Equilibrium tidal response of a non-global self-gravitating ocean on a yielding earth

Merriam, J. B. (1973) Equilibrium tidal response of a non-global self-gravitating ocean on a yielding earth. Masters thesis, Memorial University of Newfoundland.

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Abstract

It is commonly stated that the equilibrium ocean tide, measured with respect to the solid surface of the Earth, has amplitude -- ξ₂ = (1+k₂-h₂) U₂/g -- where U₂ is the tide potential of degree-2, g is the acceleration of gravity at the surface and k₂, h₂, the second degree Love numbers, are scalar quantities which characterize the elastic response of the solid Earth. In fact this equation applies strictly to the "tides" in the equipotential surfaces of oceanless, spherically symmetric planets. It is found that the mass of the oceans is sufficient to disturb the potential field to which they are responding thus creating a feedback mechanism which increases the predicted tide height by about 63%. The loading and subsequent deformation of the solid Earth by the ocean tide creates another feedback loop which decreases the tide by about 40%. The combined effect of loading and self-attraction is a 23% increase in the predicted tide height. In addition the irregular distribution of the oceans introduces complications in the response of the oceans to a prescribed potential and a single scalar equation no longer suffices. A set of matrices is developed to replace the scalar Love parameters and these are used to construct maps of several tides which are thought to be equilibrium. Matrices which give the perturbed potential and the gravity tide on a non-spherically symmetric Earth are also given, and the correct expression for the load gravimetric factor, about which there has been some confusion, is derived. Previous estimates of the influence of equilibrium ocean tides on certain aspects of rotation of the Earth are re-worked using the results of the matrix method.

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