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It is nearly three-quarters of a century since E. R. Watson (1904) and E. M. Wedderburn (1907) made the observations in Loch Ness which showed conclusively, and for the first time, that large bodies of water contain beneath their surface the wave motions which have now come to be known as internal waves. The observations and theory of these waves have developed much since those days, but the Loch is still very useful as a site in which to observe and examine phenomena which are also found in other bodies of water, particularly the ocean. In particular the Loch provides a large-scale natural ‘laboratory’ in which a variety of small-scale phenomena associated with turbulence in a stratified fluid may be studied. Observations have been made with a novel profiling instrument which measures the horizontal velocity of the water and its temperature, from which the density may be inferred. These observations serve to illustrate a variety of local conditions which occur in calm weather, as the Loch responds to the wind and during the passage of an internal surge. Analysis of the records is conducted in terms of an intermittency index (the fraction of fluid in which the density decreases with depth), the Richardson number and a length scale which characterizes the vertical scale of the regions which are found to be unstably stratified. Semi-empirical formulae for the eddy diffusion coefficient and the rate of dissipation of kinetic energy in the turbulent motion are examined to see whether they are consistent with observations. No universal value of the Richardson number is found, but this may be a consequence of the rather low values of Reynolds number found in the Loch thermocline.

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▪ Abstract Since Leibovich's comprehensive review of Langmuir circulation in 1983 there have been substantial advances in modeling (notably the construction of Large Eddy Simulation models) and in observations using novel techniques that together have led to a radical change in understanding the phenomena. It is now regarded as one of the several turbulent processes driven by wind and waves in the upper layers of large bodies of water, influential in producing and maintaining the uniform surface mixed layer and in driving dispersion.

This is a study of turbulence which results from Kelvin—Helmholtz instability at the interface between two miscible fluids in a two-dimensional shear flow in the laboratory. The growth of two-dimensional ‘billows’, their disruption by turbulence, and the eventual decay of this turbulence and the re-establishment of a gravitationally and kinematically stable interface are described. Continuous measurements of density and horizontal velocity from both fixed and vertically moving probes have been made, and the records obtained are presented, together with photographs showing the simultaneous appearance of the flow, which serve to identify the physical nature of events seen in the records. The measurements show how the fine-structure of the density field described in earlier experiments is related to velocity fluctuations. The vertical length scales of the final mean velocity and density structure are found to be different, and to depend on the Richardson number at which instability first occurred. The eventual Richardson number at the centre of layer is, however, not dependent on the initial Richardson number and has a value of about one third. The implications of these results to the eddy diffusion coefficients, to the energy exchange, and to turbulence in the ocean and the atmosphere are discussed.

Clouds of small bubbles generated by wind waves breaking and producing whitecaps in deep water have been observed below the surface by using an inverted echo sounder. The bubbles are diffused down to several metres below the surface by turbulence against their natural tendency to rise. Measurements have been made at two sites, one in fresh water at Loch Ness and the other in the sea near O ban, northwest Scotland. Sonagraph records show bubble clouds of two distinct types, ‘ columnar clouds’ which appear in unstable or convective conditions w hen the air temperature is less than the surface water temperature, and ‘ billow clouds ’ which appear in stable conditions w hen the air temperature exceeds that of the water. Clouds penetrate deeper as the wind speed increases, and deeper in convective conditions than in stable conditions at the same wind speed. The response to a change in w ind speed occurs in a period of only a few minutes.

The processes which lead to vertical mixing in stratified fluids operate in a multiparameter space, much of which has not been explored theoretically or in laboratory experiments. This review focuses on the transitional phenomena which precede, and may eventually lead to, the broadband spectra associated with turbulent flow. Conditions of static instability are known to be produced in wave-wave, wave-current, and wave-boundary interactions, but little is known of the subsequent stages of transition. Whilst there has been considerable progress in describing transition in Rayleigh-B•nard and Taylor-Couette flows, that in Kelvin-Helmholtz instability is relatively unexplored, and in consequence, our knowledge of energy exchange and of density and momentum fluxes is extremely sparse. Attention is drawn here to the flow disturbance caused by sidewalls in laboratory experiments, and some recently discovered examples of transitional phenomena in Kelvin-Helmholtz instability are described. More information is available about fluxes in double-diffusive convection, but here too the transitional processes are as yet poorly known.Applying this information to the natural environment (and emphasis is given to the oceans) poses the fundamental difficulty of estimating the probability of conditions favoring the development of any particular kind of instability.Knowledge of transition in conditions in which the background field varies in space and time is deficient.

This page intentionally left blank An Introduction to Ocean TurbulenceThis textbook provides an introduction to turbulent motion occurring naturally in the ocean on scales ranging from millimetres to hundreds of kilometres. It describes how turbulence is created and varies from one part of the ocean to another, what its properties are (particularly those relating to energy flux and the dispersal of pollutants) and how it is measured. Examples are given of real data and the instruments that are commonly used to measure turbulence. Chapters describe turbulence in the mixed boundary layers at the sea surface and seabed, turbulent motion in the density-stratified water between, and the energy sources that support and sustain ocean mixing.Little prior knowledge of physical oceanography is assumed and the book is written at an introductory level that avoids mathematical complexity. The text is supported by numerous figures illustrating the methods used to measure and analyse turbulence, and by more than 50 exercises, which are graded in difficulty, that will allow readers to expand and monitor their understanding and to develop analytical techniques. Detailed solutions to the exercises are available to instructors online at www.cambridge.org/9780521676809. Further reading lists give direction to additional information on the background and historical development of the subject, while suggestions for further study encourage readers to probe further into more advanced aspects.An Introduction to Ocean Turbulence is intended for undergraduate courses in physical oceanography, but will also form a useful guide for graduate students and researchers interested in multidisciplinary aspects of how the ocean works, from the surface to the seabed and from the shoreline to the deep abyssal plains. It complements the graduate-level text The Turbulent Ocean, also written by Professor Thorpe (Cambridge University Press, 2005).S t e v e T h o r p e was a Senior Scholar at Trinity College, Cambridge, where he studied mathematics and fluid mechanics, his PhD being awarded in 1966. He then spent 20 years at the UK Institute of Oceanographic Sciences, before being appointed Professor of Oceanography at Southampton University in 1986. He has carried out laboratory experiments on internal waves and turbulent mixing, and has measured and developed instrumental and analytical methods for studying waves and mixing in lakes, as well as making seagoing studies of turbulence in the boundary layers of the deep ocean and shelf seas. Professor Thorpe was awarded the Walter Munk Award by the US Office of Naval Research and the Oceanography Society, for his work using underwater acoustics, The Fridtjof Nansen Medal of the European Geophysical Society, for his fundamental experimental and theoretical contributions to the study of mixing and internal waves, and the Society's Golden Badge for introducing a scheme to assist young scientists.