Quasi-Geostrophic Motions in the Equatorial Area

Abstract

Quasi-horizontal wave motions in the equatorial area are discussed. A single layer of homogeneous incompressible fluid with free surface is treated. The Coriolis parameter is assumed to be proportional to the latitude. In general, waves of two different types are obtained as solutions, one being the inertio-gravity wave and the other Rossby wave. They are distinguished from each other by the difference of frequencies and by the relationships between pressure and velocity fields. For the solutions of the lowest mode (waves confined near the equator), however, the distinction between the Rossby and the inertio-gravity waves is not clear. The wave moves westward and the frequency of this wave is compared to that of the gravity wave, if wave length is large. With the increase of the wave number the frequency decreases and approaches to that of the Rossby type wave. The pressure and wind fields of this wave show somewhat mixed character of the two types, and change continuously with the wave number. In this connection it seems impossible to "filter out" gravity waves from large scale motions. Another interesting feature of the equatorial disturbances is that the low frequency waves are trapped near the equator. It is shown that the both waves of inertio-gravity type and of the Rossby type have appreciable amplitude only near the equator. The characteristic north-south extent of the waves is (c/β)1/2, where c is the velocity of long gravity waves and β is the Rossby parameter. This expression is identical with that derived by Bretherton (1964) for inertio-gravity oscillations in a meridional plane. In the later half, "forced stationary motion" in the equatorial region is treated. Based on the same model, mass sources and sinks are introduced periodically in the east-west direction. Then the motions and surface topography caused by them are calculated. As expected, high and low pressures appear where mass source and sink are given respectively. But these high and low cells are splitted into two parts separated by troughs or ridges located along the equator. Strong east-west current was formed along the equator. The flow directs from source to sink and it is intensified by the turning of the circular flow in the higher latitudes.