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

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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
ISBN (Print)978-981-283-649-6
ISBN (Electronic)978-981-283-650-2
Publication statusPublished - 2010
SeriesAdvances in Coastal and Ocean Engineering


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