Calculation of Wave Packet Trajectories and Wave Heights for Variable Water Depths and Currents

摘要

The theory and numerical methods are presented for determining the paths and wave heights of gravity water wave packets. Both variable water depths and currents are considered. The wave height is computed accounting for the effects of shoaling, refraction, and energy dissipation. A ray curvature expression is used to determine the wave packet trajectories where the speed of the packet is given by G = (d omega/dk) cos phi. The symbol (omega) denotes the angular frequency, k is the wave number, and phi is the difference between the direction of the wave packet and the direction of the wavelets within the packet. The wavelet direction is determined at each point of the wave packet trajectory. The wave packet and ray directions differ when there are currents. The calculations for variations in water depth are greatly simplified by choosing a coordinate system at each ray point in which one axis is aligned parallel with the direction of the gradient of the water depth. In a similar fashion, the calculations involving variations in current are simplified by choosing a coordinate system at each ray point in which an axis is taken parallel with the direction of the gradient of the current magnitude. Example printouts and plots are presented to illustrate the wave prediction method. (Author)