Thesis: Mohd. Ridza Mohd. Haniffah

Doctor of Philosophy, St. Edmund Hall, University of Oxford, Trinity Term 2013

Wave Evolution on Gentle Slopes - Statistical Analysis and Green-Naghdi Modelling

An understanding of extreme waves is important in the design and analysis of offshore structures, such as oil and gas platforms. With the increase of interest in the shipping of LNG, the design of import and export terminals in coastal water of slowly varying intermediate depth requires accurate analysis of steep wave shoaling. In this thesis, data from laboratory experiments involving random wave simulations on very gentle slopes have been analysed in terms of a model of large wave events, and the results interpreted by observation of the shape and magnitude of the large wave events. The auto-correlation function of the free surface elevation time histories, called NewWave, has been calculated from the wave spectrum and shown to fit very well up to the point where waves start to break (when compared to the ‘linear’ surface elevation time history). It has been shown that NewWave is an appropriate model for the shape of the ‘linear’ part of large waves provided kd ≥ 0.5. A Stokes-like expansion for NewWave analysis has been demonstrated to match the average shape of the largest waves, accounting for the dominant vertical asymmetry. Furthermore, an appropriate local wave period derived from NewWave has been inserted into a Miche-based limiting criterion, using the linear dispersion equation, to obtain estimates for the limiting wave height. Overall, the analysis confirms the Miche-type criterion applies to limiting wave height for waves passing over very mild bed slopes.
A derivation of general Green-Naghdi (GN) theory, which incorporates non-linear terms in its formulation, is also presented. This approach satisfies the boundary conditions exactly and approximates the field equations. The derived 2-dimensional vertical GN Level 1 model, capable of simulating steep waves on varying water depth, is validated against solitary waves and their interactions, and solitary waves on varying water depth and gives good qualitative agreement against the KdV equation. The developed and validated numerical model is used to simulate focussed wave groups on both constant depth and gentle slope. In general, the behaviour of waves simulated by the numerical model is very similar to that observed in the experimental data. There is evidence of vertical asymmetry as the water depth is reduced, owing to the non-linearity. Although the main physics is still controlled by linear dispersion, the higher order harmonics become increasingly important for shoaling waves. The numerical results also show a slope-induced wave set-up that keeps on increasing in amplitude as the wave group travels on the gentle slope.