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

Published online by Cambridge University Press:  10 December 2009

YARON TOLEDO  and
YEHUDA AGNON
YARON TOLEDO
Affiliation:
Civil and Environmental Engineering, Technion – Israel Institute of Technology, Technion City, Haifa 32000, Israel
YEHUDA AGNON*
Affiliation:
Civil and Environmental Engineering, Technion – Israel Institute of Technology, Technion City, Haifa 32000, Israel
*
†Email address for correspondence: [email protected]
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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.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 641 , 25 December 2009 , pp. 509 - 520
Copyright
Copyright © Cambridge University Press 2009

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