Application of Classical Coastal Trapped Wave Theory to High-Scattering Regions

Abstract

AbstractSince the 1970s, analytical models of coastal trapped waves (CTWs) have been developed using a first-order wave equation in the long-wave limit. Formulations of this kind require assumptions of a straight coastline with similar shelf bathymetry. These assumptions prevent the models from capturing the scattering and backscattering behavior of propagating CTWs that encounter changing coastlines, bathymetry, or shelf width. CTW modes from two different analytical models, one of which includes friction and stratification, are compared with CTW observations of velocity and pressure from a study region near the Outer Banks off the North Carolina coast in the United States. The coastline in the study region is relatively straight locally but is bounded by an estuary to the north and shelf narrowing to the south, both of which induce scattering. The models suggest that the CTWs in this region are insensitive to changes in stratification, implying that observed seasonal differences in wave magnitude are due to seasonal wind forcing. Furthermore, friction is found to be important, particularly for mode-1 propagation, but higher-order modes are prevalent despite the importance of friction. There is very poor agreement between the observed and modeled free and forced CTWs because of scattering. This lack of agreement indicates that this is not a globally applicable theoretical formulation because many global coastlines violate the basic assumptions.