Nonlinear refractiondiffraction of water waves: The complementary mild-slope equations

Yaron Toledo, Yehuda Agnon

Research output: Contribution to journalArticlepeer-review


A second-order nonlinear frequency-domain model extending the linear complementary mild-slope equation (CMSE) is presented. The nonlinear model uses the same streamfunction formulation as the CMSE. This allows the vertical profile assumption to accurately satisfy the kinematic bottom boundary condition in the case of nonlinear triad interactions as well as for the linear refractiondiffraction part. The result is a model with higher accuracy of wavebottom interactions including wavewave interaction. The model's validity is confirmed by comparison with accurate numerical models, laboratory experiments over submerged obstacles and analytical perturbation solutions for class III Bragg resonance.

Original languageEnglish
Pages (from-to)509-520
Number of pages12
JournalJournal of Fluid Mechanics
StatePublished - Dec 2009
Externally publishedYes


  • Bragg resonance
  • Coastal and offshore engineering
  • Mild-slope equation
  • Nonlinear waves
  • Streamfunction formulation


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