Tides affect the earth's rotation in two sharply contrasting ways. One way, caused by tidal friction, produces an extremely slow secular change in rotation. The other way, caused by the continual movements of the tides about the planet, produces very small but very rapid changes in rotation. These rapid changes occur at exactly the same periods as the tides themselves -- half-daily, daily, etc. (The IERS Special Bureau for Tides is concerned primarily with the rapid changes, but some of our data have implications for the secular changes.)
The secular change in the planet's rotation is a classical topic in geophysics. It goes back some 300 years to when Sir Edmond Halley first hypothesized that the moon was accelerating in its orbit. Most of Halley's lunar acceleration was only apparent. It was actually the earth's rotation slowing down, making the moon appear to accelerate. The moon does accelerate (strictly, it decelerates), but the larger effect is the earth's rotational braking. This braking is caused by tidal friction. Throughout the earth's history tidal braking has played, and it will continue to play, a dominant role in the rotation. Currently the secular change in the rotation rate increases the length of day by some 2.3 milliseconds per day per century.
To see what that means, consider this example: suppose the rotating earth is our clock and it's been 100 years since that clock's "standard second" was set to correspond to an atomic clock's second (which is actually almost the case, notwithstanding that atomic clocks weren't around until 1955). Then after 1000 days our earth clock loses about 2.3 seconds, falling further behind the atomic clock. This long-term slowing of the rotation is a primary reason for periodically inserting leap seconds into our timekeeping. Of course, there are other contributors to the changing rotation rate such as the changing atmosphere and the motions of the fluid core; one can't blame just tides for our timekeeping difficulties.
The tidal braking in the earth's rotation is actually caused primarily by friction in the oceans, where ``friction'' may refer to any number of physical mechanisms which have yet to be determined definitively. For example, bottom friction, induced by tidal currents flowing across the seabed, various kinds of wave breaking, and scattering of tidal waves into oceanic internal waves are all thought to play a role. For a recent overview of this subject, look up Walter Munk's paper ``Once again: once again--tidal friction,'' published in Progress in Oceanography, vol. 40, pp. 7-36, 1997.
Only in the last few years has this subject come to the fore, as our abilities to measure daily and even subdaily variations in rotation have been developed and improved. An example is shown on the following figure, which displays very rapid variations in the rotation rate (in terms of Universal Time) as observed by hourly measurements and as predicted by a numerical model of ocean tides. The measurements are from an intensive campaign of Very Long Baseline Interferometry (VLBI) observations, analyzed and provided courtesy of Chopo Ma and John Gipson (NASA/GSFC). The ocean predictions are from one of the models provided in the Special Bureau for Tides web pages.
As can be seen, both diurnal and semidiurnal variations are present in UT1, and they appear to be quite well represented by the ocean model. There are two ways that the ocean tides can cause such rapid variations. (1) As the tides move water around the globe, the moment of inertia of the earth changes. By conservation of angular momentum, the solid earth changes its rotation rate accordingly. (2) As the tidal currents slow down or speed up, they exchange angular momentum with the solid earth, which is manifested in the rotation rate. Mechanism (2) is slightly more important for rotation rate variations; both mechanisms are about equally important for polar motion variations. Hence, to predict tidal variations in earth rotation, similar to the solid curve in the figure, requires a global model of both tidal heights and tidal currents. The relevant information from several such models is provided in these web pages of the Special Bureau for Tides.
Finally, there are also tidal variations in rotation rate and polar motion caused by the near-equilibrium long-period tides, which have periods from about 9 days to 18.6 years. For rotation rate, the dominant contributor is in fact the solid-earth tides. But perturbations from the ocean are still significant. See this additional information.
These books are a bit obsolete in places, since obviously they cannot discuss the most up-to-date accuracies, measurements, and theories. But they are nonetheless classics of the literature and provide the starting point for all further study. In particular, Munk and MacDonald, more than anyone since Lord Kelvin, shaped the contours of the entire modern subject, and they laid the foundation for the succeeding 40 years of work. Their book, which justifiably won the AAAS Monograph Prize for 1959, touched on nearly all aspects of the present-day subject, save perhaps for the one addressed in these web pages: extremely rapid (daily and faster) variations.
Munk, W. H. and G. J. F. MacDonald, The Rotation of the Earth: A Geophysical Discussion, Cambridge Univ. Press, 1960.
Lambeck, K., The Earth's Variable Rotation: Geophysical Causes and Consequences, Cambridge Univ. Press, 1980.
Doodson, A. T. and H. D. Warburg, Admiralty Manual of Tides, HMSO, 1941.
Brosche, P., U. Seiler, J. Suendermann, and J. Wuensch, Periodic changes in the Earth's rotation due to oceanic tides, Astronomy and Astrophysics, 220, 318-320, 1989.
Chao, B. F. and R. D. Ray, Oceanic tidal angular momentum and Earth's rotational variations, Progress in Oceanography, 40, 399-422, 1997.
Eubanks, T. M., Variation in the orientation of the Earth, in Contributions of Space Geodesy to Geodynamics: Earth Dynamics, pp. 1-54, Amer. Geophys. Union, Washington, 1993.
Gross, R. S., The effect of ocean tides on the Earth's rotation as predicted by the results of an ocean tide model, Geophysical Research Letters, 20, 293-296, 1993.
Herring, T. A. and D. Dong, Measurement of diurnal and semidiurnal rotational variations and tidal parameters of the Earth, Journal of Geophysical Research, 99, 18051-18071, 1994.
Ray, R. D., D. J. Steinberg, B. F. Chao, and D. E. Cartwright, Diurnal and semidiurnal variations in the Earth's rotation rate induced by oceanic tides, Science, 264, 830-832, 1994.
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