Coherence and band structure of inertial motion in the sea

It is now well established by observation that a peak in the spectrum of horizontal motion should be anticipated everywhere in the ocean near the local inertia frequency, 2ω sine (latitude). The theory of wave motion in a weakly stratified, rotating ocean of constant depth explains this observation either by the existence of a frequency condensation point in wave‐number space or, alternatively, by the vanishing of the meridional group velocity. This explanation is independent of a specific generating mechanism, such as tidal forcing. The details of the wave structure and dispersion relation are readily obtained when, as seems both likely and desirable, it is permissible to ignore the discrete normal‐mode‐producing effects of distant lateral boundaries. This theory predicts a spectral peak slightly above the inertia frequency, and this displacement depends on the zonal and vertical wave numbers. The peak frequency in the North Atlantic measurements by Fofonoff and Webster implies vertical modes of O (10) and a zonal wave number of O (several hundred cycles per earth circumference). When these numbers are applied to a simple coherence model, assuming phase independence between different wave numbers, one can account for the observed lack of coherence between stations separated in depth or longitude. This theory also defines a latitudinal scale; for vertical wave number 10 this is, typically, of O (25 km), which is in qualitative agreement with Hendershott's observations in the eastern North Pacific. The present theoretical model is appropriate for random distributed sources. The observations, however, indicate a higher degree of intermittency than is implied by this model. We conclude that both random distributed sources and intermittent discrete sources must be taken into account for a satisfactory description of the phenomena.