Shelf wave dispersion in a geophysical ocean

We consider subinertial, free waves trapped along three coastlines (i.e., shelf waves) in an ocean governed by a geophysical model in which stratification is explicitly obtained by taking the Vaisala frequency N much greater than the inertial frequency f. The behavior is generalized in terms of the parameter S = (N/f)a where a is the bottom slope of the trapping region. Only when $\text{S}\text{\$}\text{?}\text{0.2}$, are the predicted shelf waves like those predicted by Laplace's tidal equations (LTE) on an f-plane. When 0.2 ? S < 1, LTE are inappropriate because the shelf waves are only qualitatively like those predicted by LTE, and when S 1, the shelf waves are like baroclinic Kelvin waves in that they can occur at any subinertial frequency up to f (in qualitative disagreement with the predictions of LTE). Since N/f is usually a large number in the real ocean (of order 50–250), S is likely to be large unless the bottom slope is very gentle throughout the trapping region. Some applications to coastal current observations are discussed.