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On turbulent entrainment at a stable density interface

Published online by Cambridge University Press:  11 April 2006

L. H. Kantha ,
O. M. Phillips  and
R. S. Azad
L. H. Kantha
Affiliation:
Department of Earth and Planetary Sciences, The Johns Hopkins University, Baltimore, Maryland 21218
O. M. Phillips
Affiliation:
Department of Earth and Planetary Sciences, The Johns Hopkins University, Baltimore, Maryland 21218
R. S. Azad
Affiliation:
Department of Earth and Planetary Sciences, The Johns Hopkins University, Baltimore, Maryland 21218 Present address: Department of Mechanical Engineering, University of Manitoba, Winnipeg, Manitoba, Canada.
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Abstract

Turbulent entrainment at the density interface of a stable two-layer stratified fluid is studied in the laboratory, a constant surface stress being applied at the free surface. Conservation of mass requires that the overall Richardson number Ri = Dgδρ/ρu*2 is constant in each experiment, where D is the depth of the mixed layer, gδρ/ρ the buoyancy difference and u* the friction velocity. If the entrainment rate E = ue/u* is a function only of Ri, it is therefore constant in each experiment and can be measured with a greater accuracy than has previously been attained. The functional dependence of ue/u* on Ri is established over the range 30 < Ri < 1000; it is found not to follow any simple power law. The entrainment rates are considerably higher than those measured by Kato & Phillips (1969), for which the fluid below the mixed layer was linearly stratified. Such a condition allows internal gravity waves to be radiated downwards and the reduction in entrainment rate is consistent with that found by Linden (1975).

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 79 , Issue 4 , 23 March 1977 , pp. 753 - 768
Copyright
© 1977 Cambridge University Press

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References

Crapper, P. F. & Linden, P. F. 1974 The structure of turbulent density interfaces. J. Fluid Mech. 65, 45–63.Google Scholar
Cromwell, T. 1960 Pycnoclines created by mixing in an aquarium tank. J. Mar. Res. 18, 73–82.Google Scholar
Kantha, L. H. 1975 Turbulent entrainment at the density interface of a two-layer stably stratified fluid system. Dept. Earth Planet. Sci., Johns Hopkins Univ. Rep. GFDL TR 75–1.Google Scholar
Kato, H. & Phillips, O. M. 1969 On the penetration of a turbulent layer into stratified fluid. J. Fluid Mech. 37, 643–655.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
Moore, M. J. & Long, R. R. 1971 An experimental investigation of turbulent stratified shearing flow. J. Fluid Mech. 49, 635–655.Google Scholar
Rouse, H. & Dodu, J. 1955 Turbulent diffusion across a density discontinuity. Houille Blanche, 10, 522–532.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, 349–368.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.
Wolanski, E. J. & Brush, L. M. 1975 Turbulent entrainment across stable density step structures. Tellus, 27, 259–268.Google Scholar