Hostname: page-component-5cf477f64f-qls9x Total loading time: 0 Render date: 2025-04-02T16:22:09.109Z Has data issue: false hasContentIssue false
  • English
  • Français

The dynamics of the head of a gravity current advancing over a horizontal surface

Published online by Cambridge University Press:  19 April 2006

J. E. Simpson  and
R. E. Britter
J. E. Simpson
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge
R. E. Britter
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge
Get access Rights & Permissions [Opens in a new window]

Abstract

The motion behind the head of a gravity current advancing over a no-slip horizontal surface is a complex three-dimensional flow. There is intense mixing between the current and its surroundings and the foremost part of the head is raised above the surface. Experimental results are obtained from (i) an apparatus in which the head is brought to rest by using an opposing flow and a moving floor and (ii) a modified lock exchange flow. The dimensionless velocity of advance, rate of mixing between the two fluids and the depth of the mixed layer left behind the head and above the following gravity current are determined for an extended range of the dimensionless gravity current depth. The mixing between the two fluids is the result of gravitational and shear instabilities at the gravity current head. A semi-empirical analysis is presented to describe the results. The influence of Reynolds number is discussed and comparison with a documented atmospheric flow is presented.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 94 , Issue 3 , 16 October 1979 , pp. 477 - 495
Copyright
© 1979 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

Abraham, G. & Vreugdenhil, C. B. 1971 Discontinuities in stratified flow. J. Hydraul. Res. 9, 292–308.Google Scholar
Allen, J. R. L. 1970 Physical Processes of Sedimentation, p. 191. London: George Alleen and Unwin.
Allen, J. R. L. 1971 Mixing at turbidity current heads, and its geological implications. J. Sell mentary Petrology 41, 97–113.Google Scholar
Barr, D. I. H. 1967 Densimetric exchange flow in rectangular channels. III. Large scale experiments. Houille Blanche 22, 619–631.Google Scholar
Benjamin, T. B. 1968 Gravity currents and related phenomena. J. Fluid Mech. 31, 209–248.Google Scholar
Braucher, E. 1950 Initial characteristics of density current flow. M.I.T. Thesis.
Britter, R. E. & Simpson, J. E. 1978 Experiments on the dynamics of a gravity current head. J. Fluid Mech. 88, 223–240.Google Scholar
Hall, F. F., Neff, W. D. & Frazier, T. V. 1976 Wind shear observations in thunderstorm density currents. Nature 264, 408–411.Google Scholar
Hoult, D. P. 1972 Oil spreading on the sea. Ann. Rev. Fluid Mech. 4, 341–368.Google Scholar
Kaåmán, T. VON 1940 The engineer grapples with non-linear problems. Bull. Amer. Math. Soc. 46, 615–683.Google Scholar
Keulegan, G. H. 1957 An experimental study of the motion of saline water from locks into fresh water channels. U.S. Nat. Bur. Stand. Rep. no. 5168.Google Scholar
Keulegan, G. H. 1958 The motion of saline fronts in still water. U.S. Nat. Bur. Stand., Rep. no. 5831.Google Scholar
Lawson, T. J. 1971 Haboob structure at Khartoum. Weather 26, 105–112.Google Scholar
Middleton, G. V. 1966 Experiments on density and turbidity currents. I. Motion of the head. Canadian J. Earth Sciences 3, 523–546.Google Scholar
O'brien, M. P. & Cherno, J. 1934 Model law for motion of salt water through fresh. Trans. Amer. Soc. Civ. Eng. 99, 576–594.Google Scholar
Simpson, J. E. 1969 A comparison between laboratory and atmospheric density currents. Quart. J. Roy. Met. Soc. 95, 758–765.Google Scholar
Simpson, J. E. 1972 Effects of the lower boundary on the head of a gravity current. J. Fluid Mech. 53, 759–768.Google Scholar
Simpson, J. E., Mansfield, D. A. & Milford, J. R. 1977 Inland penetration of sea-breeze fronts. Quart. J. Roy. Met. Soc. 103, 47–76.Google Scholar
Thorpe, S. A. 1973 Experiments on instability and turbulence in a stratified shear flow. J. Fluid Mech. 61, 731–751.Google Scholar
Turner, J. S. 1973 Buoyancy Effects in Fluids. Cambridge University Press.
Winant, C. D. & Bratkovich, A. 1977 Structure and mixing within the frontal region of a density current. Proc. 6th Austr. Hydraulics & Fluid Mech. Conf., Adelaide, Australia, pp. 9–11.
Wood, I. R. 1965 Studies in unsteady self preserving turbulent flows. Univ. N.S.W., Manly Vale, N.S.W. Australia. Rep. no. 81.Google Scholar
Yih, C.-S. 1965 Dynamics of Non-homogeneous Fluids. Macmillan.