The dispersion relation for planetary waves in the presence of mean flow and topography. Part I: analytical theory and one-dimensional examples

An eigenvalue problem for the dispersion relation for planetary waves in the presence of mean flow and bottom topographic gradients is derived, under the Wentzel–Kramers–Brillouin–Jeffreys (WKBJ) assumption, for frequencies that are low when compared with the inertial frequency. Examples are given for the World Ocean that show a rich variety of behavior, including no frequency (or latitudinal) cutoff, solutions trapped at certain depths, coalescence of waves, and a lack of dispersion for most short waves