Hostname: page-component-7c8c6479df-ph5wq Total loading time: 0 Render date: 2024-03-28T21:02:48.886Z Has data issue: false hasContentIssue false

Mixing efficiency in controlled exchange flows

Published online by Cambridge University Press:  26 March 2008

TJIPTO PRASTOWO
Affiliation:
Research School of Earth Sciences, The Australian National University, Canberra, ACT 0200, Australia
ROSS W. GRIFFITHS
Affiliation:
Research School of Earth Sciences, The Australian National University, Canberra, ACT 0200, Australia
GRAHAM O. HUGHES
Affiliation:
Research School of Earth Sciences, The Australian National University, Canberra, ACT 0200, Australia
ANDREW McC. HOGG
Affiliation:
Research School of Earth Sciences, The Australian National University, Canberra, ACT 0200, Australia

Abstract

Turbulence and mixing are generated by the shear between two counter-flowing layers in hydraulically controlled buoyancy-driven exchange flows through a constriction. From direct measurements of the density distribution and the amount of turbulent mixing in steady laboratory exchange flows we determine the overall efficiency of the mixing. For sufficiently large Reynolds numbers the mixing efficiency is 0.11(±0.01), independent of the aspect ratio and other details of constriction geometry, in good agreement with a scaling analysis. We conclude that the mixing in shear flows of this type has an overall efficiency significantly less than the maximum value widely proposed for stratified turbulence.

Type
Papers
Copyright
Copyright © Cambridge University Press 2008

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

REFERENCES

Anati, D. A., Assaf, G. & Thompson, R. O. R. Y. 1977 Laboratory models of sea straits. J. Fluid Mech. 81, 341351.CrossRefGoogle Scholar
Bryden, H. L. & Nurser, A. J. G. 2003 Effects of strait mixing on ocean stratification. J. Phys. Oceanogr. 33, 18701872.2.0.CO;2>CrossRefGoogle Scholar
Caulfield, C. P. & Peltier, W. R. 2000 The anatomy of the mixing transition in homogeneous and stratified free shear layers. J. Fluid Mech. 413, 147.CrossRefGoogle Scholar
Gregg, M. C. & Özsoy, E. 2002 Flow, water mass changes, and hydraulics in the Bosphorus. J. Geophys. Res. 107 (C3), 10.1029/2000JC000485.Google Scholar
Gu, L. & Lawrence, G. A. 2005 Analytical solution for maximal frictional two-layer exchange flow. J. Fluid Mech. 543, 117.CrossRefGoogle Scholar
Helfrich, K. L. 1995 Time-dependent two-layer hydraulic exchange flow. J. Phys. Oceanogr. 25, 359373.2.0.CO;2>CrossRefGoogle Scholar
Hogg, A. M., Ivey, G. N. & Winters, K. B. 2001 Hydraulics and mixing in controlled exchange flows. J. Geophys. Res. 106, 959972.CrossRefGoogle Scholar
Koop, C. G. & Browand, F. K. 1979 Instability and turbulence in a stratified fluid. J. Fluid Mech. 93, 135160.CrossRefGoogle Scholar
Lawrence, G. A. 1990 On the hydraulics of Boussinesq and non-Boussinesq two-layer flows. J. Fluid Mech. 215, 457480.CrossRefGoogle Scholar
Munk, W. & Wunsch, C. 1998 Abyssal recipes II: energetics of tidal and wind mixing. Deep-Sea Res. I 45, 19772010.CrossRefGoogle Scholar
Peltier, W. R. & Caulfield, C. P. 2003 Mixing efficiency in stratified shear flows. Annu. Rev. Fluid Mech. 35, 135167.CrossRefGoogle Scholar
Sherman, F. S., Imberger, J. & Corcos, G. M. 1978 Turbulence and mixing in stably stratified waters. Annu. Rev. Fluid Mech. 10, 267288.CrossRefGoogle Scholar
Thorpe, S. A. 1973 Experiments on instability and turbulence in a stably stratified shear flow. J. Fluid Mech. 61, 731751.CrossRefGoogle Scholar
Winters, K. B. & Seim, H. E. 2000 The role of dissipation and mixing in exchange flow through a contracting channel. J. Fluid Mech. 407, 265290.CrossRefGoogle Scholar
Wood, I. R. 1970 A lock exchange flow. J. Fluid Mech. 42, 671687.CrossRefGoogle Scholar
Wunsch, C. & Ferrari, R. 2004 Vertical mixing, energy, and the general circulation of the oceans. Annu. Rev. Fluid Mech. 36, 281314.CrossRefGoogle Scholar
Zhu, D. Z. & Lawrence, G. A. 1998 Non-hydrostatic effects in layered shallow water flows. J. Fluid Mech. 355, 116.CrossRefGoogle Scholar