Book chapter
High-order Boussinesq-type modelling of nonlinear wave phenomena in deep and shallow water
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.
Language: | English |
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Publisher: | World Scientific |
Year: | 2010 |
Pages: | 245-285 |
Series: | Advances in Coastal and Ocean Engineering |
ISBN: | 1282760629 , 9812836497 , 9812836500 , 9781282760622 , 9789812836496 and 9789812836502 |
Types: | Book chapter |
ORCIDs: | Madsen, Per A. and Fuhrman, David R. |