Two-Layer Flows in Rotating Channels

  • Larry J. Pratt
  • John A. Whitehead
Part of the Atmospheric And Oceanographic Sciences Library book series (ATSL, volume 36)


The exchange flow between a marginal sea or estuary and the open ocean is often approximated using two-layer stratification. Two-layer models are most convincing when the interfacial region separating the upper and lower fluids is relatively thin. The exchange flow in the Strait of Gibraltar exhibits this behavior, at least at certain locations and times (Figure I.9). The vertical density and velocity profiles taken near the Camerinal Sill show a relatively sharp transition between slab-like upper and lower water masses. Elsewhere, the Gibraltar interface can be thicker and can contribute significantly to the overall mass budget for the strait. The Bab al Mandab (BAM) exchange flow experiences variations throughout the water column that are quite continuous (Figures 1.10.7 and 5.0.1). Under such conditions, a two-layer model might still give guidance provided that motions over the water column are associated with the lowest internal mode of the stratified shear flow.


Froude Number Potential Vorticity Hydraulic Jump Deep Basin Solution Curve 
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  1. Armi, L. 1986. The hydraulics of two flowing layers of different densities. J. Fluid Mech. 163, 27–58.CrossRefGoogle Scholar
  2. Armi, L. and D. M. Farmer 1986. Maximal two-layer exchange through a contraction with barotropic net flow. J. Fluid Mech. 164, 27–51.CrossRefGoogle Scholar
  3. Armi, L. and D. M. Farmer 1988. The flow of Mediterranean water through the Strait of Gibraltar. Prog. Oceanogr. 21, 1–105.CrossRefGoogle Scholar
  4. Baines, P. G. 1984. A unified description of two-layer flow over topography. J. Fluid Mech. 146, 127–167.CrossRefGoogle Scholar
  5. Bormans, M. and C. Garrett 1989a The effects of nonrectangular cross section, friction, and barotropic fluctuations on the exchange through the Strait of Gibraltar. J. Phys. Oceanogr. 19, 1543–1557.CrossRefGoogle Scholar
  6. Bryden, H. L. and T. H. Kinder 1991. Steady two-layer exchange through the strait of Gibraltar. Deep-Sea Res. 38 (Suppl. 1), S445–S463.Google Scholar
  7. Bryden, H. L. and H. M. Stommel 1984. Limiting processes that determine basic features of the circulation in the Mediterranean Sea. Oceanologica Acta. 7, 289–296.Google Scholar
  8. Bye, J. A. T. and J. A. Whitehead, Jr. 1975. A theoretical model of the flow in the mouth of Spencer Gulf, South Australia. Estuarine and Coastal Mar. Sci. 3, 477–481.CrossRefGoogle Scholar
  9. Dalziel, S. B. 1988. Two-layer Hydraulics: Maximal Exchange Flows, PhD thesis. University of Cambridge, England.Google Scholar
  10. Dalziel, S. B. 1991. Two-layer hydraulics: A functional approach. J. Fluid Mech. 223, 135–163.CrossRefGoogle Scholar
  11. Finnigan, T. D. and G. N. Ivey 1999. Submaximal exchange between a convectively forced basin and a large reservoir. J. Fluid Mech. 378, 357–378.CrossRefGoogle Scholar
  12. Finnigan, T. D. and G. N. Ivey 2000. Convectively driven exchange flow in a stratified sill-enclosed basin. J. Fluid Mech. 418, 313–338.CrossRefGoogle Scholar
  13. Garrett, C. 2004. Frictional processes in straits. Deep-Sea Res. II 51, 393–410.CrossRefGoogle Scholar
  14. Gill, A. E. 1977. The hydraulics of rotating-channel flow. J. Fluid Mech. 80, 641–671.CrossRefGoogle Scholar
  15. Grimm, Th. and T. Maxworthy 1999. Buoyancy-driven mean flow in a long channel with a hydraulically constrained exit condition. J. Fluid Mech. 398, 155–180.CrossRefGoogle Scholar
  16. Hogg, N. G. 1983. Hydraulic control and flow separation in a multi-layered fluid with application to the Vema Channel. J. Phys. Oceanogr. 13, 695–708.CrossRefGoogle Scholar
