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

  • YARON TOLEDO (a1) and YEHUDA AGNON (a1)
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.

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Corresponding author
Email address for correspondence: agnon@tx.technion.ac.il
References
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Agnon Y., Pelinovsky E. & Sheremet A. 1998 Disintegration of cnoidal waves over smooth topography. Stud. Appl. Math. 101 (1), 4971.
Agnon Y. & Sheremet A. 1997 Stochastic nonlinear shoaling of directional. J. Fluid Mech. 345, 7999.
Agnon Y., Sheremet A., Gonsalves J. & Stiassnie M. 1993 Nonlinear evolution of a unidirectional shoaling wave field. Coastal Engng 20, 2958.
Beji S. & Battjes J. A. 1993 Experimental investigation of wave propagation over a bar. Coastal Engng 19, 151162.
Dingemans M. W. 1994 Comparison of computations with Boussinesq-like models and laboratory measurements. Tech Rep. h1684.12. Delft Hydraulics.
Eldeberky Y. & Madsen P. A. 1999 Deterministic and stochastic evolution equations for fully dispersive and weakly nonlinear waves. Coastal Engng 38 (1), 124.
Ertekin R. C. & Becker J. M. 1998 Nonlinear diffraction of waves by a submerged shelf in shallow water. J. Offshore Mech. Arctic Engng 120 (4), 212220.
Green A. E. & Naghdi P. M. 1976 Oblique wave incidence on a plane beach: the classical problem revisited. Proc. R. Soc. Lond. A 347, 447473.
Kaihatu J. M. & Kirby J. T. 1995 Nonlinear transformation of waves in finite water depth. Phys. Fluids 8, 175188.
Kim J. W. & Bai K. J. 2004 A new complementary mild-slope equation. J. Fluid Mech. 511, 2540.
Kim J. W., Bai K. J., Ertekin R. C. & Wbster W. C. 2001 A derivation of the Green–Naghdi equations for irrotational flows. J. Engng Math. 40, 1742.
Kim J. W., Bai K. J., Ertekin R. C. & Wbster W. C. 2003 A strongly nonlinear model for water waves in water of variable depth – the irrotational Green–Naghdi model. J. Offshore Mech. Arctic Engng 125, 2532.
Kim J. W., Ertekin R. C. & Bai K. J. 2007 Linear and nonlinear wave models based on Hamilton's principle and stream-funcion theory: CMSE and IGN. In ASME 2007 26th International Conference on Offshore Mechanics and Arctic Engineering, 10–15 June 2007, San Diego, CA.
Liu Y. & Yue D. K. P. 1998 On generalized Bragg scattering of surface waves by bottom ripples. J. Fluid Mech. 356, 297326.
Luth H. R., Klopman G. & Kitou N. 1980 Kinematics of waves breaking partially on an offshore bar; ldv measurements for waves with and without a net onshore current. Tech Rep. h1573. Delft Hydraulics.
Madsen P. A., Fuhrman D. R. & Wang B. 2006 A Boussinesq-type method for fully nonlinear waves interacting with a rapidly varying bathymetry. Coastal Engng 53, 487504.
Mei C. C. 1985 Resonant reflection of surface water waves by periodic sandbars. J. Fluid Mech. 152, 315335.
Ohyama T., Kioka W. & Tada A. 1995 Applicability of numerical models to nonlinear dispersive waves. Coastal Engng 24, 297313.
Ohyama T. & Nadaoka K. 1991 Development of a numerical wave tank for analysis of nonlinear and irregular wave field. Fluid Dyn. Res. 8, 23l251.
Stiassnie M. & Drimer N. 2006 Prediction of long forcing waves for harbour agitation studies. J. Waterway Port Coastal Ocean Engng 132 (3), 166171.
Toledo Y. 2008 Refraction and diffraction of linear and nonlinear waves. PhD thesis, Technion–Israel Institute of Technology, Haifa, Israel.
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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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