On long waves in a stratified, equatorial ocean caused by a travelling disturbance

Abstract

Long waves, including Rossby waves and gravity waves, caused by a meteorological disturbance in an equatorial region are discussed by use of a theoretical model of a two-layer ocean. With the assumption that the frequency of wind stress variation is larger than the Coriolis' parameter, wave equations with a wind stress divergence as a forcing function are obtained. Forced waves initiated by a westward moving disturbance similar to the equatorial easterly waves indicate a resonance in the frequency range of gravity waves in a baroclinic mode and also in that of Rossby waves in both modes. The resonance in the gravity wave range seems to be responsible for the pronounced 4-day period oscillation detected at some Pacific islands.

Waves initiated by a sudden wind show no resonance, but interference between forced and free waves occurs near the period of resonance. The effect of a linear frictional force is shown to be more important in the Rossby wave range than in the gravity wave range. The effect of coasts is also studied and the proper oscillation of an ocean between two coasts is found to occur both in the Rossby wave range and gravity wave range.

When the frequency of the waves is decreased, the north-south distribution of the amplitudes must be modified owing to an increasing effect of the Coriolis' force in the sub-tropical zone of the wind. Analysis of the effect of the South Equatorial Current indicated that the response of sea-level has another resonant period in the intermediate range between Rossby waves and gravity waves. On the other hand, the current makes the resonant spectra of a period in Rossby waves so sharp that the resonance may be considered for practical purposes to vanish. The current also increases the amplitude of waves with periods of several days.