High-order Boussinesq-type modelling of nonlinear wave phenomena in deep and shallow water

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Abstract

In this work, we start with a review of the development of Boussinesq theory for water waves covering the period from 1872 to date. Previous reviews have been given by Dingemans,1 Kirby,2,3 and Madsen & Schäffer.4 Next, we present our most recent high-order Boussinesq-type formulation valid for fully nonlinear and highly dispersive waves traveling over a rapidly varying bathymetry. Finally, we cover applications of this Boussinesq model, and we study a number of nonlinear wave phenomena in deep and shallow water. These include (1) Kinematics in highly nonlinear progressive deep-water waves; (2) Kinematics in progressive solitary waves; (3) Reflection of solitary waves from a vertical wall; (4) Reflection and diffraction around a vertical plate; (5) Quartet and quintet interactions and class I and II instabilities; (6) Extreme events from focused directionally spread waveelds; (7) Bragg scattering from an undular sea bed; (8) Run-up of non-breaking solitary waves on a beach; and (9) Tsunami generation from submerged landslides.
Original languageEnglish
Title of host publicationAdvances in numerical simulation of nonlinear water waves
EditorsQingwei Ma
Number of pages700
PublisherWorld Scientific
Publication date2010
Pages245-285
ISBN (Print)978-981-283-649-6
ISBN (Electronic)978-981-283-650-2
Publication statusPublished - 2010
SeriesAdvances in Coastal and Ocean Engineering
Number11

Cite this

Madsen, P. A., & Fuhrman, D. R. (2010). High-order Boussinesq-type modelling of nonlinear wave phenomena in deep and shallow water. In Q. Ma (Ed.), Advances in numerical simulation of nonlinear water waves (pp. 245-285). World Scientific. Advances in Coastal and Ocean Engineering, No. 11