Journal of Fluid Mechanics

Papers

Nonlinear refraction–diffraction of water waves: the complementary mild-slope equations

YARON TOLEDOa1 and YEHUDA AGNONa1 c1

a1 Civil and Environmental Engineering, Technion – Israel Institute of Technology, Technion City, Haifa 32000, Israel

Abstract

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 refraction–diffraction part. The result is a model with higher accuracy of wave–bottom interactions including wave–wave 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.

(Received March 08 2009)

(Revised September 13 2009)

(Accepted September 20 2009)

Key words:

  • Bragg resonance;
  • coastal and offshore engineering;
  • mild-slope equation;
  • nonlinear waves;
  • streamfunction formulation

Correspondence:

c1 Email address for correspondence: agnon@tx.technion.ac.il

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