9 9 1 Introduction Internal Waves and Small Scale Processes Walter Munk Gravity waves in the ocean s interior are as common as waves at the sea surface perhaps even more so for no one has ever reported an interior calm Typical scales for the internal waves are kilometers and hours Amplitudes are remarkably large of the order of 10 meters and for that reason internal waves are not difficult to observe in fact they are hard not to observe in any kind of systematic measurements conducted over the appropriate space time scales They show up also where they are not wanted as shortperiod fluctuations in the vertical structure of temperature and salinity in intermittent hydrocasts I believe that Nansen 1902 was the first to report such fluctuations l they were subsequently observed on major expeditions of the early nineteen hundreds the Michael Sars expedition in 1910 the Meteor expeditions in 1927 and 1938 and the Snellius expedition in 1929 1930 A comprehensive account is given in chapter 16 of Defant 1961a In all of these observations the internal waves constitute an undersampled small scale noise that is then aliased into the larger space time scales that are the principal concern of classical oceanography From the very beginning the fluctuations in the hydrocast profiles were properly attributed to internal waves The earliest theory had preceded the observations by half a century Stokes 1847 treated internal waves at the interface between a light fluid overlaying a heavy fluid a somewhat minor extension of the theory of surface waves The important extension to the case of a vertical mode structure in continuously stratified fluids goes back to Rayleigh 1883 But the discreteness in the vertical sampling by hydrocasts led to an interpretation in terms of just the few gravest modes with the number of such modes increasing with the number of sample depths giving j equations in j unknowns And the discreteness in sampling time led to an interpretation in terms of just a few discrete frequencies with emphasis on tidal frequencies The development of the bathythermograph in 1940 made it possible to repeat soundings at close intervals Ufford 1947 employed three vessels from which bathythermograph lowerings were made at 2 minute intervals In 1954 Stommel commenced three years of temperature observations offshore from Castle Harbor Bermuda initially at half hour intervals later at 5 minute intervals 2 Starting in 1959 time series of isotherm depths were obtained at the Navy Electronics Laboratory NEL oceanographic tower off Mission Beach California using isotherm followers Lafond 1961 installed in a 200 m triangle Cox 1962 By this time oceanographers had become familiar with the concepts of continuous spectra long before 264 Walter Munk II I routinely applied in the fields of optics and acoustics and the spectral representation of surface waves had proven very useful It became clear that internal waves too occupy a frequency continuum over some six octaves extending from inertial to buoyant frequencies The high frequency cutoff had been made explicit by Groen 1948 With regard to the vertical modes there is sufficient energy in the higher modes that for many purposes the discrete modal structure can be replaced by an equivalent three dimensional continuum We have already referred to the measurements by Ufford and by Lafond at horizontally separated points Simultaneous current measurements at vertically separated points go back to 1930 Ekman and HellandHansen 1931 In all these papers there is an expression of dismay concerning the lack of resemblance between measurements at such small spatial separations of oscillations with such long periods I believe from discussions with Ekman in 1949 that this lack of coherence was the reason why Ekman postponed for 23 years until one year before his death the publication of Results of a Cruise on Board the Armauer Hansen in 1930 under the Leadership of Bjrnm Helland Hansen Ekman 1953 But the decorrelation distance is just the reciprocal of the bandwidth waves separated in wavenumber by more than Ak interfere destructively at separations exceeding Ak The small observed coherences are simply an indication of a large bandwidth The search for an analytic spectral model to describe the internal current and temperature fluctuations goes back over many years prompted by the remarkable success of Phillips s 1958 saturation spectrum for surface waves I shall mention only the work of Murphy and Lord 1965 who mounted temperature sensors in an unmanned submarine at great depth They found some evidence for a spectrum depending on scalar wavenumber as k 5 3 which they interpreted as the inertial subrange of homogeneous isotropic turbulence But the inertial subrange is probably not applicable except perhaps at very small scales and the fluctuations are certainly not homogeneous and not isotropic Briscoe 1975a has written a very readable account of developments in the early 1970s The interpretation of multipoint coherences in terms of bandwidth was the key for a model specturm proposed by Garrett and Munk 1972b The synthesis was purely empirical apart from being guided by dimensional considerations and by not violating gross requirements for the finiteness of certain fundamental physical properties Subsequently the model served as a convenient strawman for a wide variety of moored towed and dropped experiments and had to be promptly modified Garrett and Munk 1975 which became known as GM75 in the spirit of planned obsolescence There have been further modifications see a review paper by Garrett and Munk 1979 the most recent version is summarized at the end of this chapter The best modem accounts on internal waves are by O M Phillips 1966b Phillips 1977a and Turner 1973a Present views of the time and space scales of internal waves are based largely on densely sampled moored towed and dropped measurements The pi oneeringwork with mooringswas done at site D in the western North Atlantic Fofonoff 1969 Webster 1968 Horizontal tows of suspended thermistor chains Lafond 1963 Charnock 1965 were followed by towed and self propelled isotherm following fishes Katz 1973 McKean and Ewart 1974 Techniques for dropped measurements were developed along a number of lines rapidly repeated soundings from the stable platform FLIP by Pinkel 1975 vertical profiling of currents from free fall instruments by Sanford 1975 and Sanford Drever and Dunlap 1978 and vertical profiling of temperature from
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