The Extension of Baroclinic Coastal-Trapped Wave Theory to Superinertial Frequencies

Abstract

The problem of finding baroclinic coastal-trapped wave modes is generalized from subinertial to superinertial frequencies at which complete trapping can only occur in special cases. Modes are found by a numerical resonance searching method in which forcing is applied to a vertical slice normal to the shelf, and resonant responses identified. An example is considered with topography approximating the Iberian shelf and uniform stratification. The buoyancy frequency is chosen such that the lowest subinertial trapped wave modes combine buoyancy and vorticity effects, and their dispersion curves approach the inertial frequency from below. Superinertial analogs of the first three subinertial modes are identified and have a small imaginary component of wavenumber corresponding to alongshelf decay due to leakage of energy to the ocean. These superinertial modes are apparently not physically realizable, however, since they contain components that do not decay into the ocean. Nevertheless, they can be interpreted physically since waves with a near-modal shape could propagate alongshelf, though would necessarily become distorted in shape and decay as they did so. In the ocean, tides provide forcing at discrete superinertial frequencies and could produce resonant responses leading to an alongshelf dependence of the internal tide.