Lunar and Solar Torques on the Oceanic Tides

A general flamework for calculating lunar and solar torques on the oceanic tides is developed in terms of harmonic constituents. Axial torques and their associated angular momentum and Earth rotation variations are deduced from recent satellite-altimeter and satellite-tracking tide solutions. Torques on the prograde components of the tide produce the familiar secular braking of the rotation rate. The estimated secular acceleration is approximately -1300 arcseconds/century 2 (less 4% after including atmospheric tides); the implied rate of change in the length of day is 2.28 milliseconds/century. Torques on the retrograde components of the tide produce periodic rotation variations at twice the tidal frequency. Interaction torques (for example, solar torques on lunar tides) generate a large suite of rotation-rate variations at sums and differences of the original tidal frequencies. These are estimated for periods from 18.6 years to 6 hours. At subdaily periods the angular momentum variations are 5 to 6 orders of magnitude smaller than the variations caused by ocean tidal currents. Brosche and Seiler ( 1996) recently called attention to the interesting role that direct lunar and solar torques on the ocean tide play in the Earth's short-period angular momen- tum balance ("short-period" here meaning daily and sub- daily). Brosche and Seiler noted that such torques are a potential source of angular momentum in the Earth-ocean system and that this source had been neglected in previous Earth rotation studies. The purpose of the present paper is to reexamine, clarify, and extend these ideas. We limit the discussion to the Earth's spin rate and ignore the additional complications of wobble and nutation. It suffices therefore to examine only axial torques. We also limit the discussion to diurnal and semidiurnal tides of the second degree in the tidal potential, that is, to the "major" short-period tides. A qualitative understanding of the consequences of tidal torques can be obtained from the diagram in Figure 1, which is drawn for the principal semidiurnal tide M2. Two spher- ical harmonic components of the ocean tide--the only two that induce nonzero torques--are displayed: prograde and retrograde components of degree 2, order 2. The prograde component is the classical tidal "bulge" that propagates west- ward under the moon; the retrograde component is a similar bulge, generally smaller, that propagates eastward. ("Pro- grade" here implies moving in the same direction as the tide- generating body; this prograde/retrograde terminology fol-