Non-linear evolution of uni-directional focussed wave-groups on a deep water: A comparison of models

Up until the point at which ocean waves break, their dynamics are generally assumed to be accurately modelled by potential flow theory. For practical and computational reasons it is often useful to approximate the full potential flow solution with bandwidth and amplitude limited equations. A approximation used for waves on deep water is the Broad-banded Modified Non-linear Schrödinger equation (also known as the modified Dysthe equation). In this paper we compare this approximate model with potential flow simulations of focussing uni-directional wave-groups. We find that for moderate non-linearity the approximate model predicts very similar changes to the potential flow model. However, one of the dominant non-linear changes to the wave-group is a localised increase in the bandwidth and contraction in physical length, and beyond a certain point the approximate model fails to accurately reproduce this causing other elements, such as the maximum wave amplitude, to be poorly modelled. This modelling inaccuracy occurs in cases where, based on the initial conditions of the simulation, the approximate model would be expected to be accurate.