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Dependence of mixed-layer entrainment on shear stress and velocity jump

Published online by Cambridge University Press:  20 April 2006

J. W. Deardorff  and
G. E. Willis
J. W. Deardorff
Affiliation:
Department of Atmospheric Sciences, Oregon State University, Corvallis, Oregon 97331
G. E. Willis
Affiliation:
Department of Atmospheric Sciences, Oregon State University, Corvallis, Oregon 97331
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Abstract

From rotating-screen annulus experiments the entrainment rate, we, normalized by the friction velocity, u*, has been found to be a function of both the overall Richardson number, RT, and the inverse Froude number, Rv. The RT−½ dependence deduced by Price (1979) and Thompson (1979) satisfactorily explains the present data if multiplied by an approximate Rv−1·4 dependence. The measurements indicate that Rv is a variable that is influenced by side-wall friction, time after onset of the surface stress, or other factors. The greater we/u* values of experiments of the type of Kantha, Phillips & Azad (1977) over that of the Kato & Phillips (1969) experiment can be explained by somewhat greater Rv values in the latter case.

A close connection is now apparent between entrainment experiments in two-layer systems designed to have only one velocity scale (the interfacial velocity jump, Δv), and the rotating-screen annulus experiments having two velocity scales (u* and Δv). The former also have (at least) two velocity scales, the second one being associated with the presence of turbulence throughout one or both of the fluid layers.

The turbulent layer is found to be quite well mixed in density only if we/u* does not exceed about 0·03, or we/|Δv| does not exceed about 0·003. The present data suggest more rapid entrainment when temperature rather than salt provides the density jump, as first noted by Turner (1968) in oscillating grid experiments. If this is a Péclet-number effect, the trend did not continue for still greater Pe values, the data for kaolin (clay) being very compatible with that for salt.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 115 , February 1982 , pp. 123 - 149
Copyright
© 1982 Cambridge University Press

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