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Symmetric Holmboe instabilities in a laboratory exchange flow

Published online by Cambridge University Press:  25 September 2009

EDMUND W. TEDFORD ,
R. PIETERS  and
G. A. LAWRENCE
EDMUND W. TEDFORD*
Affiliation:
Department of Civil Engineering, University of British Columbia, Vancouver, BC V6T 1Z4, Canada
R. PIETERS
Affiliation:
Department of Civil Engineering, University of British Columbia, Vancouver, BC V6T 1Z4, Canada Department of Earth and Ocean Sciences, University of British Columbia, Vancouver, BC V6T 1Z4, Canada
G. A. LAWRENCE
Affiliation:
Department of Civil Engineering, University of British Columbia, Vancouver, BC V6T 1Z4, Canada
*
†Email address for correspondence: [email protected]
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Abstract

Laboratory experiments have been conducted that test the predictions of Holmboe (Geofys. Publ., vol. 24, 1962, pp. 67–112). Symmetric Holmboe instabilities are observed during steady, maximal two-layer exchange flow in a long laboratory channel of rectangular cross-section. Internal hydraulic controls at each end of the channel isolate the subcritical region within the channel from disturbances in the reservoirs. Inside the channel, the instabilities form cusp-like waves that propagate in both directions. The phase speed of the instabilities is consistent with Holmboe's theory and increases along the length of the channel as a result of the gradual acceleration of each layer. This acceleration causes the wavelength of any given instability to increase in the flow direction until it is approximately twice the most amplified wavelength. At this point new waves develop with the result that the average wavelength is almost constant along the length of the channel.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 636 , 10 October 2009 , pp. 137 - 153
Copyright
Copyright © Cambridge University Press 2009

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References

REFERENCES

Alexakis, A. 2005 On Holmboe's instability for smooth shear and density profiles. Phys. Fluids 17, 084103.CrossRefGoogle Scholar
Armi, L. 1986 The hydraulics of two flowing layers with different densities. J. Fluid Mech. 163, 27–58.CrossRefGoogle Scholar
Carpenter, J. R., Lawrence, G. A. & Smyth, W. D. 2007 Evolution and mixing of asymmetric Holmboe instabilities. J. Fluid Mech. 582, 103–132.Google Scholar
Farmer, D. M. & Armi, L. 1998 The flow of Atlantic water through the Strait of Gibraltar. Prog. Oceanogr. 21, 1–98.Google Scholar
Geyer, W. R. & Smith, J. D. 1987 Shear instability in a highly stratified estuary. J. Phys. Oceanogr. 17, 1668–1679.Google Scholar
Gu, L. & Lawrence, G. 2005 Analytical solution for maximal frictional two-layer exchange flow. J. Fluid Mech. 543, 1–17.Google Scholar
Hogg, A. McC. & Ivey, G. N. 2003 The Kelvin–Helmholtz to Holmboe instability transition in stratified exchange flows. J. Fluid Mech. 477, 339–362.Google Scholar
Holmboe, J. 1962 On the behaviour of symmetric waves in stratified shear layers. Geofys. Publ. 24, 67–112.Google Scholar
Koop, C. G. & Browand, F. K. 1979 Instability and turbulence in a stratified fluid with shear. J. Fluid Mech. 93, 135–159.Google Scholar
Lawrence, G. A., Browand, F. K. & Redekopp, L. G. 1991 The stability of a sheared density interface. Phys. Fluids 3 (10), 2360–2370.Google Scholar
Miles, J. & Munk, W. 1961 Harbor paradox. J. Waterways Harb. Am. Soc. Civ. Engrs WW3 87, 111–130.Google Scholar
Peregrine, D. H. 1976 Interaction of water waves and currents. Adv. Appl. Mech. 16, 9–117.Google Scholar
Pouliquen, O., Chomaz, J. M. & Huerre, P. 1994 Propagating Holmboe waves at the interface between two immiscible fluids. J. Fluid Mech. 266, 277–302.Google Scholar
Smyth, W. D. 2006 Secondary circulations in Holmboe waves. Phys. Fluids 18 (064104), 1–13.Google Scholar
Smyth, W. D., Carpenter, J. R. & Lawrence, G. A. 2007 Mixing in symmetric Holmboe waves. J. Phys. Oceanogr. 37, 1566–1583.Google Scholar
Smyth, W. D. & Winters, K. B. 2003 Turbulence and mixing in Holmboe waves. J. Phys. Oceanogr. 33, 694–711.Google Scholar
Tedford, E. W., Carpenter, J. R., Pawlowicz, R., Pieters, R. & Lawrence, G. A. 2009 Observation and analysis of shear instability in the Fraser River Estuary. J. Geophys. Res. Accepted subject to revision.Google Scholar
Thorpe, S. 1971 Experiments on instability of stratified shear flows: miscible fluids. J. Fluid Mech. 46, 299–319.Google Scholar
Wesson, J. C. & Gregg, M. C. 1994 Mixing at Camarinal Sill in the Strait of Gibraltar. J. Geophys. Res. 99, 9847–9878.Google Scholar
Yoshida, S., Ohtani, M., Nishida, S. & Linden, P. F. 1998 Mixing processes in a highly stratified river. In Physical Processes in Lakes and Oceans, Coastal and Estuarine Studies (ed. Imberger, J.), vol. 54, pp. 389–400. American Geophysical Union.Google Scholar
Zhu, D. & Lawrence, G. A. 2001 Holmboe's instability in exchange flows. J. Fluid Mech. 429, 391–409.CrossRefGoogle Scholar