Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-28T07:00:46.041Z Has data issue: false hasContentIssue false
  • English
  • Français

Turbulent entrainment: the development of the entrainment assumption, and its application to geophysical flows

Published online by Cambridge University Press:  21 April 2006

J. S. Turner
J. S. Turner
Affiliation:
Research School of Earth Sciences, Australian National University, G.P.O. Box 4, Canberra, A.C.T. 2601, Australia
Get access Rights & Permissions [Opens in a new window]

Abstract

The entrainment assumption, relating the inflow velocity to the local mean velocity of a turbulent flow, has been used successfully to describe natural phenomena over a wide range of scales. Its first application was to plumes rising in stably stratified surroundings, and it has been extended to inclined plumes (gravity currents) and related problems by adding the effect of buoyancy forces, which inhibit mixing across a density interface. More recently, the influence of viscosity differences between a turbulent flow and its surroundings has been studied. This paper surveys the background theory and the laboratory experiments that have been used to understand and quantify each of these phenomena, and discusses their applications in the atmosphere, the ocean and various geological contexts.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 173 , December 1986 , pp. 431 - 471
Copyright
© 1986 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Batchelor, G. K. 1954 Heat convection and buoyancy effects in fluids. Q. J. R. Met. Soc. 80, 339–358.Google Scholar
Baines, W. D. & Hopfinger, E. J. 1984 Thermals with large density differences. Atmos. Environ. 18, 1051–1057.Google Scholar
Baines, W. D. & Turner, J. S. 1969 Turbulent buoyant convection from a source in a confined region. J. Fluid Mech. 37, 51–80.Google Scholar
Briggs, G. A. 1969 Plume Rise. U.S. Atomic Energy Commission Critical Review Series. 81 pp.
Britter, R. E. & Linden, P. F. 1980 The motion of the front of a gravity current travelling down an incline. J. Fluid Mech. 99, 531–543.Google Scholar
Brown, G. L. & Roshko, A. 1974 On density effects and large structure in turbulent mixing layers. J. Fluid Mech. 64, 775–816.Google Scholar
Campbell, I. H. & Turner, J. S. 1985 Turbulent mixing between fluids with different viscosities. Nature 313, 39–42.Google Scholar
Campbell, I. H. & Turner, J. S. 1986 The influence of viscosity on fountains in magma chambers. J. Petrol. 27, 1–30.Google Scholar
Campbell, I. H., McDougall, T. J. & Turner, J. S. 1984 A note on fluid dynamic processes which can influence the deposition of massive sulfides. Econ. Geol. 79, 1905–1913.Google Scholar
Campbell, I. H., Naldrett, A. J. & Barnes, S. J. 1983 A model for the origin of the platinum-rich sulfide horizons in the Bushveld and Stillwater Complexes. J. Petrol. 24, 133–165.Google Scholar
Cantwell, B. J. 1981 Organized motion in turbulent flow. Ann. Rev. Fluid Mech. 13, 457–515.Google Scholar
Carruthers, D. J. & Hunt, J. C. R. 1986 Velocity fluctuations near an interface between a turbulent region and a stably stratified layer. J. Fluid Mech. 165, 475–501.Google Scholar
Chandrsuda, C., Mehta, R. D., Weir, A. D. & Bradshaw, P. 1978 Effect of free-stream turbulence on large structure in turbulent mixing layers. J. Fluid Mech. 85, 693–704.Google Scholar
Chu, V. H., Senior, C. & List, E. J. 1981 Transition from a turbulent jet into a turbulent plume. ASME Conference, Boulder, Colorado, June 1981.
Corcos, G. M. & Sherman, F. S. 1976 Vorticity concentrations and the dynamics of unstable free shear layers. J. Fluid Mech. 73, 241–264.Google Scholar
Corcos, G. M. & Sherman, F. S. 1984 The mixing layer: deterministic models of a turbulent flow. Part 1. Introduction and the two-dimensional flow. J. Fluid Mech. 139, 29–65.Google Scholar
Crapper, P. F. & Linden, P. F. 1974 The structure of turbulent density interfaces. J. Fluid Mech. 65, 45–63.Google Scholar
