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2D parametric model for surface wave development in wind field varying in space and time
  • Vladimir N. Kudryavtsev,
  • Maria V. Yurovskaya,
  • Bertrand Chapron
Vladimir N. Kudryavtsev
Russian State Hydrometeorological University / Marine Hydrophysical Institute

Corresponding Author:kudr@rshu.ru

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Maria V. Yurovskaya
Marine Hydrophysical Institute
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Bertrand Chapron
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A fully consistent 2D parametric model of waves development under spatially and temporally varying winds is suggested. The 2D model is based on first-principle conservation equations, consistently constrained by self-similar fetch-laws. Derived coupled equations written in the characteristic form provide practical means to rapidly assess how the energy, frequency and direction of dominant surface waves are distributed under varying wind forcing. For young waves, non-linear interactions are essential to drive the peak frequency downshift, and the wind energy input and wave breaking dissipation are the governing sources of the wave energy evolution. With a prescribed wind wave growth rate, proportional to ustar/c squared, wave breaking dissipation becomes a power-function of the dominant wave slope. Under uniform wind conditions, this growth rate imposes solutions for peak frequency and energy development to follow fetch-laws, with exponents q=-1/4 p=3/4 correspondingly. This set of exponents recovers the Toba’s laws, and imposes the wave breaking exponent equal to 3. A smooth transition from wind driven seas to swell is obtained. Varying wind direction is the only source to drive spectral peak direction changes. This can lead to occurrence of focusing/defocusing wave groups and formation of areas where wave-rays merge and cross. Solutions predict significant (but finite) local enhancements of the energy. Further propagating, wave rays diverge, leading to wave attenuation away from the storm area