EXTREMA OF FRACTAL RANDOM WATER-WAVES

Herein we review the statistical properties of the visibly random beha vior of sea waves and the resulting stochastic forces loading off-shor e structures and ships. The traditional assumption is that the statist ics of the sea surface displacement produced by waves is Gaussian, or equivalently that the statistics of the wave amplitudes are Rayleigh. We examine this and a more general statistical hypothesis in this revi ew, that being that the statistics of surface waves are Levy stable, a nd investigate the response of dynamical models of off-shore structure s to such stochastic forcing. We find that such familiar results as th e Weibull distribution for the failure of a dynamical system may be a consequence of the statistics of the driver rather than any nonlineari ty in the structure response.