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On mixing across an interface in stably stratified fluid

Published online by Cambridge University Press:  21 April 2006

E Xuequan  and
E. J. Hopfinger
E Xuequan
Affiliation:
Institut de Mécanique, Université de Grenoble et C.N.R.S., Grenoble, France Permanent address: Institute of Mechanics, Chinese Academy of Sciences, Beijing.
E. J. Hopfinger
Affiliation:
Institut de Mécanique, Université de Grenoble et C.N.R.S., Grenoble, France
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Abstract

Mixed-layer deepening in stratified fluid has been studied experimentally in mean-shear-free turbulence generated by an oscillating grid. Conditions were varied over a wide range and both two-layered and constant-gradient fluid systems were considered. It is shown that the mixed-layer deepening rate is represented well by power laws, and when local scaling is used all the data can be collapsed on an entrainment relation E = K Ri−n with n = 1.50±0.05 when Ri [gsim ] 7. This power law suggests that the turbulent kinetic energy is made available for mixing on a buoyancy timescale characteristic of eddy recoil or internal-wave breaking rather than a turbulent-eddy overturning timescale. In the constant-gradient situation internal waves are generated which radiate energy away from the interface. An evaluation of the radiated energy indicates, however, that generally energy radiation does not affect the entrainment rate. The coefficient K therefore has the same value (K ≈ 3.8) in linearly stratified fluid as in the two-layer situation. The interface thickness is found to be a function of stability, but reaches an asymptotic value of h/D = 0.055 when Ri is very large. There is some indication that the interface thickness is also a weak function of Reynolds number.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 166 , May 1986 , pp. 227 - 244
Copyright
© 1986 Cambridge University Press

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References

Barla, K. 1980 Etude de l'entrainement turbulent à travers une interface de densité. Thèse de Docteur-Ingénieur, Université de Grenoble I.
Browand, F. K. & Hopfinger, E. J. 1985 The inhibition of vertical turbulent scale by stable stratification. IMA Conf. Proc. Cambridge, 1983. Clarendon.
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.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 the 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
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
Fernando, H. J. S. & Long, R. R. 1985 On the nature of the entrainment interface of a two-layer fluid subjected to zero-mean-shear turbulence. J. Fluid Mech. 151, 21.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. 1973 The interaction of a vortex ring with a sharp density interface: a model for turbulent entrainment. J. Fluid Mech. 60, 467.Google Scholar
Linden, P. F. 1975 The deepening of a mixed layer in a stratified fluid. J. Fluid Mech. 71, 385.Google Scholar
Linden, P. F. 1979 Mixing in stratified fluids. Geophys. Astrophys. Fluid Dyn. 13, 3.Google Scholar
Long, R. R. 1978 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
Mory, M. & Hopfinger, E. J. 1985 Rotating turbulence evolving freely from an initial quasi 2D state. Macroscopic Modelling of Turbulent Flows. Lecture Notes in Physics, vol. 230. Springer.
Rouse, H. & Dodu, J. 1955 Turbulent diffusion across a density discontinuity. Houille Blanche 10, 522.Google Scholar
Thomson, 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
Turner, J. S. 1968 The influence of molecular diffusivity on turbulent entrainment across a density interface. J. Fluid Mech. 33, 639.Google Scholar
Turner, J. S. 1973 Buoyancy Effects in Fluids. Cambridge University Press.