. These waves induce jets perpendicular to their direction of propagation, which may have a role in mixing. We also derive an equivalent reduced system for the evolution of perturbations to a mean geostrophic flow.

Original languageEnglish (US)
Pages (from-to)139-159
Number of pages21
JournalGeophysical and Astrophysical Fluid Dynamics
Issue number3-4
StatePublished - 1999


  • Coastal waves
  • Equatorial waves
  • Geophysical flows
  • Nonlinear waves

ASJC Scopus subject areas

  • Computational Mechanics
  • Astronomy and Astrophysics
  • Geophysics
  • Mechanics of Materials
  • Geochemistry and Petrology


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