| 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.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 the model. Wave breaking inception is modelled using new regular and irregular wave breaking criteria which embody the spatial surface elevation slope as a parameter. These have been formulated based on laboratory experiments carried out on waves propagating in a basin over an elliptic shoal (2D bathymetry), and in a flume over a plane slope followed by a horizontal platform (1D bathymetry). Existing regular and irregular wave breaking criteria are reviewed and assessed with the aid of the collected data.Computations have been carried out for a range of wave propagation/transformation problems. Agreement of computed results with analytical results, existing laboratory data and the present laboratory data is very good.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, second-order, 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. |
