The Effect of Reduced Water Depth on the Description of Extreme Waves and the Prediction of the Water Particle Kinematics

This paper concerns the description of large waves in intermediate and shallow water depths. In deep water it is well known that the evolution of the largest waves is governed by linear dispersion. In contrast, as the water depth reduces the effects of wave dispersion are weakened and the relative significance of wave modulation shown to be increasingly important. This leads to very different extreme wave groups, the properties of which are critically dependent upon the directionality of the wave field. The paper also concerns the water particle kinematics arising beneath these nonlinear wave groups and contrasts fully non-linear predictions based on a state-of-the-art wave model with the results of the commonly applied design wave solutions. To explore these effects, and to provide a physical explanation for their occurrence, two wave models are employed. The first, proposed by Bateman, Swan & Taylor [1, 2], allows fully-nonlinear descriptions of the evolution of large waves in realistic seas, involving a significant spread of wave energy in both frequency and direction. The second is a wave evolution equation based upon the early work of Zakharov [3] and written in Hamiltonian form by Kasitskii [4]. This model is only valid to a fourth-order of wave steepness, but has the over-riding advantage that it gives physical insight into the evolution process.