Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-08T07:55:50.851Z Has data issue: false hasContentIssue false
  • English
  • Français

Boundary mixing in stratified reservoirs

Published online by Cambridge University Press:  26 April 2006

J. Imberger  and
G. N. Ivey
J. Imberger
Affiliation:
Centre for Water Research, University of Western Australia, Nedlands 6009, Australia
G. N. Ivey
Affiliation:
Centre for Water Research, University of Western Australia, Nedlands 6009, Australia
Get access Rights & Permissions [Opens in a new window]

Abstract

We consider the steady flow driven by turbulent mixing in a benthic boundary layer along a sloping boundary in the general case of a non-uniform background density gradient. The velocity and density fields are decomposed into barotropic and baroclinic components, and a solution is obtained by taking an expansion in the small parameter A, the aspect ratio of the boundary layer defined as the thickness divided by the alongslope length. The flow in the boundary layer is governed by a balance between alongslope baroclinic and barotropic density fluxes. A number of flow regimes can exist, and we show that in the regimes relevant to lakes and reservoirs, the barotropic flow is divergent and drives an exchange flow between the boundary layer and the interior. This leads to changes in the interior density gradient which are significant when compared to field observations.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 248 , March 1993 , pp. 477 - 491
Copyright
© 1993 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– 1977.Google Scholar
Bejan, A. & Imberger, J. 1979 Heat transfer by forced and free convection in a horizontal channel with differentially heated ends. Trans. ASME C: J. Heat Transfer 101, 417– 421.Google Scholar
Cormack, D. E., Leal, L. G. & Imberger, J. 1974 Natural convection in a shallow cavity with differentially heated end walls. Part 1. Asymptotic Theory. J. Fluid Mech. 65, 209– 229.Google Scholar
Eriksen, C. C. 1985 Implications of ocean bottom reflection for internal wave spectra and mixing. J. Phys. Oceanogr. 15, 1145– 1156.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.
Garrett, C. 1990 The role of secondary circulation in boundary mixing. J. Geophys. Res. 95, 3181– 3188.Google Scholar
Garrett, C. 1991 Marginal mixing theories. Atmos. Ocean 29, 313– 339.Google Scholar
Gilbert, D. & Garrett, C. 1989 Implications for ocean mixing of internal wave scattering off irregular topography. J. Phys. Oceanogr. 19, 1716– 1729.Google Scholar
Gregg, M. C. & Sanford, T. B. 1980 Signatures of mixing from the Bermuda slope, the Sargasso Sea and the Gulf Stream. J. Phys. Oceanogr. 10, 105– 127.Google Scholar
Imberger, J. 1974 Natural convection in a shallow cavity with differentially heated end walls. Part 3. Experimental results. J. Fluid Mech. 65, 247– 260.Google Scholar
Imberger, J. 1989 Vertical heat flux in the hypolimnion of a lake. In Proc. 10th AFMC, Melbourne, 1989, vol. I, pp. 2.13– 2.16.
Imberger, J. & Ivey, G. N. 1991 On the nature of turbulence in a stratified fluid, Part 2: Application to lakes. J. Phys. Oceanogr. 21, 659– 680.Google Scholar
Imberger, J. & Patterson, J. C. 1990 Physical limnology. Adv. Appl. Mech. 27, 303– 475.Google Scholar
Ivey, G. N. 1987 Boundary mixing in a rotating, stratified fluid. J. Fluid Mech. 183, 25– 44.Google Scholar
Ivey, G. N. & Corcos, G. M. 1982 Boundary mixing in a stratified fluid. J. Fluid Mech. 121, 1– 26.Google Scholar
Ivey, G. N. & Nokes, R. I. 1989 Vertical mixing due to the breaking of critical internal waves on sloping boundaries. J. Fluid Mech. 204, 479– 500.Google Scholar
Ledwell, J. R. & Watson, A. J. 1991 The Santa Monica Basin tracer experiment: A study of diapycnal and isopycnal mixing. J. Geophys. Res. 96, 8695– 8718.Google Scholar
MacCready, P. & Rhines, P. B. 1991 Buoyant inhibition of Ekman transport on a slope and its effect on stratified spin-up. J. Fluid Mech. 223, 631– 661.Google Scholar
Munk, W. H. 1966 Abyssal Recipes. Deep-Sea Res. 13, 707– 730.Google Scholar
Phillips, O. M. 1970 On flows induced by diffusion in a stably, stratified fluid. Deep-Sea Res. 17, 435– 443.Google Scholar
Phillips, O. M., Shyu, J.-H. & Salmun, H. 1986 An experiment on boundary mixing: mean circulation and transport rates. J. Fluid Mech. 173, 473– 499.Google Scholar
Salmun, H., Killworth, P. D. & Blundell, J. R. 1991 A two-dimensional model of boundary mixing. J. Geophys. Res. 96, 18,447– 18,474.Google Scholar
Salmun, H. & Phillips, O. M. 1992 An experiment on boundary mixing. Part 2. The slope dependence at small angles. J. Fluid Mech. 240, 355– 377.Google Scholar
Taylor, G. I. 1954 Observations of the atmospheric boundary layer over the ocean. Proc. R. Soc. Lond. A 223, 446– 468.Google Scholar
Thorpe, S. A. 1982 On the layers produced by rapidly oscillating a vertical grid in a uniform stratified fluid. J. Fluid Mech. 124, 391– 409.Google Scholar
Thorpe, S. A. 1987 Current and temperature variability on the continental slope. Phil. Trans. R. Soc. Lond. A 323, 471– 517.Google Scholar
Thorpe, S. A., Hall, P. & White, M. 1990 The variability of mixing at the continental slope. Phil. Trans. R. Soc. Lond. A 331, 183– 194.Google Scholar
Woods, A. W. 1991 Boundary-driven mixing. J. Fluid Mech. 226, 625– 654.Google Scholar
Wunsch, C. 1970 On oceanic boundary mixing. Deep-Sea Res. 17, 293– 301.Google Scholar
Young, W. R. & Jones, S. 1991 Shear dispersion. Phys. Fluids A 3, 1087– 1101.Google Scholar