Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-19T14:56:37.505Z Has data issue: false hasContentIssue false
  • English
  • Français

On the nature of the entrainment interface of a two-layer fluid subjected to zero-mean-shear turbulence

Published online by Cambridge University Press:  20 April 2006

Harindra J. S. Fernando  and
Robert R. Long
Harindra J. S. Fernando
Affiliation:
Department of Earth and Planetary Sciences, The Johns Hopkins University, Baltimore, MD 21218 Present address: W. M. Keck Laboratory of Hydraulics and Water Resources, California Institute of Technology, Pasadena, CA 91125.
Robert R. Long
Affiliation:
Department of Earth and Planetary Sciences, The Johns Hopkins University, Baltimore, MD 21218
Get access Rights & Permissions [Opens in a new window]

Abstract

An experimental study was performed to further understanding of turbulent mixing in a two-layer fluid subjected to shear-free turbulence. At low Richardson numbers Ri (= ΔbD3*/K2, where Δb is the buoyancy jump, D* is the depth of a mixed layer and K is ‘action’) the entrainment seems to occur through the eroding effect of large eddies, whereas at high Ri the large eddies flatten at the density interface and the quasi-isotropic eddies near the interface are responsible for the entrainment. The buoyancy transfer can be well described by a gradient-transport model when the eddy diffusivity is properly defined. At or just above the entrainment interface, the buoyancy flux is of the same order as the dissipation, and the diffusive-flux Richardson number tends to a constant.

The thickness h of the interfacial layer was measured in three different ways and was found to grow linearly with D* in agreement with preliminary findings of an earlier investigation of Fernando & Long (1983). The buoyancy gradient in the interfacial layer was found to be constant, and the resulting buoyancy conservation law was experimentally verified. The frequency of the interfacial-layer waves appears to vary as Ri½. The present results, together with the results of the earlier work of Fernando & Long, show a good agreement with a theory of Long (1978b) for behaviour at high values of Ri. The closure assumptions of that theory were also verified by our measurements.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 151 , February 1985 , pp. 21 - 53
Copyright
© 1985 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

