Physical and numerical modelling of irregular wave propagation in coastal waters

Abstract

The present research work concentrates on the development and verification of a numerical model capable of simulating wave transformation in coastal waters over uneven, two-dimensional bathymetry.The so-called mild-slope equation, which includes the combined effects of shoaling, refraction, diffraction and reflection is adopted as the basis of the numerical model. Solutions are obtained on unstructured triangular meshes using a Godunov-type, secondorder, upwind, cell-centred finite volume formulation, whereby the numerical fluxes are computed using Roe's flux function. Appropriate conditions for driving, transparent and fully reflecting boundaries are derived. The unknown variables are updated in time through an accurate implicit scheme. It is the first time that such a solution methodology is used for the solution of the mild-slope equation.Apart from monochromatic waves, irregular waves which are those actually encountered in nature are also taken into account. Furthermore, the processes of non-linear wave phase speed distortion due to amplitude dispersion as well as energy dissipation due to bottom friction, whose effects are intensified in shallow waters, are also incorporated in I would like to express my gratitude to my supervisor Dr. K. Anastasiou for his consistent and truly inspired guidance. His support and encouragement throughout the course of this research work are highly appreciated.