Part Two Physical Processes in Oceanography 8 1 Introduction 8 Small Scale Forty years ago the detailed physical mechanisms responsible for the mixing of heat salt and other properties in the ocean had hardly been considered Using profiles obtained from water bottle measurements and their variations in time and space it was deduced that mixing must be taking place at rates much greater than could be accounted for by molecular diffusion It was taken for granted that the ocean because of its large scale must be everywhere turbulent and this was supported by the observation that the major constituents are reasonably well mixed It seemed a natural step to define eddy viscosities and eddy conductivities or mixing coefficients to relate the deduced fluxes of momentum or heat or salt to the mean smoothed gradients of corresponding properties Extensive tables of Mixing Processes J S Turner these mixing coefficients KM for momentum KH for heat and Ks for salinity and their variation with position and other parameters were published about that time see e g Sverdrup Johnson and Fleming 1942 p 482 Much mathematical modeling of oceanic flows on various scales was and still is based on simple assumptions about the eddy viscosity which is often taken to have a constant value chosen to give the best agreement with the observations This approach to the theory is well summarized in Proudman 1953 and more recent extensions of the method are described in the conference proceedings edited by Nihoul 1975 Though the preoccupation with finding numerical values of these parameters was not in retrospect always helpful certain features of those results contained the seeds of many later developments in this subject The lateral and vertical mixing coefficients evaluated in this way differ by many orders of magnitude and it was recognized that the much smaller rates of vertical mixing must in some way be due to the smaller scale of the vertical motions Qualitatively it was also known that the vertical eddy coefficients tended to be smaller when the density gradients were larger The analysis of Taylor 1931 had shown that in very stable conditions Ks was smaller than KM which he interpreted to mean that the vertical transport of salt requires an intimate mixing between water parcels at different levels whereas momentum can be transported by wave motion and is less affected by a strong vertical density gradient In contrast to these direct considerations of vertical mixing Iselin 1939a introduced the far reaching idea that because of the vertical stability virtually all the large scale mixing in the ocean might be accounted for in terms of lateral mixing along isopycnals rather than horizontally In particular he pointed to the striking similarity of the T S relations for a vertical section and a surface section in the North Atlantic each of which crossed the same isopycnals 236 J S Turner L I I A strong constraint on achieving a fuller understanding of the small scale mixing processes implicit in early measurements was the lack of suitable instruments to resolve the scales that are directly involved Most of the data came from water bottle samples and widely spaced current meters and it was tacitly assumed that the smooth profiles drawn through the discrete points actually represented the state of the ocean Even when continuous temperature profiles became available in the upper layers of the ocean through the development of the bathythermograph there was a tendency to attribute abrupt changes in slope to malfunctions in the instrument The parameterization in terms of eddy coefficients implied that turbulence is distributed uniformly through depth and is maintained by external processes acting on a smaller scale than the flows of interest but in the absence of techniques to observe the fluctuations and how they are maintained little progress could be made Many such instruments are already in existence see chapter 14 their use has rapidly transformed our view of the ocean and in particular the understanding of the nature of the mixing processes Temperature salinity and velocity fluctuations can be measured down to centimeter scales and these records show that the distribution of properties is far from smooth Rapid changes of vertical gradients are common amounting in many cases to steps in the profiles At some times the temperature and salinity variations are nearly independent while at others they are closely correlated in a manner that has a profound effect on the vertical fluxes of the two properties see Section 8 4 2 Viewed on a small scale the ocean is not everywhere turbulent on the contrary turbulence in the deep ocean occurs only intermittently and in patches which are often thin and elongated horizontally while the level of fluctuations through most of the volume is very low for most of the time This is now more clearly recognized to be a consequence of the stable density gradient which can limit the vertical extent of mixing motions and thus keep the relevant Reynolds numbers very small The newly acquired ability to study various mixing processes in the ocean has produced a corresponding increase in activity by theoretical and laboratory modelers in this field The stimulation has been in both directions theoreticians have been made aware of striking new observations requiring explanation and they have developed more and more sophisticated theories and experiments that in turn suggest new observations to test them Some of the work has required subtle statistical analysis of fluctuating signals while many of the most exciting developments have been based on identifying individual mixing events in the laboratory or the ocean followed by a recognition of their more general significance Perhaps the most important factor of all has been the change in attitude to observational oceanography which took place in the early 1960s Henry Stommel in particular advocated an approach more akin to the formulation and testing of hypotheses in other experimental sciences Experiments designed to test specific physical ideas in a limited geographical area are now commonplace but it is easy to forget how recently such uses of ship time have replaced the earlier expedition approach in which the aim was to explore as large an area as possible in a given time chapter 14 This chapter will concentrate on the scales of mixing in the ocean ranging from the smallest that have been studied to those with vertical dimensions of some tens
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