Arya S. P. S.1975 Buoyancy effects in a horizontal flat-plate boundary layer. J. Fluid Mech. 68, 321.Google Scholar
Batchelor G. K.1953 Theory of Homogeneous Turbulence. Cambridge University Press.
Bouvard, M. & Dumas H.1967 Application de la méthode du fil chaud à la mesure de la turbulence dans l'eau. Houille Blanche 22, 257.Google Scholar
Corrsin, S. & Kistler A. L.1955 Free stream boundaries of turbulent flow. NACA Tech. Note 3133.Google Scholar
Crapper, P. F. & Linden P. F.1974 The structure of turbulent density interfaces. J. Fluid Mech. 65, 45.Google Scholar
Deardorff J. W., Willis, G. E. & Stockton B. H.1980 Laboratory studies of entrainment zone of a convective mixed layer. J. Fluid Mech. 100, 41.Google Scholar
Dickey, T. D. & Mellor G. L.1980 Decaying turbulence in neutral and stratified fluids. J. Fluid Mech. 99, 13.Google Scholar
Dickinson S. C.1980 Oscillating grid turbulence including effects of rotation. Ph.D. thesis, The Johns Hopkins University.
Dickinson, S. C. & Long R. R.1978 Laboratory study of the growth of a turbulent layer of fluid Phys. Fluids 21, 1698.Google Scholar
Dickinson, S. C. & Long R. R.1983 Oscillating-grid turbulence including effects of rotation. J. Fluid Mech. 126, 315.Google Scholar
Dillon, T. M. & Powell T. M.1979 Observations of a surface mixed layer. Deep-Sea Res. 26A, 915.Google Scholar
Fernando H. J. S.1983 Studies on turbulent mixing in stably stratified fluids. Ph.D. thesis, The Johns Hopkins University.
Fernando, H. J. S. & Long R. R.1983 The growth of a grid-generated turbulent mixed layer in a two-fluid system. J. Fluid Mech. 133, 377.Google Scholar
Fisher H., List J., Koh R., Imberger, J. & Brooks N.1979 Mixing in Inland and Coastal Waters. Academic.
Folse R. F., Cox, T. P. & Schexnayder K. R.1981 Measurements of the growth of a turbulently mixed layer in a linearly stratified fluid. Phys. Fluids 24, 396.Google Scholar
Grant H. L., Moilliet, A. & Vogel W. M.1968 Some observations of the occurrence of turbulence in and above the thermocline. J. Fluid Mech. 34, 443.Google Scholar
Hinze J. O.1975 Turbulence, 2nd edn. McGraw-Hill.
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.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.Google Scholar
Linden P. F.1979 Mixing in stratified fluids. Geophys. Astrophys. Fluid Dyn. 13, 3.Google Scholar
Linden P. F.1980 Mixing across a density interface produced by grid turbulence. J. Fluid Mech. 100, 691.Google Scholar
Liu H.-T.1982 Grid-generated turbulence in a stably stratified fluid. Fluid Res. Rep. 224, Flow Ind. Inc., Washington.Google Scholar
Long R. R.1970 A theory of turbulence in stratified fluids. J. Fluid Mech. 42, 349.Google Scholar
Long R. R.1978a Theory of turbulence in a homogeneous fluid induced by an oscillating grid. Phys. Fluids 21, 1887.Google Scholar
Long R. R.1978b A theory of mixing in a stably stratified fluid. J. Fluid Mech. 84, 113.Google Scholar
Mcdougall T. J.1979 Measurements of turbulence in a zero-mean-shear mixed layer. J. Fluid Mech. 94, 409.Google Scholar
Mcewan A. D.1983 Internal mixing in stratified fluids. J. Fluid Mech. 128, 59.Google Scholar
Moore, M. J. & Long R. R.1971 An experimental investigation of turbulent stratified shearing flow. J. Fluid Mech. 49, 635.Google Scholar
Ozmidov R. V.1965 On the turbulent exchange in a stably stratified ocean. Izv. Atmos. Ocean Phys. 1, 853.Google Scholar
Phillips O. M.1955 The irrotational motion outside a free turbulent boundary. Proc. Camb. Phil. Soc. 51, 220.Google Scholar
Phillips O. M.1977 Dynamics of the Upper Ocean, 2nd edn. Cambridge University Press.
Piat, J. F. & Hopfinger E. J.1981 A boundary layer topped by a density interface. J. Fluid Mech. 113, 411.Google Scholar
Price J. F.1979 Observations of a rain-formed mixed layer. J. Phys. Oceanogr. 9, 643.Google Scholar
Roshko A.1976 Structure of turbulent shear flows: a new look. AIAA J. 14, 1349.Google Scholar
Rouse, H. & Dodu J.1955 Turbulent diffusion across a density discontinuity. Houille Blanche 10, 522.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.Google Scholar
Thorpe S. A.1977 Turbulence and mixing in a Scottish loch. Proc. Camb. Phil. Soc. 286, A 1334.Google Scholar
Thorpe S. A.1982 On the layers produced by rapidly oscillating a vertical grid in a uniformly stratified fluid. J. Fluid Mech. 124, 391.Google Scholar
Townsend A. A.1957 Turbulent flow in a stably stratified atmosphere. J. Fluid Mech. 3, 361.Google Scholar
Townsend A. A.1976 The Structure of Turbulent Shear Flow, 2nd edn. Cambridge University Press.
Turner J. S.1965 The coupled turbulent transports of salt and heat across a sharp density interface. Int. J. Heat Mass Transfer 8, 759.Google Scholar
Turner J. S.1968 The influence of molecular diffusivity on turbulent entrainment across a density interface. J. Fluid Mech. 33, 639.Google Scholar
Wyatt L. R.1978 The entrainment interface in a stratified fluid. J. Fluid Mech. 86, 293.Google Scholar
Wolanski, E. J. & Brush L. M.1975 Turbulent entrainment across stable density step structures. Tellus 27, 259.Google Scholar