Deterministic modelling of driving and dissipation for ocean surface gravity waves

Jorge F. Willemsen

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


Consider two questions. What qualitative features should a spectrum of wind driven wave amplitudes possess in deep water? Then, is it possible to compute such a spectrum ab initio? In answer to the first question, at the least the spectrum should exhibit a spectral peak determined by the acting wind; an asymptotic power law tail; and an angular dependence between the dominant wind and wave directions. The principal result of this paper is that a model to calculate a wind-driven sea spectrum that satisfies the first two requirements starting from a broad suite of initial conditions has been constructed and exercised. To this end, wind driving mechanisms and models for dissipation caused by wave breaking are investigated. This study does not include detailed hydrodynamic calculations, but rather an evaluation of physically plausible model interaction terms. These are appended to Hamilton's equations for a wave field in deep water. This methodology leads to deterministic ordinary differential equations for the evolution of the wave field in which three and four wave nonlinear interactions are incorporated. The deterministic form of the equations is preserved through the introduction of nonstochastic driving and dissipation terms. The time evolution results presented fulfill the qualitative expectations desired for the spectrum. The calculations also yield much more information. Full phase information is retained. The relative magnitudes of the nonlinear interaction terms may be assessed as functions of time. The same applies for the magnitudes of the driving and dissipating terms. This information will be used to improve the model to where it is ready to confront experimental data.

Original languageEnglish (US)
Article number2000JC000325
Pages (from-to)27187-27204
Number of pages18
JournalJournal of Geophysical Research: Oceans
Issue numberC11
StatePublished - Nov 15 2001

ASJC Scopus subject areas

  • Geophysics
  • Forestry
  • Oceanography
  • Aquatic Science
  • Ecology
  • Water Science and Technology
  • Soil Science
  • Geochemistry and Petrology
  • Earth-Surface Processes
  • Atmospheric Science
  • Earth and Planetary Sciences (miscellaneous)
  • Space and Planetary Science
  • Palaeontology


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