Oceanic Tides - Cartwright, D. E. (The International Hydrographic Review, 2015)
Tidal research has had a long history, but the outstanding problems still defeat current research techniques, including large-scale computation. The definition of the tide-generating potential, basic to all research, is reviewed in modern terms. Modern usage in analysis introduces the concept of tidal ’admittance’ functions, though limited to rather narrow frequency bands. A ’radiational potential’ has also been found useful in defining the parts of tidal signals which are due directly or indirectly to solar radiation. Laplace’s tidal equations (LTE) omit several terms from the full dynamical equations, including the vertical acceleration. Controversies about the justification for LTE have been fairly well settled by Miles’ (1974) demonstration that, when regarded as the lowest order internal wave mode in a stratified fluid, solutions of the full equations do converge to those of LTE. Solutions in basins of simple geometry are reviewed and distinguished from attempts, mainly by Proudman, to solve for the real oceans by division into elementary strips, and from localized syntheses as Used by Munk for the tides off California. The modern computer seemed to provide a ‘ breakthrough ’ in solving LTE for the world’s oceans, but the results of independent workers differ, mostly because of the inadequacy in their treatment of friction and for the elastic yielding of the Earth. The difference between estimates of the rate of working of the Moon on the tides, about 3.5 X 1012 W, and of the power loss in shallow seas, about 1.7 X 1012W, marks a serious unidentified sink of energy. Conversion to internal tides has been suggested as a sink, but calculations are at present inconclusive. Computed models of the global tides do, however, agree well with recent estimates of the Moon’s deceleration in longitude. Calculations based on such astronomical measures suggest an even higher figure for the rate of working, 4.3 X 1012 W. This is considerably greater than the figure of 2.7 X 1012W accepted until about 1970, thus accentuating the problem of the missing energy sink. Future progress will require more extensive programmes of pelagic tidal measurement. The technology for this is well developed but slow. Altimetry of the sea surface from satellites could provide the much needed global coverage if properly backed up by high-precision tracking of the instrumented satellite.