EXTREMA OF FRACTAL RANDOM WATER WAVES

Abstract

Herein we review the statistical properties of the visibly random behavior of sea waves and the resulting stochastic forces loading off-shore structures and ships. The traditional assumption is that the statistics 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 review, that being that the statistics of surface waves are Lévy stable, and investigate the response of dynamical models of off-shore structures to such stochastic forcing. We find that such familiar results as the Weibull distribution for the failure of a dynamical system may be a consequence of the statistics of the driver rather than any nonlinearity in the structure response.