On the 'Nearly Diurnal Wobble' of the Earth

Summary Serious confusion is evident in the original literature and several review articles from the past decade which have claimed that a second free wobble of the Earth, stemming from gyroscopic coupling with our core fluid, has been detected marginally from latitude or time data. The confusion is betrayed even by the recent labelling of that mode as a nearly diurnal wobble. In fact such a conceivable free mode, as implied for instance by the analysis of Molodenskii, consists fundamentally of a 460-day retrograde nutation in space of the supposedly misaligned angular momenta of the core and the mantle. This slow spatial coning of even the mantle axis has to have an amplitude roughly 460 times greater than that of the associated body-related wobble; a motion as large as that would have been noticed long ago if the recent claims of detection of the wobble were sound. Besides helping to rectify that oversight, the present article (i) comments on the somewhat incomplete theories of such a fluid mode in a realistic Earth, (ii) determines that its combined viscous and magnetic time of damping can hardly exceed 103 years, and (iii) estimates the effects of such friction also upon our forced, astronomical nutations. In particular, it appears that the kinematic viscosity of the uppermost core fluid cannot exceed lo5 stokes without affecting excessively our observed 18.6-year principal nutation. Furthermore, the tidal deceleration of the spin rate of the Earth must have carried us through an exact annual resonance with the free nutation roughly 200 My ago; however, even such resonant coning would probably have had an amplitude only comparable to that of the above principal nutation.

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