Fast and local non-linear evolution of steep wave-groups on deep water: A comparison of approximate models to fully non-linear simulations

摘要

The non-linear Schrodinger equation and its higher order extensions are routinely used for analysis of extreme ocean waves. This paper compares the evolution of individual wave-packets modelled using non-linear Schrodinger type equations with packets modelled using fully non-linear potential flow models. The modified nonlinear Schrodinger Equation accurately models the relatively large scale non-linear changes to the shape of wave-groups, with a dramatic contraction of the group along the mean propagation direction and a corresponding extension of the width of the wave-crests. In addition, as extreme wave form, there is a local non-linear contraction of the wave-group around the crest which leads to a localised broadening of the wave spectrum which the bandwidth limited non-linear Schrodinger Equations struggle to capture. This limitation occurs for waves of moderate steepness and a narrow underlying spectrum. (C) 2016 AIP Publishing LLC.