A Resonating Triad of Gravity—Capillary Waves on a Long Gravity Wave

  • Karsten Trulsen
  • Chiang C. Mei
Part of the Fluid Mechanics and Its Applications book series (FMIA, volume 34)


Resonant interaction of wave trains on the sea surface has been recognized as a fundamental mode of energy interchange between waves of different lengths, directions and frequencies. To predict the development of the entire sea-wave spectrum, it is further necessary to understand the mutual influence of short and long waves. Such understanding is also useful for interpreting remote sensing data by microwave radar. In the high frequency end of the spectrum, corresponding to microwaves in the X-band, resonance of three trains of short gravity—capillary McGoldrick waves has been examined by McGoldrick (1965), Simmons (1969), Meiss and Watson (1978) and others. It is natural to ask how this resonance behavior might change in the presence of a much longer wave. Our purpose here is to study the evolution of three resonating gravity—capillary waves propagating in different directions on a long gravity wave. This topic has been considered in the closely related paper Trulsen and Mei (1995) which we subsequently refer to as TM


Gravity Wave Short Wave Modulational Resonance Longe Wave Stochastic Layer 
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Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • Karsten Trulsen
    • 1
  • Chiang C. Mei
    • 2
  1. 1.Department of Civil and Environmental EngineeringMassachusetts Institute of TechnologyCambridgeUSA
  2. 2.Department of MathematicsUniversity of BergenBergenNorway

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