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Spatially decaying turbulence and its relation to mixing across density interfaces

Published online by Cambridge University Press:  11 April 2006

E. J. Hopfinger  and
J.-A. Toly
E. J. Hopfinger
Affiliation:
Laboratoire de Mécanique des Fluides (Laboratoire Associé au C.N.R.S.), Université de Grenoble, France
J.-A. Toly
Affiliation:
Laboratoire de Mécanique des Fluides (Laboratoire Associé au C.N.R.S.), Université de Grenoble, France
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Abstract

The turbulence generated by a vertically oscillating grid in a water tank and the entrainment across a salinity interface caused by this turbulence have been investigated experimentally. Measurements were carried out in a homogeneous layer of fluid as well as a two-layered fluid, which permitted us to determine the decay law of this turbulence and the way in which the structure of the turbulence depends on the mesh size and on the frequency and amplitude of the grid oscillation. It was found that the turbulent kinetic energy decays with distance from the grid according to a power law $\overline{q^2}\propto z^{-n}$, with n close to 2, and that the turbulent Reynolds number remains approximately constant during decay. The linear dependence of the r.m.s. turbulent velocity on the grid oscillation frequency found by Thompson & Turner (1975) in the case of a square-bar grid has been confirmed. It is shown here that this linear relation remains valid when an interface is present and consequently the dependence of the entrainment velocity on the local Richardson number is of the form $u_e/u \propto Ri^{-\frac{3}{2}}$, the Péclet number being high. While the bearing of these results on the problem of the thermocline or an inversion is clear we wish to emphasize that the spatial decay of turbulence is interesting in itself.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 78 , Issue 1 , 5 November 1976 , pp. 155 - 175
Copyright
© 1976 Cambridge University Press

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