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Critical conditions and composite Froude numbers for layered flow with transverse variations in velocity

Published online by Cambridge University Press:  23 May 2008

LARRY J. PRATT
LARRY J. PRATT*
Affiliation:
Woods Hole Oceanographic Institution, Mail Stop 21, 360 Woods Hole Road, Woods Hole, MA, 02543, USA lpratt@whoi.edu
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Abstract

A condition is derived for the hydraulic criticality of a 2-layer flow with transverse variations in both layer velocities and thicknesses. The condition can be expressed in terms of a generalized composite Froude number. The derivation can be extended in order to obtain a critical condition for an N-layer system. The results apply to inviscid flows subject to the usual hydraulic approximation of gradual variations along the channel and is restricted to flows in which the velocity remains single-signed within any given layer. For an intermediate layer with a partial segment of sluggish flow, the long-wave dynamics of the overlying and underlying layers become decoupled.

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Type
Papers
Information
Journal of Fluid Mechanics , Volume 605 , 25 June 2008 , pp. 281 - 291
Copyright
Copyright © Cambridge University Press 2008

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References

REFERENCES

Armi, L. & Farmer, D. M. 1988 The flow of Mediterranean water through the Strait of Gibraltar. Prog. Oceanogr. 21, 1–105.Google Scholar
Baines, P. G. 1995 Topographic Effects in Stratified Flows. Cambridge University Press.Google Scholar
Engqvist, A. 1996. Self-similar multi-layer exchange flow through a contraction. J. Fluid Mech. 328, 49–66.Google Scholar
Garrett, C. & Gerdes, F. 2003 Hydraulic control of homogeneous shear flows. J. Fluid Mech. 475, 163–172.Google Scholar
Gill, A. E. 1977 The hydraulics of rotating-channel flow. J. Fluid Mech. 80, 641–671.Google Scholar
Gregg, M. & Özsoy, E. 2002 Flow, water mass changes, and hydraulics in the Bosphorus. J. Geophys. Res. 107, 3016.CrossRefGoogle Scholar
Henderson, F. M. 1966 Open Channel Flow. Macmillan.Google Scholar
Klymak, J. M. & Gregg, M. C. 2001 Three-dimensional nature of flow near a sill. J. Geophys. Res. 106, 22295–22311.Google Scholar
Sannino, G., Bargagli, A. & Artale, V. 2002 Numerical modeling of the mean exchange through the Strait of Gibraltar. J. Geophys. Res. 107, 3094.Google Scholar
Sannino, G., Bargagli, A. & Artale, V. 2004 Numerical modeling of the semidiurnal tidal exchange through the Strait of Gibraltar. J. Geophys. Res. 109, doi:10.1029/2003JC002057.CrossRefGoogle Scholar
Sannino, G., Carillo, A. & Artale, V. 2007 Three-layer view of transports and hydraulics in the Strait of Gibraltar: A three-dimensional model study. J. Geophys. Res. 112, doi:10.1029/2006JC003717.Google Scholar
Smeed, D. A. 2000 Hydraulic control of three-layer exchange flows: application to the Bab al Mandab. J. Phys. Oceanogr. 30, 2574–2588.2.0.CO;2>CrossRefGoogle Scholar
Stern, M. E. 1974 Comment on rotating hydraulics. Geophys. Fluid Dyn. 6, 127–130.Google Scholar
Stommel, H. M. & Farmer, H. G. 1952 Abrupt change in width in two-layer open channel flow. J. Mari. Res. 11, 205–214.Google Scholar