  17. Houghton, D. D. and E. Isaacson 1970. Mountain winds. Stud. Numer. Anal. 2, 21–52.Google Scholar
  18. Hunkins, K. and J. A. Whitehead 1992. Laboratory simulation of exchange through Fram Strait. J. Geophys. Res. 97 (C7) 11,299–11,321.CrossRefGoogle Scholar
  19. Jiang, Q. and R. B. Smith 2001a. Ideal shocks in two-layer flow. Part I: Under a rigid lid. Tellus 53A, 129–145.Google Scholar
  20. Koop, C. G. and F. K. Browand 1979. Instability and turbulence in a stratified fluid with shear. J. Fluid Mech., 93, 135–159.CrossRefGoogle Scholar
  21. Lawrence, G. A. 1990. On the hydraulics of Boussinesq and non-Boussinesq two-layer flows. J. Fluid Mech. 215, 457–480.CrossRefGoogle Scholar
  22. Lawrence, G. A. 1993. The hydraulics of steady two-layer flow over a fixed obstacle. J. Fluid Mech. 254, 605–633.CrossRefGoogle Scholar
  23. Long, R. R. 1954. Some aspects of the flow of stratified fluids. II. Experiments with a two-fluid system. Tellus 6, 97–115.CrossRefGoogle Scholar
  24. Phillips, O. M. 1966. On turbulent convection currents and the circulation of the Red Sea. Deep-Sea Res. 13, 1147–1160.Google Scholar
  25. Pratt, L. J. and L. Armi 1990. Two-layer rotating hydraulics: strangulation, remote and virtual controls. Pure Appl. Geophys. 133(4), 587–617.CrossRefGoogle Scholar
  26. Stommel, H. M. and H. G. Farmer 1952. Abrupt change in width in two-layer open chanel flow. J. Marine Res. 11, 205–214.Google Scholar
  27. Stommel, H. M. and H. G. Farmer 1953. Control of salinity in an estuary by a transition. J. Marine Res. 12, 13–20.Google Scholar
  28. Thorpe, S. A. 1973. Experiments on instability and turbulence in a stratified shear flow. J. Fluid Mech., 61, 731–751.CrossRefGoogle Scholar
  29. Timmermans M.-L. E. and L. J. Pratt 2005. Two-layer exchange flow between two deep basins: Theory and application to the Strait of Gibraltar. J. Phys. Oceanogr. 35, 1568–1592.CrossRefGoogle Scholar
  30. Tsimplis, M. N. and H. L. Bryden 2000. Estimation of the transports through the Strait of Gibraltar. Deep-Sea Res. Part I 47, 2,219–2,242.CrossRefGoogle Scholar
  31. Whitehead, J. A., A. Leetma and R. A. Knox 1974. Rotating hydraulics of strait and sill flows. Geophys. Fluid Dyn. 6, 101–125.CrossRefGoogle Scholar
  32. Whitehead, J. A. and A. R. Miller 1979. Laboratory simulation of the gyre in the Alboran Sea. J. Geophys. Res. 84, 3733–3742.CrossRefGoogle Scholar
  33. Whitehead, J. A., M.-L. Timmermans, W. Gregory Lawson, S. N. Bulgakov, A. M. Zatarian, J. F. A. Medina and J. Salzig 2003. Laboratory studies of thermally and/or/salinity driven flows with partial mixing 1. Stommel transitions and multiple flow states. J. Geophys. Res. 108(C2), 3036, doi:10.1029/2001JC000902.CrossRefGoogle Scholar
  34. Wilkinson, D. L. and I. R. Wood 1983. The formation of an intermediate layer by horizontal convection in a two-layered shear flow. J. Fluid Mech., 136, 167–187.CrossRefGoogle Scholar
  35. Woelk, S. and D. Quadfasel 1996. Renewal of deep water in the Red Sea during 1982–1987. J. Geophys. Res., 101(c8), 18155–18166.CrossRefGoogle Scholar
  36. Wood, I. R. 1970. A lock exchange flow. J. Fluid Mech. 42, 671–687.CrossRefGoogle Scholar
  37. Yih, C. S. 1980. Stratified Flows. Academic Press, San Diego, 418pp.Google Scholar
  38. Zhu, D. Z. and G. A. Lawrence 2000. Hydraulics of exchange flows. J. Hydr. Engrg., ASCE 126, 921–928.CrossRefGoogle Scholar
  39. Zhu, D. Z. and G. A. Lawrence 1998. Nonhydrostatic effects in layered shallow water flows. J. Fluid Mech. 355, 1–16.CrossRefGoogle Scholar

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© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Physical Oceanography DepartmentWoods Hole Oceanographic InstitutionWoods HoleUSA

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