pure and applied geophysics

, Volume 133, Issue 4, pp 635–664 | Cite as

Resonant forcing of coastally trapped waves in a continuously stratified ocean

  • H. Mitsudera
  • R. Grimshaw


In a previous paper (Grimshaw, 1987) the resonant forcing of coastally trapped waves was discussed in the barotropic case. In order to extend that theory to more realistic situations, we have considered the analogous theory whereby a longshore current interacts with a longshore topographic feature, or the forcing is due to longshore wind stress, for the case of the continuously stratified ocean. As in the previous theory, near resonance, when a long-wave phase speed is close to zero (in the reference frame of the forcing), the wave motion is governed by a forced evolution equation of the KdV-type. The behaviour of the wave field is characterized by three parameters representing the bandwidth for resonance, the forcing amplitude and the dissipation. We have evaluated these parameters in various practical cases, and found that the bandwidths, which scale with α1/2 when the forcing has dimensionless amplitude α, can often be quite broad. Typically the second, third, or higher, modes may be resonant. Concurrently, the dissipation is also usually significant, leading to a steady state balance between the forcing, dissipation and nonlinear terms.

Key words

Resonant forcing coastally trapped waves KdV equation 


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Copyright information

© Birkhäuser Verlag 1990

Authors and Affiliations

  • H. Mitsudera
    • 1
  • R. Grimshaw
    • 1
  1. 1.School of MathematicsUniversity of New South WalesKensingtonAustralia

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