Evidence for phase coupling between edge wave modes

Abstract

Assuming a nearshore wave field made up of linear combinations of several phase‐coupled edge wave modes at each frequency, we have calculated the form of the cospectra between two alongshore‐separated horizontal velocity components. Cospectra between two measurements of alongshore velocity are shown to be very insensitive to the presence or absence of phase coupling between the modes, while cospectra between two cross‐shore velocities are sensitive to a wide range of mode coupling. Cospectra between alongshore and cross‐shore velocities are particularly sensitive to coupling between a low‐mode edge wave, dominating the alongshore velocity, and higher mode edge waves dominating the cross‐shore velocity. Measured cospectra between alongshore and cross‐shore velocities from the alongshore arrays at the Nearshore Sediment Transport Study experiments on Torrey Pines Beach and Leadbetter Beach have been examined for evidence of mode coupling in the low‐frequency (0.005–0.027Hz) surf beat band. Clear evidence for mode coupling is found at both sites. The influence of the mode coupling on the cospectra varies with frequency in qualitative agreement with the simulated cospectra. Although phase locking between the edge waves can be shown not to be complete, it is not possible directly from the cospectra to quantify the degree of phase coupling, primarily because the number of modes involved is not known. Although the approach taken in this paper is essentially descriptive, it clearly indicates that coupling between edge wave modes must be seriously considered when modelling the nearshore wave field. This is important since previous theoretical work has shown that phase‐coupling is a necessary requirement for the development, by edge waves, of nearshore topography with alongshore structure.