Quasi- determinism of sea wave groups

Abstract

Provided we know that at a point x0,y0within an irregular gravity wave field, like those generated by wind on sea, at a time instant t0there is a wave with a height H great with respect to the mean, we can predict that that wave, with high probability, has been formed because of the transit of a well defined (deterministic) group, like that in Fig. 1. In mathematical terms: if the ratio between the known wave height H and the mean wave height tends to infinity, the probability that the true wave group is equal to the deterministic wave group plus a lower order random noise approaches 1 [1]. The effect of the random noise is the object of this paper. In particular, the effect on the mean heights and periods of the waves forming the group is estimated within errors of an order smaller than (H/ √m0)−1 (m0being the variance of the free surface elevation of the irregular wave field), The knowledge of the infinitesimal differences between the true wave group and the deterministic wave group, for H/ √m0→∞,proves to be useful for assessing the differences in the case that H is realistically great for a sea state. To that end data from numerical simulations of irregular gravity wave fields are used too. The conclusion is that, for a realistically great H, the deterministic wave group closely reflects the essential features of the true wave group.