Simulation of unidirectional propagating wave trains in deep water using a fully non-hydrostatic model

Abstract

A new fully non-hydrostatic model is developed and then applied to simulate the evolution of unidirectional propagating waves in intermediate and deep water. The ability and efficiency of the model are examined using experimental data. Then, the evolutions of initially uniform and perturbed wave trains are simulated. Frequency downshift phenomena occur during the wave evolution. For a small initial steepness, there are approximately two incidents of partial recurrence. However, with increasing initial wave steepness, the energy transfers from the lower sideband to the carried wave decreases, and a permanent frequency downshift is more likely to occur. For the initially imposed wave trains, if the wave steepness is lower than 0.11, an approximate Fermi-Pasta-Ulam (FPU) phenomenon occurs. For wave trains with a steepness of approximately 0.13, a partial recurrence still can appear. Recurrence is not observed in larger wave trains. Additionally, the kinematics of extreme waves formed during the wave evolution are also investigated, and the non-dimensional horizontal velocity profiles under the extreme crests are converged and can be well modelled by the theoretically exponential curve. In addition, the crest speeds of the steep waves are less than the linear wave speeds. It is found that larger waves have slower crest speeds.