Turbulence and mixing in a Scottish Loch

TLDR

Internal waves in large bodies of water were first conclusively observed in Loch Ness, and the Loch remains a valuable natural laboratory for studying turbulence and stratified fluid phenomena relevant to other water bodies, especially the ocean. The study used a novel profiling instrument to measure horizontal velocity and temperature, inferred density, and analyzed the data with intermittency index, Richardson number, and vertical length scale, while testing semi‑empirical eddy diffusion and kinetic‑energy dissipation formulas against observations. The observations revealed varied local conditions during calm weather, wind, and internal surges, and showed that no universal Richardson number exists, likely because of the low Reynolds numbers in the Loch thermocline.

Abstract

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.