Turbulence and mixing in a Scottish Loch

The Royal Society - Tập 286 Số 1334 - Trang 125-181 - 1977
S. A. Thorpe1
1Institute of Oceanographic Sciences, Wormley, Godalming, Surrey

Tóm tắt

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.

Từ khóa


Tài liệu tham khảo

Abram ow itz M . & Stegun L A. 1965 Handbook o f mathematicalfunctions. N ew York: Dover.

Byrne M ., 1975, Observations o f oceanic internal waves from the Earth Resources T echnology Satellite. J.geophys, Res., 80, 865

Batchelor G. K ., 1953, T he conditions for dynam ical similarity o f m otions o f a frictionless perfect-gas atmosphere. Qu.Jl R. met, Soc., 79, 224

Chandrasekhar S. 1961 Hydrodynamic and hydromagnetic stability. Oxford U niversity Press.

Crofts I. 1975 Microstructure o f density and velocity in the thermocline (observations in Loch N ess). Ph.D. dissertation. U niv. C ollege o f N . W ales Bangor.

Crystal G. 1910 Bathymetrical survey of the Scottish fresh water lakes (eds M urray & Puller) vol. 1 pp. 29-90. Edinburgh: Challenger Office.

Dobroklonskiy S. V ., 1973, Empirical relationships between steady-state waves and w ind speeds for a w ide range o f fetches, Oceanology, 13, 640

Gardener R . 1745 Letter X X I to D r John Stevenson published in connection w ith the great Lisbon earthquake. Phil. Trans. R. Soc. Lond. 387-389.

10.1017/S0022112072003027

Goldstein 8 . 1938 Modern developments influid dynamics vol. 1. Clarendon Press Oxford.

10.1017/S0022112068002004

10.1175/1520-0485(1975)005<0253:MAIITC>2.0.CO;2

10.1175/1520-0485(1973)003<0458:VMMITC>2.0.CO;2

10.1017/S0022112074001832

Johnston T . N . 1904 T he bathymetrical survey o f Loch Ness. J. 24 429-430.

10.3402/tellusa.v23i2.10372

Kullenberg G ., 1973, A n experimental study o f diffusion characteristics in the therm ocline and hypolim nion regions o f Lake Ontario. Proc. 16 Cons, Great Lakes Res., 774

Lafond E. C. 1962 Internal Waves Part 1. In The sea (ed. M . N . H ill) vol. 1 p. 731. N ew York: Interscience.

Longuet-H iggins M . S. 1952 On the statistical distribution o f the heights o f sea waves. 11 245-266.

1962, O n the turbulence spectrum in a therm ally stratified atmosphere. ( ), Sci. U.S.S.R, Geophys. Ser. (3), 266

1955, Some effects o f the Earth's rotation on water m ovem ents in stratified lakes, Proc. Intern. Assoc. Limnol., 12, 66

Obukhov A. M ., 1959, T he influence o f hydrostatic forces on the structure o f the temperature field in turbulent flow, Proc. ( Doklady) Acad.Sci. U.S.S.R., 125, 1246

Orlanski I., 1969, Form ation o f the thermocline step structure by large-amplitude internal gravity waves. J.geophys, Res., 74, 6975

Osborne T . R . 1974 Vertical profiling of velocity microstructure.

Osborne T . R . & Cox C. 1972 Oceanic fine structure. Geophys.

Phys. Oceanogr. 4 109-115. 3 321-345.

1965, O n the turbulent exchange in a stably stratified ocean. Izvestiya, Acad. Sci. U.S.S.R., Atmos. & Ocean Phys., 1, 861

10.1098/rstb.1972.0012

Phillips O. M . 1966 The dynamics of the upper ocean. Cambridge University Press.

Simpson J. H ., 1972, A free fall probe for the measurement o f velocity microstructure, Deep-Sea Res., 19, 331

10.1038/226832a0

Stewart R ., 1962, Determination o f the rate o f dissipation o f turbulent energy near the sea surface in the presence o f waves. J.geophys, Res., 67, 3177

10.1007/BF02265235

10.1098/rsta.1968.0033

10.1017/S0022112068000972

10.1038/231306a0

10.1007/BF02188314

10.1017/S0022112073000911

10.1017/S0022112074001753

Thorpe S. A. & H all A. J. 1974 Evidence o f K elvin-H elm holtz billows in Loch Ness. Limnology db Oceanography 19 973-976.

10.1038/265719a0

10.1038/237096b0

10.1016/0146-6291(77)97000-X

Townsend A. A. 1956 The structure of turbulent shearflow. Cambridge University Press.

Turner J. S. 1973 Buoyancy effects influids. Cambridge University Press.

10.2307/1775951

10.1017/S0080456800022791

1909, Observations with a current meter in Loch Ness, R. Soc. Edinb., 19, 619

10.1029/RS004i012p01289

Thông tin
Thông tin xuất bản

The Royal Society

Tập 286 Số 1334

125-181

Thông tin tác giả