Standing edge waves reinvestigated: A comparison between two different bathymetries

Abstract

As a result of wave refraction caused by variable water depth within enclosed or semi-enclosed nearshore areas like harbors and bays, standing edge waves play an important part in the circulation patterns. The bathymetries of these areas may fall into two categories as follows: one is a reflective beach with a moving shoreline where the waves run up and down and the other has a certain water depth at a fixed backwall. A comparison of the standing edge waves trapped on these two types of bathymetries is made. Analytical investigations show that the trapped modes may behave dissimilarly on each type of bathymetry, especially for relatively high modes when the bathymetry is not simply a constantly sloping beach but a piecewise one. Wave patterns induced by water surface disturbances of the numerical simulations are analyzed with wavelet spectra. Frequencies of different components of the standing edge waves are compared with theoretical predictions. The results of the bathymetry with a reflective backwall are consistent with the findings of previous studies. For the case with a moving shoreline, several very low modes of the standing edge waves can survive and persist into a steady state, whereas higher modes may suffer from a quick attenuation. The occurrence of the trapped modes is revealed sensitive to the initial position of the water surface agitations in this case.