Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-26T07:24:12.387Z Has data issue: false hasContentIssue false
  • English
  • Français

Barotropically induced interfacial waves in two-layer exchange flows over a sill

Published online by Cambridge University Press:  14 November 2007

M. ELETTA NEGRETTI ,
DAVID Z. ZHU  and
GERHARD H. JIRKA
M. ELETTA NEGRETTI
Affiliation:
Institute for Hydromechanics, University of Karlsruhe, Germany
DAVID Z. ZHU
Affiliation:
Department of Civil and Environmental Engineering, University of Alberta, Canada
GERHARD H. JIRKA
Affiliation:
Institute for Hydromechanics, University of Karlsruhe, Germany
Get access Rights & Permissions [Opens in a new window]

Abstract

Two-layer exchange flows are observed in the channels/straits connecting two water bodies of different densities. This study examines the nature of the barotropic forcing and its effect on the interfacial waves in two-layer exchange flows over a smooth/break underwater sill. Experiments were conducted with different initial conditions, distinguishing the case of hydrostatic disequilibrium and the case of a global pressure-balanced state. The experiments demonstrate that the baroclinic exchange flow is dominated by the barotropic-forcing-induced oscillations. A simplified barotropic model is developed to predict the period of the barotropic oscillation with an excellent agreement with experimental measurements. Detailed velocity and flow-rate measurements also indicate the importance of the barotropic forcing in exchange flows. The effect of the superimposed barotropic forcing on the interfacial wave characteristics is also investigated. Large two-dimensional surge-like structures are observed during the experiments, whose generation is shown to be related to the flow-rate oscillations. The length scales of these structures is comparable with the total water depth and is shown to increase with increasing Reynolds numbers.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 592 , 10 December 2007 , pp. 135 - 154
Copyright
Copyright © Cambridge University Press 2007

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

Armi, L. 1986 The hydraulics of two flowing layers with different densities. J. Fluid Mech. 163, 27–58.CrossRefGoogle 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
Baines, P. G. 1975 Entrainment by a plume or a jet at a density interface. J. Fluid Mech. 68, 309–320.Google Scholar
Baines, P. G. 1995 Topographic Effects in Stratified Flows. Cambridge University Press.Google Scholar
Dean, R. G. & Dalrymple, R. A. 1984 Water Wave Mechanics for Engineers and Scientists. Prentice-Hall.Google Scholar
Ellison, T. H. & Turner, J. S. 1959 Turbulent entrainment in stratified flows. J. Fluid Mech. 6, 423–448.CrossRefGoogle Scholar
Farmer, D. M. & Armi, L. 1988 The flow of Atlantic Water through the Strait of Gibraltar. Prog. Oceanogr. 21, 1–105.Google Scholar
Farmer, D. M. & Armi, L. 1999 Stratified flow over topography: the role of small scale entrainment and mixing in flow establishment. Proc. R. Soc. Lond. A 455, 3221–3258.CrossRefGoogle Scholar
Fernando, H. J. S. 1991 Turbulent mixing in stratified fluids. Annu. Rev. Fluid Mech. 23, 455–493.CrossRefGoogle Scholar
Fouli, H. R. S. 2006 An experimental study of interfacial waves and instabilities in exchange flows over a smooth sill. PhD thesis, Department of Civil and Environmental Engineering, Edmonton, University of Alberta.Google Scholar
Hansen, B. & Osterhus, S. 2000 North Atlantic–Nordic Seas exchanges. Prog. Oceanog. 45 (2), 109–208.CrossRefGoogle Scholar
Helfrich, K. R. 1995 Time-dependent two-layer exchange flows. J. Phys. Oceanogr. 25, 359–373.Google Scholar
Koop, C. G. & Browand, F. K. 1976 Instability and turbulence in a stratified fluid with shear. J. Fluid Mech. 24, 67–113.Google Scholar
Lawrence, G. A. 1993 The hydraulics of steady two-layer flow over a fixed obstacle. J. Fluid Mech. 254, 605–633.CrossRefGoogle Scholar
Lawrence, G., Pieters, R., Zaremba, L., Tedford, T., Gu, L., Greco, S. & Hamblin, P. F. 2004 Summer exchange between Hamilton Harbour and Lake Ontario. Deep-Sea Research II, 51, 475–487.CrossRefGoogle Scholar
Lien, R.-C., D'Asaro, E. A. & Dairiki, G. T. 1998 Lagrangian frequency spectra of vertical velocity and vorticity in high-Reynolds-number oceanic turbulence. J. Fluid Mech. 362, 177–198.Google Scholar
Morin, V. M., Zhu, D. Z. & Loewen, M. R. 2004 Supercritical exchange flow down a sill. J. Hydraul. Engng ASCE 130, 521–531.CrossRefGoogle Scholar
Pawlak, G. & Armi, L. 1998 Vortex dynamics in a spatially accelerating shear layer. J. Fluid Mech. 376, 1–35.CrossRefGoogle Scholar
Pawlak, G. & Armi, L. 2000 Mixing and entrainment in developing stratified currents. J. Fluid Mech. 424, 1–37.CrossRefGoogle Scholar
Pratt, L. J. 1987 Rotating shocks in a separated laboratory channel flow. J. Phys. Oceanogr. 17, 483–491.Google Scholar
Scinocca, J. F. & Peltier, W. R. 1989 Pulsating downslope windstorms. J. Atmos. Sci. 46, 2885–2914.Google Scholar
Sherwin, T. J. & Turrell, W. R. 2005 Mixing and advection of a cold water cascade over the Wyville Thomson Ridge. Deep-Sea Res. 52, 1392–1413.Google Scholar
Stigebrandt, A. 1977 On the effect of barotropic current fluctuations on the two-layer transport capacity of a constriction. J. Phys. Oceanogr. 7, 118–122.Google Scholar
Stommel, H. & Farmer, H. G. 1953 Control of salinity in an estuary by a transition. J. Mar. Res. 12, 13–20.Google Scholar
Thorpe, S. 1985 Laboratory observation of secondary structures in Kelvin–Helmholtz billows and consequences for ocean mixing. Geophys. Astrophys. Fluid Dyn. 35, 175–199.CrossRefGoogle Scholar
Turner, J. S. 1963 Model experiments relating to thermals with increasing buoyancy. Q. J. R. Met. Soc. 89, 62–74.Google Scholar
Welander, M. V. 1984 Flow around circular cylinder-kaleidoscope of challenging fluid phenomena. Proc. Symp. Fully Separated Flows, vol. 1, p. 102.Google Scholar
Wüest, A., Imboden, D. M. & Schurter, M. 1988 Origin and size of hypolimnic mixing in Urnersee, the southern basin of Vierwaldstaettersee (Lake Lucerne), Schweiz. Schweiz. Z. Hydrol. 50, 40–70.Google Scholar
Zhu, D. Z. & Lawrence, G. A. 1998 Non-hydrostatic effects in layered shallow water flows. J. Fluid Mech. 355, 1–16.Google Scholar
Zhu, D. Z. & Lawrence, G. A. 2000 Hydraulics of exchange flows. J. Hydraul. Engng ASCE 126, 921–928.CrossRefGoogle Scholar