Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-20T04:33:15.219Z Has data issue: false hasContentIssue false
  • English
  • Français

Two-layer hydraulics: a functional approach

Published online by Cambridge University Press:  26 April 2006

Stuart B. Dalziel
Stuart B. Dalziel
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CBS 9EW, UK
Get access Rights & Permissions [Opens in a new window]

Abstract

A new approach for investigating two-layer hydraulic exchange flows in channels is introduced. The approach is based on the functional formalism of Gill (1977) and applied to the flow through a contraction in width and to flow over a simple sill. The sill geometry is an extension of that looked at by earlier workers, in particular Farmer & Armi (1986) who used a Froude-number-plane approach. In the present paper a simple relationship between the composite Froude number and the hydraulic functional is derived, though the functional approach may also be applied to channels where a Froude number is not readily defined. The ability to trace roots of this functional from one reservoir to the other is a prerequisite for the flow to be realizable. Two hydraulic transitions are required for the flow to be fully controlled and the exchange flow rate to be maximal. If only one hydraulic transition is present, the flow is governed by the conditions in one of the reservoirs and the exchange flow rate is found to be submaximal. The flow along a channel is found to be very sensitive to small departures from symmetry about a horizontal plane. The response of the interface to the introduction of a net (barotropic) flow is found to be a discontinuous function of the strength of the forcing for some range of sill heights.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 223 , February 1991 , pp. 135 - 163
Copyright
© 1991 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.: 1986 The hydraulics of two flowing layers of different densities. J. Fluid Mech. 163, 27–58.Google Scholar
Armi, L. & Farmer, D. M., 1986 Maximal two-layer exchange through a contraction with barotropic net flow. J. Fluid Mech. 164, 27–51.Google Scholar
Armi, L. & Farmer, D. M., 1987 A generalisation of the concept of maximal exchange in a strait. J. Geophys. Res. 92 (C13), 14679–14680.Google Scholar
Armi, L. & Farmer, D. M., 1988 The flow of Atlantic water through the Strait of Gibraltar. Prog. Oceanogr. 21, 1–105.Google Scholar
Dalziel, S. B.: 1988 Two-layer hydraulics: maximal exchange flows. PhD thesis, Department of Applied Mathematics and Theoretical Physics, University of Cambridge.
Dalziel, S. B.: 1990 Rotating two-layer sill flows. In The Physical Oceanography of Sea Straits (ed. L. J. Pratt) NATO/ASI Series. Kluwer.
Dalziel, S. B. & Lane-Serff, G. F. 1990 The hydraulics of doorway exchange flows. Building and Environ, (to appear).Google Scholar
Farmer, D. M. & Armi, L., 1986 Maximal two-layer exchange over a sill and through the combination of a sill and contraction with barotropic flow. J. Fluid Mech. 164, 53–76.Google Scholar
Gill, A. E.: 1977 The hydraulics of rotating-channel flow. J. Fluid Mech. 80, 641–671.Google Scholar
Lawrence, G. A.: 1985 The hydraulics and mixing of two-layer flow over an obstacle. PhD thesis, Hydraulic Engineering Laboratory, University of California, Berkeley.
Long, R. R.: 1956 Long waves in a two-fluid system. J. Met. 13, 70–74.Google Scholar
Mehrotra, S. C.: 1973 Boundary contractions as controls in two layer flows. J. Hydraul. Div. A8CE 99 (HY11), 2003–2012.Google Scholar
Pratt, L. J.: 1984 On nonlinear flow with multiple obstructions. J. Atmos. Sci. 41, 1214–1225.Google Scholar
Pratt, L. J. & Armi, L., 1987 Hydraulic control of flows with nonuniform potential vorticity. J. Phys Oceanog 17, 2016–2029.Google Scholar
Steckler, K. D., Baum, H. R. & Quintiere, J. G., 1984 Fire induced flows through room openings – flow coefficients. Rep. NBSIR 83–2801, National Bureau of Standards, US Department of Commerce.Google Scholar
Stommel, H. & Farmer, H. G., 1953 Control of salinity in an estuary by a transition. J. Mar. Res., 12, 3–20.Google Scholar
Whitehead, J., Leetmaa, A. & Knox, R., 1974 Rotating hydraulics of strait and sill flows. Geophys. Fluid Dyn. 6, 101–125.Google Scholar
Wood, I. R.: 1968 Selective withdrawal from a stably stratified fluid. J. Fluid Mech. 32, 209–223.Google Scholar
Wood, I. R.: 1970 A lock exchange flow. J. Fluid Mech. 42, 671–687.Google Scholar
Yih, C.: 1965 Dynamics of Nonhomogeneous Fluids. Macmillan.