TABLE OF CONTENTS When modelling the sea surface one faces conflicting requirements of realism and tractability. The hydrodynamic description of the sea surface and its interaction with the wind is a problem of such complexity that its complete solution is essentially impossible; the detail required to both define the problem (through appropriate boundary conditions) and specify its solution would be over whelming. To make progress towards a physically useful model, simplifying assumptions must be made.
The most common approximation is to line arise the hydrodynamic equations for surface waves and to obtain the solutions of small amplitude, sinusoidal waves. As the system is approximated to be linear the overall sea structure may be modelled as the superposition of many such waves generated by the interaction of the wind and sea over an area of much greater dimensions than the correlation lengths typical of the sea surface. Thus we would expect Gaussian statistics, as a consequence of the central limit theorem. Experimental measurements of the sea surface slope and height, for example, approximate well to a Gaussian form.
The key property that defines a Gaussian process is the average power spectrum. This expresses how the wave energy is distributed (on average) across spatial and temporal frequencies. There are many experimentally derived models for the average power spectrum for the sea. A widely used formula based on the Pierson-Moskowitz [1] spectrum is:
where
| q | is the spatial frequency vector (and q is its magnitude), ? is the temporal... |
