A comparatively general solution of the shelf-wave problem

It is demonstrated how a hyperbolic-tangential shelf bathymetry can be used to mimic classical convex and concave bottom profiles employed for previous investigations of coastally trapped waves. This bathymetry permits a transformation of the governing wave equation which makes it possible to use Frobenius series expansions for solving the associated eigenvalue problems which yield the dispersion relations. ► Low-frequency coastally trapped waves were studied focusing on bottom topographies. ► A hyperbolic tangential function was adapted to different bathymetry approximations. ► Wave eigenfrequencies were calculated for two cases applying Frobenius' method.