On tidal friction and the decelerations of the earth's rotation and moon's revolution

Abstract

This paper develops and analyzes the basic principles of the hydrodynamic, mechanical, and thermodynamic workings of the moon, ocean, and earth (MOE) tidal interaction system from the energy conservation law alone. With the introduction of effective densities of spherical harmonic tides, it became possible to define consistent power and torque quantities and to establish fundamental relationships between them. These relationships made it possible to interpret hydrodynamic energy terms into corresponding heat dissipation and/or mechanical energy changes of the earth's rotation and moon's revolution. Without specifying any particular ocean tide model, it became possible to reveal the important mechanism by which the moon's gravitating forces brake the earth's rotation essentially via the medium of the ocean tides. While the moon pulls the earth and ocean tides around in a nonsynchronous manner, the oceans gear into the distortions of their floors and brake the earth essentially with their tidal pressure. The braking is accompanied by tidal friction, which burns about 53% of the total gravitational energy supply to the oceans without holding any noteworthy torque on the earth. The wasteful oceanic clutch of 47% efficiency leads to a surprisingly accelerated moon's orbit by the ocean tides. This stunning ocean‐tide‐model independent result can be reversed by improved earth and earth ocean‐load tide models. Using the author's particular M₂ ocean tide model, it is demonstrated, in principle, that an earth tide phase lag of about 0.5° is alone sufficient to turn the accelerated moon into a decelerated moon which matches exactly the presently known satellite observations.

The new derivations and results are in striking conflict with earlier estimation procedures. The corresponding formulas, which yielded unexplainable energy gaps that puzzled ocean tidalists for more than two decades, were found inaccurate by derivation and by diagnostic and empirical tests. The present derivations strongly back the seismically founded consensus that the earth acts as an almost perfectly elastic body, which supports only a tidal phase shift of a few thousandths of one degree (Zschau, 1978b) by dissipation. However, analogous experience in ocean tide modeling indicates that the apparent contradiction with the estimated earth tide phase lag of about 0.5° can be resolved by allowing proper tidal interactions in future earth tide models. It must be emphasized that most numerical results are sensitively dependent on the postulated earth tide models, and, hence, should be viewed as preliminary.