IO 10 1 Introduction Long Waves and Ocean Tides The main purpose of this chapter is to summarize what was generally known to oceanographers about long waves and ocean tides around 1940 and then to indicate how the subject has developed since then with particular emphasis upon those aspects that have had significance for oceanography beyond their importance in understanding tides themselves I have begun with a description of astronomical and radiational tide generating potentials section 10 2 but say no more than is necessary to make this chapter self contained Cartwright 1977 summarizes and documents recent developments and I have followed his discussion closely The fundamental dynamic equations governing tides and long waves Laplace s tidal equations LTE remained unchanged and unchallenged from Laplace s formulation of them in 1776 up to the early twentieth century By 1940 they had been extended to allow for density stratification in the absence of bottom relief and criticized for their exclusion of half of the Coriolis forces Without bottom relief this exclusion has recently been shown to be a good approximation the demonstration unexpectedly requires the strong stratification of the ocean Bottom relief appears able to make long waves in stratified oceans very different from their flat bottom counterparts section 10 4 a definitive discussion has not yet been provided Finally LTE have had to be extended to allow for the gravitational self attraction of the oceans and for effects due to the tidal yielding of the solid earth I review these matters in section 10 3 Laplace s study of the free oscillations of a global ocean governed by LTE was the first study of oceanic long waves Subsequent nineteenth and twentiethcentury explorations of the many free waves allowed by these equations extended to include stratification have evolved into an indispensible part of geophysical fluid dynamics By 1940 most of the flat bottom solutions now known had at least in principle been constructed But Rossby s rediscovery and physical interpretation in 1939 of Hough s oscillations of the second class began the modem period of studying solutions of the long wave equations by inspired or systematic approximation and of seeking to relate the results to nontidal as well as tidal motions Since then flat bottom barotropic and baroclinic solutions of LTE have been obtained in mid latitude and in equatorial approximation and Laplace s original global problem has been completely solved The effects of bottom relief on barotropic motion are well understood Significant progress has been made in understanding the effects of bottom relief on baroclinic motions I have attempted to review all those developments in a selfcontained manner in section 10 4 In order to treat this Myrl C Hendershott 292 Myrl C Hendershott 1 IC vast subject coherently I have had to impose my own view of its development upon the discussion I have cited observations when they appear to illustrate some property of the less familiar solutions but the central theme is a description of the properties of theoretically possible waves of long period greater than the buoyancy period and consequently of length greater than the ocean s mean depth Although the study of ocean surface tides was the original study of oceanic response to time dependent forcing tidal studies have largely proceeded in isolation from modem developments in oceanography on account of the strength of the tide generating forces their well defined discrete frequencies and the proximity of these to the angular frequency of the earth s rotation A proper historical discussion of the subject although of great intellectual interest is beyond the scope of this chapter To my mind the elements of such a discussion probably reasonably complete through the first decade of this century are given in Darwin s 1911 Encyclopedia Britannica article Tides Thereafter with a few notable exceptions real progress had to await modem computational techniques both for solving LTE and for making more complete use of tide gauge observations Cartwright 1977 has recently reviewed the entire subject and therefore I have given a discussion in section 1 0 5that although self contained emphasizes primarily changes of motivation and viewpoint in tidal studies rather than recapitulates Cartwright s or other recent reviews This discussion of tides as long waves continuously forced by lunar and solar gravitation logically could be followed by a discussion of tsunamis impulsively forced by submarine earthquakes But lack of both space and time has forced omission of this topic Internal tides were first reported at the beginning of this century By 1940 a theoretical framework for their discussion had been supplied by the extension of LTE to include stratification and their generation was probably properly ascribed to scattering of barotropic tidal energy from bottom relief The important developments since then are recognition of the intermittent narrow band nature of internal tides as opposed to the near line spectrum of surface tides plus the beginnings of a statistically reliable characterization of the internal tidal spectrum and its variation in space and time The subject has recently been reviewed by Wunsch 1975 Motivation for studying internal tides has shifted from the need for an adequate description of them through exploration of their role in global tidal dissipation now believed to be under 10 to speculation about their importance as energy sources for oceanic mixing In section 10 6 I have summarized modem observational studies and their implications for tidal mixing of the oceans Many features of the presentday view of ocean circulation have some precedent in tidal and long wave studies although often unacknowledged and apparently not always recognized The question of which parts of the study of tides have in fact influenced the subsequent development of studies of ocean circulation is a question for the history of science In some cases developments in the study of ocean circulation subsequently have been applied to ocean tides In section 10 7 I have pointed out some of the connections of which I am aware 10 2 Astronomical Tide Generating Forces Although correlations between ocean tides and the position and phase of the moon have been recognized and utilized since ancient times the astronomical tide generating force ATGF was first explained by Newton in the Principia in 1687 Viewed in an accelerated
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