Part Two PhysicalProcesses inOceanography8Small-ScaleMixing ProcessesJ. S. Turner8.1 IntroductionForty years ago, the detailed physical mechanisms re-sponsible for the mixing of heat, salt, and other prop-erties in the ocean had hardly been considered. Usingprofiles obtained from water-bottle measurements, andtheir variations in time and space, it was deduced thatmixing must be taking place at rates much greater thancould be accounted for by molecular diffusion. It wastaken for granted that the ocean (because of its largescale) must be everywhere turbulent, and this was sup-ported by the observation that the major constituentsare reasonably well mixed. It seemed a natural step todefine eddy viscosities and eddy conductivities, or mix-ing coefficients, to relate the deduced fluxes of mo-mentum or heat (or salt) to the mean smoothed gra-dients of corresponding properties. Extensive tables ofthese mixing coefficients, KM for momentum, KH forheat, and Ks for salinity, and their variation with po-sition and other parameters, were published about thattime [see, e.g., Sverdrup, Johnson, and Fleming (1942,p. 482)]. Much mathematical modeling of oceanic flowson various scales was (and still is) based on simpleassumptions about the eddy viscosity, which is oftentaken to have a constant value, chosen to give the bestagreement with the observations. This approach to thetheory is well summarized in Proudman (1953), andmore recent extensions of the method are described inthe conference proceedings edited by Nihoul 1975).Though the preoccupation with finding numericalvalues of these parameters was not in retrospect alwayshelpful, certain features of those results contained theseeds of many later developments in this subject. Thelateral and vertical mixing coefficients evaluated inthis way differ by many orders of magnitude, and itwas recognized that the much smaller rates of verticalmixing must in some way be due to the smaller scaleof the vertical motions. Qualitatively, it was alsoknown that the vertical eddy coefficients tended to besmaller when the density gradients were larger. Theanalysis of Taylor (1931) had shown that in very stableconditions Ks was smaller than KM, which he inter-preted to mean that the vertical transport of salt re-quires an intimate mixing between water parcels atdifferent levels, whereas momentum can be trans-ported by wave motion and is less affected by a strongvertical density gradient.In contrast to these direct considerations of verticalmixing, Iselin (1939a) introduced the far-reaching ideathat, because of the vertical stability, virtually all thelarge-scale mixing in the ocean might be accounted forin terms of lateral mixing (along isopycnals, rather thanhorizontally). In particular, he pointed to the strikingsimilarity of the T-S relations for a vertical section anda surface section in the North Atlantic, each of whichcrossed the same isopycnals.236J. S. Turner·L_ __I___ I_ ___ ___ __A strong constraint on achieving a fuller understand-ing of the small-scale mixing processes implicit in earlymeasurements, was the lack of suitable instruments toresolve the scales that are directly involved. Most ofthe data came from water-bottle samples and widelyspaced current meters, and it was tacitly assumed thatthe smooth profiles drawn through the discrete pointsactually represented the state of the ocean. Even whencontinuous temperature profiles became available inthe upper layers of the ocean through the developmentof the bathythermograph, there was a tendency to at-tribute abrupt changes in slope to malfunctions in theinstrument. The parameterization in terms of eddycoefficients implied that turbulence is distributed uni-formly through depth, and is maintained by externalprocesses acting on a smaller scale than the flows ofinterest; but in the absence of techniques to observethe fluctuations, and how they are maintained, littleprogress could be made.Many such instruments are already in existence (seechapter 14); their use has rapidly transformed our viewof the ocean, and in particular the understanding of thenature of the mixing processes. Temperature, salinity,and velocity fluctuations can be measured down tocentimeter scales, and these records show that the dis-tribution of properties is far from smooth. Rapidchanges of vertical gradients are common, amountingin many cases to "steps" in the profiles. At some timesthe temperature and salinity variations are nearly in-dependent, while at others they are closely correlatedin a manner that has a profound effect on the verticalfluxes of the two properties (see Section 8.4.2). Viewedon a small scale, the ocean is not everywhere turbulent:on the contrary, turbulence in the deep ocean occursonly intermittently and in patches (which are oftenthin, and elongated horizontally), while the level offluctuations through most of the volume is very lowfor most of the time. This is now more clearly recog-nized to be a consequence of the stable density gra-dient, which can limit the vertical extent of mixingmotions and thus keep the relevant Reynolds numbersvery small.The newly acquired ability to study various mixingprocesses in the ocean has produced a correspondingincrease in activity by theoretical and laboratory mod-elers in this field. The stimulation has been in bothdirections: theoreticians have been made aware ofstriking new observations requiring explanation, andthey have developed more and more sophisticated the-ories and experiments that in turn suggest new obser-vations to test them. Some of the work has requiredsubtle statistical analysis of fluctuating signals, whilemany of the most exciting developments have beenbased on identifying individual mixing events (in thelaboratory or the ocean), followed by a recognition oftheir more general significance.Perhaps the most important factor of all has beenthe change in attitude to observational oceanographywhich took place in the early 1960s. Henry Stommelin particular advocated an approach more akin to theformulation and testing of hypotheses in other exper-imental sciences. Experiments designed to test specificphysical ideas in a limited geographical area are
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