With a continuing and rising demand for hydrocarbons, the energy companies are installing infrastructure ever further offshore, where such infrastructure is often exposed to extreme waves. This thesis explores some aspects of wave-structure interaction, particularly the maximum water surface elevation increase in severe storms due to these local interactions. The effects on wave-structure interactions of column cross-sectional shape are investigated using linear and second-order wave diffraction theory. For multi-column structures, the excitation of locally resonant wave modes (near-trapping) is studied for several column cross-sectional shapes, and a simple method for estimating the surface elevation mode shape is given. The structure of the quadratic transfer functions for second-order sum wave elevation is investigated and an approximation assuming these QTFs are flat perpendicular to the leading diagonal is shown to be adequate for the first few lowest frequency modes. NewWave-type focused wave groups can be used as a more realistic model of extreme ocean waves. A Net Amplification Factor based on the NewWave model is given as an efficient tool for finding the incident frequencies most likely to cause a violent wave-structure interaction and where these violent responses are likely to occur. Statistics are collected from Monte Carlo type simulations of random waves to verify the use of the Net Amplification Factor. Going beyond linear calculations, surface elevation statistics are collected to second-order and a `designer' wave is found to model the most extreme surface elevation responses. A `designer' wave can be identified at required levels of return period to help to understand the relative size of harmonic components in extreme waves. The methods developed with a fixed body are then applied to an identical hull which is freely floating, and the responses between the fixed and moving cases are compared. The vertical heave motion of a semi-submersible in-phase with the incident wave crests is shown to lead to a much lower probability of water-deck impact for the same hull shape restrained vertically. The signal processing methods developed are also applied to a single column to allow comparison with experimental results. Individual harmonic components of the hydrodynamic force are identified up to at least the fifth harmonic. Stokes scaling is shown to hold even for the most violent interactions. It is also shown that the higher harmonic components of the hydrodynamic force can be reconstructed from just the fundamental force time history, and a transfer function in the form of a single phase and an amplitude for each harmonic. The force is also reconstructed well to second-order from the surface elevation time history using diffraction transfer functions. Finally, possible causes of damage to a platform high above mean water level in the North Sea are investigated.

A significant proportion of the world's population and physical assets are located in low lying coastal zones. Accurate prediction of wave induced run-up and overtopping of sea defences are important in defining the extent and severity of wave action, and in assessing risk to people and property from severe storms and tsunamis. This thesis describes a one-dimensional numerical model based on the Boussinesq equations of Madsen and Sorensen (1992) and the non-linear shallow water equations. The model is suitable for simulating propagation of weakly non-linear and weakly dispersive waves from intermediate to zero depth, such that any inundation and/or overtopping caused by the incoming waves is also calculated as part of the simulation. Wave breaking is approximated by locally switching to the non-linear shallow water equations, which can model broken waves as bores. A piston paddle wavemaker is incorporated into the model for complete reproduction of laboratory experiments. A domain mapping technique is used in the vicinity of the paddle to transform a time-varying domain into a fixed domain, so that the governing equations can be more readily solved. First, various aspects of the numerical model are verified against known analytical and newly derived semi-analytical solutions. The complete model is then validated with laboratory measurements of run-up and overtopping involving solitary waves. NewWave focused wave groups, which give the expected shape of extreme wave events in a linear random sea, are used for further validation. Simulations of experiments of wave group run-up on a plane beach yield very good agreement with the measured run-up distances and free surface time series. Wave-by-wave overtopping induced by focused wave groups is also successfully simulated with the model, with satisfactory agreement between the experimental and the predicted overtopping volumes. Repeated simulations, now driven by second order paddle displacement signals, give insight into second order error waves spuriously generated by using paddle signals derived from linear theory. Separation of harmonics reveals that the long error wave is significantly affecting the wave group shape and leading to enhanced runu-up distances and overtopping volumes. An extensive parameter study is carried out using the numerical model investigating the influence on wave group run-up of linear wave amplitude at focus, linear focus location, and wave group phase at focus. For a given amplitude, both the phase and the focus location significantly affect the wave group run-up. It is also found that the peak optimised run-up increases with the wave amplitude, but wave breaking becomes an inhibiting factor for larger waves. This methodology is proposed for extreme storm wave induced run-up analysis.