Crawford, T. V. & Leonard, A. S. 1962 Observations of buoyant plumes in calm stably stratified air. J. Appl. Meteorol. 1, 251–256.Google Scholar
Deardorff, J. W., Willis, G. E. & Stockton, B. H. 1980 Laboratory studies of the entrainment zone of a convectively mixed layer. J. Fluid Mech. 100, 41–64.Google Scholar
Denton, R. A. & Wood, I. R. 1981 Penetrative convection at low Péclet number. J. Fluid Mech. 113, 1–21.Google Scholar
E. X. & Hopfinger, E. J. 1986 On mixing across an interface in stably stratified fluid. J. Fluid Mech. 166, 227–244.Google Scholar
Ellison, T. H. & Turner, J. S. 1959 Turbulent entrainment in stratified flows. J. Fluid Mech. 6, 423–448.Google Scholar
Escudier, M. P. & Maxworthy, T. 1973 On the motion of turbulent thermals. J. Fluid Mech. 61, 541–552.Google Scholar
Fernando, H. J. S. & Long, R. R. 1983 The growth of a grid-generated turbulent mixing layer in a two-fluid system. J. Fluid Mech. 133, 377–395.Google Scholar
Fischer, H. B., List, E. J., Koh, R. C. Y., Imberger, J. & Brooks, N. H. 1979 Mixing in Inland and Coastal Waters. Academic. 483 pp.
Gaster, M., Kit, E. & Wygnanski, I. 1985 Large-scale structures in a forced turbulent mixing layer. J. Fluid Mech. 150, 23–39.Google Scholar
Gill, A. E. & Turner, J. S. 1976 A comparison of seasonal thermocline models with observation. Deep-Sea Res. 23, 391–401.Google Scholar
Gorshkov, G. S. 1959 Gigantic eruption of the Volcano Bezymianny. Bull. Volcanol. 20, 77–109.Google Scholar
Ho, C.-M. & Huerre, P. 1984 Perturbed free shear layers. Ann. Rev. Fluid Mech. 16, 365–424.Google Scholar
Hopfinger, E. J. 1983 Snow avalanche motion and related phenomena. Ann. Rev. Fluid Mech. 15, 47–76.Google Scholar
Hopfinger, E. J. & Beghin, P. 1980 Buoyant clouds appreciably heavier than the ambient fluid on sloping boundaries. In Proc. 2nd Intl. IAHR Symp. on Stratified Flows, Trondheim, pp. 495–504.
Hopfinger, E. J. & Linden, P. F. 1982 Formation of thermoclines in zero-mean-shear turbulence subjected to a stabilizing buoyancy flux. J. Fluid Mech. 114, 157–173.Google Scholar
Hopfinger, E. J. & Toly, J. A. 1976 Spatially decaying turbulence and its relation to mixing across density interfaces. J. Fluid Mech. 78, 155–175.Google Scholar
Hunt, J. C. R. & Graham, J. M. R. 1978 Free stream turbulence near plane boundaries. J. Fluid Mech. 84, 209–235.Google Scholar
Hunt, J. C. R., Rottman, J. W. & Britter, R. E. 1983 Some physical processes involved in the dispersion of dense gases. In Proc. IUTAM Symp. on Atmospheric Dispersion of Heavy Gases and Small Particles, Delft (ed. G. Oomes & H. Tennekes), pp. 361–395. Springer.
Huppert, H. E., Turner, J. S., Carey, S. N., Sparks, R. S. J. & Hallworth, M. A. 1986 A laboratory simulation of pyroclastic flows down slopes. J. Volcanol. Geotherm. Res. (in press).Google Scholar
Kantha, L. H., Phillips, O. M. & Azad, R. S. 1977 On turbulent entrainment at a stable density interface. J. Fluid Mech. 79, 753–768.Google Scholar
Kato, H. & Phillips, O. M. 1969 On the penetration of a turbulent layer into stratified fluid. J. Fluid Mech. 37, 643–665.Google Scholar
Koop, C. G. & Browand, F. K. 1979 Instability and turbulence in a stratified fluid with shear. J. Fluid Mech. 93, 135–159.Google Scholar
Kraus, E. B. & Turner, J. S. 1967 A one-dimensional model of the seasonal thermocline. II. The general theory and its consequences. Tellus 19, 98–106.Google Scholar
Kumagai, M. 1984 Turbulent buoyant convection from a source in a confined two-layered region. J. Fluid Mech. 147, 105–131.Google Scholar
Lin, S. J. & Corcos, G. M. 1984 The mixing layer: deterministic models of a turbulent flow. Part 3. The effect of plane strain on the dynamics of streamwise vortices. J. Fluid Mech. 141, 139–178.Google Scholar
Linden, P. F. 1973 The interaction of a vortex ring with a sharp density interface: a model for turbulent entrainment. J. Fluid Mech. 60, 467–480.Google Scholar
Linden, P. F. 1975 The deepening of a mixed layer in a stratified fluid. J. Fluid Mech. 71, 385–405.Google Scholar
