Hostname: page-component-8448b6f56d-qsmjn Total loading time: 0 Render date: 2024-04-24T12:41:32.522Z Has data issue: false hasContentIssue false
  • English
  • Français

Boundary mixing in a stratified fluid

Published online by Cambridge University Press:  20 April 2006

G. N. Ivey  and
G. M. Corcos
G. N. Ivey
Affiliation:
Canada Centre for Inland Waters, P.O. Box 5050, Burlington, Ontario L7R 4A6
G. M. Corcos
Affiliation:
Department of Mechanical Engineering, University of California, Berkeley, CA94720
Get access Rights & Permissions [Opens in a new window]

Abstract

A vertically oscillating grid is used to simulate boundary mixing in the laboratory. The oscillation of the grid creates a turbulent mixing region in its vicinity, and mixing within this region creates a step-like structure in an initial density distribution which varies linearly with depth. If the initial density varies only at the boundary between two homogeneous layers, the same grid turbulence generates additional steps above and below the initial one. The steps, in turn, drive multiple intrusions of mixed fluid away from the boundary and into the non-turbulent interior of the fluid. A compensat- ing return flow carries fluid from the interior into the turbulent mixing region. From the data, the inference is made that the intrusions make a negligible direct contribution to the vertical mass transport. An analytical model of the intrusions, which employs only molecular values of the transport coefficients and also demonstrates negligible vertical mass transport, is consissent with the laboratory observations.

Nevertheless, the data indicate that the fluid eventually reaches a homogeneous density by means of the gradual change of the gradient at a rate which is essentially the same both near the grid and far from it. For an initially uniform density profile this change occurs at all heights simultaneously, and for an initial density step it occurs preferentially near the step. Thus in both cases the interior flow must include slow vertical advection away from the horizontal centre plane. These advective currents can be made part of a consistent dynamic model, the buoyant equivalent of the spin- down in a rotating flow, provided that the net effect of the grid mixing includes a decrease in the local slope of the density gradient. This mode of adjustment explains satisfactorily the experimentally observed negligible horizontal density gradients. For the cme of an initially uniform density stratification, the shape of the evolving density gradient is not accounted for. In particular, it is not clear why the gradient changes at mid-depth almost simultaneously with variations at top and bottom boundaries.

The vertical mass flux is found to be independent of container length, and it increases with grid frequency of oscillation, amplitude of oscillation and with the mean density gradient.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 121 , August 1982 , pp. 1 - 26
Copyright
© 1982 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Armi, L. 1978 Some evidence for boundary mixing in the deep ocean. J. Geophys. Res. 83, 1971–1979.Google Scholar
Armi, L. 1979 Effects of variation in eddy diffusivity on property distributions in the ocean. J. Mar. Res. 37, 515–530.Google Scholar
Armi, L. & D'Asaro, E.1980 Flow structures of the benthic ocean. J. Geophys. Res. 85, 469–484.Google Scholar
Armi, L. & Millard, R. C. 1976 The bottom boundary layer of the deep ocean. J. Geophys. Res. 81, 4983–4990.Google Scholar
Caldwell, D. R., Brubaker, J. M. & Neal, V. T. 1978 Thermal microstructure on a lake slope. J. Limn. Oceanog. 23, 372–374.Google Scholar
Chen, C. F., Briggs, D. G. & Wirtz, R. A. 1971 Stability of thermal convection in a salinity gradient due to lateral heating. Int. J. Heat Mass Transfer 14, 57–65.Google Scholar
Fischer, H. B., List, E. J., Koh, R. C. Y., Imberger, J. & Brooks, N. H. 1979 Mixing in Inland and Coastal Waters. Academic.
Fortuin, J. 1960 Theory and application of two supplementary methods of constructing density gradient columns. J. Polymer Sci. 44, 505–515.Google Scholar
Garrett, C. 1979a Mixing in the ocean interior. Dyn. Oceans Atmos. 3, 239–266.Google Scholar
Garrett, C. 1979b Comment on ‘Some evidence for boundary mixing in the deep ocean’ by L. Armi. J. Geophys. Res. 84, 5095–5096.Google Scholar
Greenspan, H. P. & Howard, L. N. 1963 On a time-dependent motion of a rotating fluid. J. Fluid Mech. 17, 385–404.Google Scholar
Gregg, M. C. & Sanford, T. B. 1980 Signatures of mixing from the Bermuda slope, the Sargossa Sea and the Gulf Stream. J. Phys. Oceanog. 10, 105–127.Google Scholar
Hogg, N. G., Katz, E. J. & Sanford, T. B. 1978 Eddies, islands and mixing. J. Geophys. Res. 83, 2921–2938.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
Imberger, J., Thompson, R. T. & Fandry, C. 1976 Selective withdrawal from a finite rectangular tank. J. Fluid Mech. 78, 489–512.Google Scholar
Krauss, E. B. (ed.) 1977 Modelling and Prediction of the Upper Layers of the Ocean. Pergamon.
Manins, P. C. 1976 Intrusion into a stratified fluid. J. Fluid Mech. 74, 547–560.Google Scholar
Maxworthy, T. 1972 Experimental and theoretical studies of horizontal jets in a stratified fluid. In Proc. Int. Symp. on Stratified Flows, Novosibirsk.
Munk, W. 1966 Abyssal recipes. Deep-Sea Res. 13, 707–730.Google Scholar
Sherman, F. S., Imberger, J. & Corcos, G. M. 1978 Turbulence and mixing in stably stratified waters. Ann. Rev. Fluid Mech. 10, 267–288.Google Scholar
Thorpe, S. A., Hutt, P. K. & Soulsby, R. 1969 The effect of horizontal gradients on thermohaline convection. J. Fluid Mech. 38, 375–400.Google Scholar
Turner, J. S. 1973 Buoyancy Effects in Fluids. Cambridge University Press.
Veronis, G. 1970 The analogy between rotating and stratified fluids. Ann. Rev. Fluid Mech. 2, 37–66.Google Scholar
Wunsch, C. 1972 Temperature microstructure on the Bermuda Slope with application to the mean flow. Tellus 24, 350–367.Google Scholar