Profiles of fully developed (Airy) waves in different water depths

Abstract

Airy waves have a sinusoidal profile in deep water that can be modeled by a time series at any point x and time t, given by eta(x,t)=(H-o/2) cos[2 pi x/L-o-2 pi t/T-w], where H-o is the deepwater height, L-o is the deepwater wavelength, and T-w is the wave period. However, as these waves approach the shore they change in form and dimension so that this equation becomes invalid. A method is presented to reconstruct the wave profile showing the correct wavelength, wave height, wave shape, and displacement of the water surface with respect to the still water level for any water depth.