A Reduced Order Parameterization of Random Wave Fields With Deterministic Wave Groups

Abstract

Abstract Under a linear model of gravity wave evolution the expected shape of large events is given by Quasi-determinism theory. However, nonlinear physics modifies the averaged shape of the largest events. In this study, we examine these nonlinear modifications to the averaged shape of the largest events for directionally spread random wave fields. We first compare these nonlinear changes from the extreme events in random wave fields with the nonlinear changes during the evolution of deterministic wave groups. We then explore whether it is possible to predict these nonlinear changes observed in random wave fields with only nonlinear wave group simulations. We applied a modified version of the wave group detection algorithm in [1, 2] to isolate the individual wave groups from random wave fields. We perform the nonlinear wave group simulations with the initial conditions matching these isolated individual wave groups extracted from linear random wave field. The nonlinear evolution of these isolated wave groups can predict the envelope contraction of averaged shape of extreme events in random wave fields quantitatively over a wide range of local steepness under current conditions. This suggests some statistical connections between the nonlinear evolution of deterministic wave groups and the evolution of the largest waves in the random wave fields.