9Internal Wavesand Small-ScaleProcessesWalter Munk9.1 IntroductionGravity waves in the ocean's interior are as commonas waves at the sea surface-perhaps even more so, forno one has ever reported an interior calm.Typical scales for the internal waves are kilometersand hours. Amplitudes are remarkably large, of theorder of 10 meters, and for that reason internal wavesare not difficult to observe; in fact they are hard not toobserve in any kind of systematic measurements con-ducted over the appropriate space-time scales. Theyshow up also where they are not wanted: as short-period fluctuations in the vertical structure of temper-ature and salinity in intermittent hydrocasts.I believe that Nansen (1902) was the first to reportsuch fluctuations;l they were subsequently observedon major expeditions of the early nineteen hundreds:the Michael Sars expedition in 1910, the Meteor ex-peditions in 1927 and 1938, and the Snellius expeditionin 1929-1930. [A comprehensive account is given inchapter 16 of Defant (1961a)]. In all of these observa-tions the internal waves constitute an undersampledsmall-scale noise that is then "aliased" into the largerspace- time scales that are the principal concern of clas-sical oceanography.From the very beginning, the fluctuations in the hy-drocast profiles were properly attributed to internalwaves. The earliest theory had preceded the observa-tions by half a century. Stokes (1847) treated internalwaves at the interface between a light fluid overlayinga heavy fluid, a somewhat minor extension of the the-ory of surface waves. The important extension to thecase of a vertical mode structure in continuously strat-ified fluids goes back to Rayleigh (1883). But the dis-creteness in the vertical sampling by hydrocasts led toan interpretation in terms of just the few gravestmodes, with the number of such modes increasing withthe number of sample depths (giving j equations in junknowns). And the discreteness in sampling time ledto an interpretation in terms of just a few discretefrequencies, with emphasis on tidal frequencies.The development of the bathythermograph in 1940made it possible to repeat soundings at close intervals.Ufford (1947) employed three vessels from which bath-ythermograph lowerings were made at 2-minute inter-vals! In 1954, Stommel commenced three years of tem-perature observations offshore from Castle Harbor,Bermuda, initially at half-hour intervals, later at 5-min-ute intervals.2Starting in 1959, time series of isothermdepths were obtained at the Navy Electronics Labora-tory (NEL) oceanographic tower off Mission Beach, Cal-ifornia, using isotherm followers (Lafond, 1961) in-stalled in a 200-m triangle (Cox, 1962).By this time oceanographers had become familiarwith the concepts of continuous spectra (long before264Walter Munk II_____I____ _ _ _ _routinely applied in the fields of optics and acoustics),and the spectral representation of surface waves hadproven very useful. It became clear that internal waves,too, occupy a frequency continuum, over some six oc-taves extending from inertial to buoyant frequencies.[The high-frequency cutoff had been made explicit byGroen (1948).] With regard to the vertical modes, thereis sufficient energy in the higher modes that for manypurposes the discrete modal structure can be replacedby an equivalent three-dimensional continuum.We have already referred to the measurements byUfford and by Lafond at horizontally separated points.Simultaneous current measurements at vertically sep-arated points go back to 1930 Ekman and Helland-Hansen, 1931). In all these papers there is an expressionof dismay concerning the lack of resemblance betweenmeasurements at such small spatial separations of os-cillations with such long periods. I believe (from dis-cussions with Ekman in 1949) that this lack of coher-ence 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' in1930 under the Leadership of Bjrnm Helland-Hansen"(Ekman, 1953). But the decorrelation distance is justthe reciprocal of the bandwidth; waves separated inwavenumber by more than Ak interfere destructivelyat separations exceeding (Ak)-. The small observedcoherences are simply an indication of a large band-width.The search for an analytic spectral model to describethe internal current and temperature fluctuations goesback over many years, prompted by the remarkablesuccess of Phillips's (1958) saturation spectrum for sur-face waves. I shall mention only the work of Murphyand Lord (1965), who mounted temperature sensors inan unmanned submarine at great depth. They foundsome evidence for a spectrum depending on scalarwavenumber as k-5'3, which they interpreted as theinertial subrange of homogeneous, isotropic turbu-lence. But the inertial subrange is probably not appli-cable (except perhaps at very small scales), and thefluctuations are certainly not homogeneous and notisotropic.Briscoe (1975a) has written a very readable accountof developments in the early 1970s. The interpretationof multipoint coherences in terms of bandwidth wasthe key for a model specturm proposed by Garrett andMunk (1972b). The synthesis was purely empirical,apart from being guided by dimensional considerationsand by not violating gross requirements for the finite-ness of certain fundamental physical properties. Sub-sequently, the model served as a convenient "straw-man" for a wide variety of moored, towed and"dropped" experiments, and had to be promptly mod-ified [Garrett and Munk (1975), which became knownas GM75 in the spirit of planned obsolescence]. Therehave been further modifications [see a review paper byGarrett and Munk (1979)]; the most recent version issummarized at the end of this chapter.The best modem accounts on internal waves are byO. M. Phillips '(1966b), Phillips (1977a), and Turner(1973a). Present views of the time and space scales ofinternal waves are based largely on densely sampledmoored, towed, and dropped measurements. The pi-oneering work with moorings was done at site D in thewestern North Atlantic (Fofonoff, 1969; Webster,1968). Horizontal tows of suspended thermistor chains(Lafond, 1963; Charnock, 1965) were followed by towedand
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