Linden, P. F. 1979 Mixing in stratified fluids. Geophys. Astrophys. Fluid Dyn. 13, 3–23.Google Scholar
List, E. J. 1982 Turbulent jets and plumes. Ann. Rev. Fluid Mech. 14, 189–212.Google Scholar
List, E. J. & Imberger, J. 1973 Turbulent entrainment in buoyant jets. Proc. ASCE, J. Hydraul. Div. 99, 1461–1474.Google Scholar
Long, R. R. 1978 A theory of mixing in a stably stratified fluid. J. Fluid Mech. 84, 113–124.Google Scholar
Longuet-Higgins, M. S. & Turner, J. S. 1974 An ‘entraining plume’ model of a spilling breaker. J. Fluid Mech. 63, 1–20.Google Scholar
Maxworthy, T. 1972 The structure and stability of vortex rings. J. Fluid Mech. 51, 15–32.Google Scholar
Maxworthy, T. 1974 Turbulent vortex rings. J. Fluid Mech. 64, 227–239.Google Scholar
Mcdougall, T. J. 1979 Measurements of turbulence in a zero-mean-shear mixed layer. J. Fluid Mech. 94, 409–431.Google Scholar
Morton, B. R. 1957 Buoyant plumes in a moist atmosphere. J. Fluid Mech. 2, 127–144.Google Scholar
Morton, B. R. 1959 Forced plumes. J. Fluid Mech. 5, 151–163.Google Scholar
Morton, B. R., Taylor, G. I. & Turner, J. S. 1956 Turbulent gravitational convection from maintained and instantaneous sources. Proc. R. Soc. Lond. A 234, 1–23.Google Scholar
Nairn, I. A. & Self, S. 1978 Explosive eruptions and pyroclastic avalanches from Ngauruhoe in February 1975. J. Volcanol. Geotherm. Res. 3, 39–60.Google Scholar
Narimousa, S., Long, R. R. & Kitaigorodskii, S. A. 1986 Entrainment due to turbulent shear flow at the interface of a stably stratified fluid. Tellus 38 A, 76–87.Google Scholar
Niiler, P. P. & Kraus, E. B. 1977 One-dimensional models of the upper ocean. In Modelling and Prediction of the Upper Layers of the Ocean (ed. E. B. Kraus), pp. 143–172. Pergamon.
Phillips, O. M. 1972 The entrainment interface. J. Fluid Mech. 51, 97–118.Google Scholar
Price, J. F. 1979 On the scaling of stress-driven entrainment experiments. J. Fluid Mech. 90, 509–529.Google Scholar
Ricou, F. P. & Spalding, D. B. 1961 Measurements of entrainment by axisymmetric turbulent jets. J. Fluid Mech. 11, 21–32.Google Scholar
Sherman, F. S., Imberger, J. & Corcos, G. M. 1978 Turbulence and mixing in stably stratified waters. Ann. Rev. Fluid Mech. 10, 267–288.Google Scholar
Simpson, J. E. 1982 Gravity currents in the laboratory, atmosphere, and ocean. Ann. Rev. Fluid Mech. 14, 213–234.Google Scholar
Sparks, R. S. J. 1986 The dimensions and dynamics of volcanic eruption columns. Bull. Volcanol. 48, 3–15.Google Scholar
Squires, P. & Turner, J. S. 1962 An entraining jet model for cumulonimbus updraughts. Tellus 14, 422–434.Google Scholar
Thompson, S. M. & Turner, J. S. 1975 Mixing across an interface due to turbulence generated by an oscillating grid. J. Fluid Mech. 67, 349–367.Google Scholar
Thorpe, S. A. 1973 Turbulence in stably stratified fluids: a review of laboratory experiments. Boundary-Layer Met. 5, 95–119.Google Scholar
Turner, J. S. 1957 Buoyant vortex rings. Proc. R. Soc. Lond. A 239, 61–75.Google Scholar
Turner, J. S. 1960 A comparison between buoyant vortex rings and vortex pairs. J. Fluid Mech. 7, 419–432.Google Scholar
Turner, J. S. 1962 The starting plume in neutral surroundings. J. Fluid Mech. 13, 356–368.Google Scholar
Turner, J. S. 1963 Model experiments relating to thermals with increasing buoyancy. Q. J. R. Met. Soc. 89, 62–74.Google Scholar
Turner, J. S. 1966 Jets and plumes with negative or reversing buoyancy. J. Fluid Mech. 26, 779–792.Google Scholar
Turner, J. S. 1968 The influence of molecular diffusivity on turbulent entrainment across a density interface. J. Fluid Mech. 33, 639–656.Google Scholar
Turner, J. S. 1973 Buoyancy Effects in Fluids. Cambridge University Press, 367 pp.
Turner, J. S. 1981 Small-scale mixing processes. In Evolution of Physical Oceanography (ed. B. A. Warren & C. Wunsch), pp. 236–262. MIT Press.
Wilson, L., Sparks, R. S. J., Huang, T. C. & Watkins, N. D. 1978 The control of volcanic column heights by eruption energetics and dynamics. J. Geophys. Res. 83, 1829–1836.Google Scholar