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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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References

André, J. C., Lacarrère, P. & Mahrt, L. J. 1979 Sur la distribution verticale de l'humidité dans une couche limite convective. J. Rech. Atmos. 13, 135–146.Google Scholar
Crapper, P. F. & Linden, P. F. 1974 The structure of turbulent density interfaces. J. Fluid Mech. 65, 45–63.Google Scholar
Deardorff, J. W., Willis, G. E. & Stockton, P. 1980 Laboratory studies of the entrainment zone of a convectively mixed layer. J. Fluid Mech. 100, 41–64.Google Scholar
Ellison, T. H. & Turner, J. S. 1959 Turbulent entrainment in stratified flows. J. Fluid Mech. 6, 423–448.Google Scholar
Kantha, L. H. 1978 On surface-stress-induced entrainment at a buoyancy interface. Dept. Earth Planet. Sci., Johns Hopkins Univ. Rep. GFDL TR 78-1.Google Scholar
Kantha, L. H., Phillips, O. M. & Azad, R. S. 1977 On turbulent entrainment at a stable density interface. J. Fluid Mech. 79, 753–768.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
Kitaigorodskii, S. A. 1981 On the theory of the surface-stress induced entrainment at a buoyancy interface (toward interpretation of KP and KPA experiments). Tellus 33, 89–101.Google Scholar
Lofquist, K. 1960 Flow and stress near an interface between stratified fluids. Phys. Fluids 3, 158–175.Google Scholar
Mahrt, L. & Lenschow, D. H. 1976 Growth dynamics of the convectively mixed layer. J. Atmos. Sci. 33, 41–51.Google Scholar
Mcdougall, T. J. 1979 Measurements of turbulence in a zero-mean-shear mixed layer. J. Fluid Mech. 94, 409–432.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
Pollard, R. T., Rhines, P. B. & Thompson, R. O. R. Y. 1973 The deepening of the wind-mixed layer. Geophys. Fluid Dyn. 3, 381–404.Google Scholar
Price, J. F. 1979 On the scaling of stress-driven entrainment experiments. J. Fluid Mech. 90, 509–529.Google Scholar
Price, J. F., Mooers, C. N. K. & Van Leer, J. C. 1978 Observation and simulation of storm-driven mixed-layer deepening. J. Phys. Oceanog. 8, 582–599.Google Scholar
Thompson, R. O. R. Y. 1979 A re-examination of the entrainment process in some laboratory flows. Dyn. Atmos. Oceans 4, 45–55.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
Veronis, G. 1970 The analogy between rotating and stratified fluids. Ann. Rev. Fluid Mech. 2, 37–66.Google Scholar
Wolanski, E. J. & Brush, L. M. 1975 Turbulent entrainment across stable density step structures. Tellus 27, 259–268.Google Scholar
Zeman, O. & Tennekes, H. 1977 Parameterization of the turbulent energy budget at the top of the daytime atmospheric boundary layer. J. Atmos. Sci. 34, 111–123.Google Scholar