Inertial oscillations of tidal period

Abstract

Horizontal currents rotating (clockwise in the northern hemisphere) with period 12 hr/sin (latitude) are commonly observed in the sea. MUN~ and PHILLIPS (1968) explain these motions as a field of low-frequency gravity waves whose meridional group velocity vanishes near their inertial + arc sin (12 hr/wave period) on account of the rotation and sphericity of the earth. We shall adopt Munk and Phillips' designation of these waves as planetary-gravity or pg waves. The concentration of energy near the latitudes resulting from either local or global generation of baroclinic pg waves is sufficiently pronounced that a variety of generating mechanisms could cause motions to appear. POLLARD and MILLARD (1970) have calculated the motion generated by variable local winds. We here estimate the diurnal motion generated when tidal energy is scattered into baroclinic pg waves as the barotropic tide passes over bottom roughness (Cox and SANDS~OM, 1962). The predicted horizontal motion is most intense a fraction of a degree equatorward of the diurnal latitudes (30°). It is there of order a few cm/sec. Further equatorward, the horizontal motion decays slowly in an oscillatory manner; poleward it decreases rapidly and monotonically. The primary maximum is about 1⁄2o wide with very small vertical velocity throughout its extent. The vertical structure of the flow resembles that of a high mode baroclinic (internal) pg wave. Wind generation would produce motion at all latitudes in the sea, tidal generation only near 30°N or 30°S (or at very high latitudes). The ubiquity of motion is well established (W~BsTER, 1968), but time series of currents sufficiently long to detect the degree of tidal enhancement of diurnal motion predicted here have not yet been obtained. A representative series of observations is analysed in detail at the conclusion of this paper.