Continental Shelf Wave Propagation in the Mid-Atlantic Bight: A General Dispersion Relation

The authors address the propagation of continental shelf waves in the Mid-Atlantic Bight. An analytical model of the bathymetry in the region is constructed by representing the continental shelf as a gently sloping bottom, which deepens linearly with offshore distance to the place where it meets the continental slope. Seaward of that point, the bathymetry is modeled with an exponentially decaying function of distance. The linearized, barotropic equations of hydrostatic motion, subject to the long-wave approximation, yield separate shelf and slope solutions, which are matched at the shelf break to specify the eigenfunctions. The associated eigenvalues define the dispersion relations for each of the modes. Wavenumber frequency pairs derived from NOAA sea surface height stations along the coast are plotted on the first-mode dispersion curve, and the agreement is good. The theory also shows good agreement with the wave data of D. P. Wang.