Envelope equation for water waves: Soliton turbulence and wavebreaking

A. I. Dyachenko, D. I. Kachulin, V. E. Zakharov

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


Water waves have long been a subject of attention of both mathematicians and physicists. The formulation of the problem is simple enough to be considered fundamental, but as of yet many questions still remain unanswered and many phenomena associated with wind-driven turbulence remain puzzling. We consider a “unidirectional” motion of weakly nonlinear gravity waves, i.e., we assume that the spectrum of the free surface contains only nonnegative wavenumbers. We use remarkably simple form of the water wave equation that we named “the super compact equation”. This new equation includes a nonlinear wave term (à la NLSE) together with an advection term that can describe the initial stage of wave breaking. This equation has also very important property. It allows to introduce exact envelope for waves without assumption of narrowness bandwidth.

Original languageEnglish (US)
Pages (from-to)409-415
Number of pages7
JournalJournal of Ocean Engineering and Marine Energy
Issue number4
StatePublished - Nov 1 2017


  • Envelope equation
  • Hamiltonian formalism
  • Modulational instability
  • Wave breaking

ASJC Scopus subject areas

  • Renewable Energy, Sustainability and the Environment
  • Water Science and Technology
  • Energy Engineering and Power Technology
  • Ocean Engineering


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