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A model of turbulent mixing across a density interface including the effect of rotation

Published online by Cambridge University Press:  26 April 2006

Mathieu Mory
Mathieu Mory
Affiliation:
Institut de Mécanique de Grenoble, Domaine Universitaire, BP 53X, 38041 Grenoble Cédex, France
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Abstract

A new theoretical approach is presented, which determines the entrainment laws with and without background rotation in a two-layer stratified fluid with one layer stirred by turbulent motions. The model gives the entrainment coefficient E as a function of the local turbulent Richardson number Ri = g′l/u2, the Rossby number Ro = u/fl and the Péelet number Pe = ul/κ. The following entrainment laws are obtained: (i) without rotation and for a high Péclet number: $E \propto Ri^{-\frac{3}{2}}$; (ii) without rotation and for a low to moderate Péclet number: $E \propto Pe^{-\frac{1}{3}}Ri^{-1}$ (iii) with rotation and for a high Péclet number: E ∝ RoRi−l. These entrainment laws are consistent with experiments for the three different cases. The model relies to a great extent on the spectral distribution of interface oscillations measured in experiments. Comparison is made with experiments and with earlier models of entrainment.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 223 , February 1991 , pp. 193 - 207
Copyright
© 1991 Cambridge University Press

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References

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
Chandrasekhar, S.: 1961 Hydrodynamic and Hydromagnetic Stability. Dover.
Crapper, F. P. & Linden, F. P., 1974 The structure of turbulent density interfaces. J. Fluid Mech. 65, 45–63.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
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, 21–53.Google Scholar
Fleury, M.: 1988 Transferts turbulents à travers une interface de densité en milieu tournant. Thesis, Université J. Fourier, Grenoble.
Fleury, M., Mory, M., Hopfinger, E. J. & Auchere, D., 1991 Effects of rotation on turbulent mixing across a density interface. J. Fluid Mech. 223, 165–191.Google Scholar
Gibson, C. H.: 1981 Fossil turbulence and internal waves. In Non-linear Properties of Internal Waves (ed. B. West). AIP Conf. Proc. 76.
Hannoun, I. A., Fernando, H. J. S. & List, E. J. 1988 Turbulence structure near a sharp density interface. J. Fluid Mech. 189, 189–209.Google Scholar
Hannoun, I. A. & List, E. J., 1988 Turbulent mixing at a shear-free density interface. J. Fluid Mech. 189, 211–234.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
Huppert, H. E.: 1968 On Kelvin-Helmholtz instability in a rotating fluid. J. Fluid Mech. 33, 353–359.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
Long, R. R.: 1978 A theory of mixing in a stably stratified fluid. J. Fluid Mech. 84, 113–124.Google Scholar
Maxworthy, T.: 1986 On turbulent mixing across a density interface in the presence of rotation. J. Phys. Oceanogr. 16, 1136–1137.Google Scholar
Mory, M. & Hopfinger, E. J., 1985 Rotating turbulence evolving freely from an initial quasi-2D state. Lecture Notes in Physics, vol. 230. Springer.
Noh, Y. & Long, R. R., 1987 Turbulent mixing in a rotating fluid. 3rd Intl Symp. on Stratified Flows, Pasadena.Google Scholar
Phillips, O. M.: 1977 Dynamics of the Upper Ocean. Cambridge University Press.
Stillinger, D. C., Helland, K. N. & Van Atta, C. W. 1983 Experiments on the transition of homogeneous turbulence to internal waves in a stratified fluid. J. Fluid Mech. 131, 91–122.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 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.