Hostname: page-component-77c89778f8-vpsfw Total loading time: 0 Render date: 2024-07-20T19:23:44.907Z Has data issue: false hasContentIssue false
  • English
  • Français

Mixing in a density-driven current flowing down a slope in a rotating fluid

Published online by Cambridge University Press:  14 May 2008

CLAUDIA CENEDESE  and
CLAUDIA ADDUCE
CLAUDIA CENEDESE
Affiliation:
Woods Hole Oceanographic Institution, Woods Hole, MA 02543, USA
CLAUDIA ADDUCE
Affiliation:
Universita' RomaTre, Via Vito Volterra, 62, 00146 Roma, Italy
Get access Rights & Permissions [Opens in a new window]

Abstract

We discuss laboratory experiments investigating mixing in a density-driven current flowing down a sloping bottom, in a rotating homogenous fluid. A systematic study spanning a wide range of Froude, 0.8 < Fr < 10, and Reynolds, 10 < Re < 1400, numbers was conducted by varying three parameters: the bottom slope; the flow rate; and the density of the dense fluid. Different flow regimes were observed, i.e. waves (non-breaking and breaking) and turbulent regimes, while changing the above parameters. Mixing in the density-driven current has been quantified within the observed regimes, and at different locations on the slope. The dependence of mixing on the relevant non-dimensional numbers, i.e. slope, Fr and Re, is discussed. The entrainment parameter, E, was found to be dependent not only on Fr, as assumed in previous studies, but also on Re. In particular, mixing increased with increasing Fr and Re. For low Fr and Re, the magnitude of the mixing was comparable to mixing in the ocean. For large Fr and Re, mixing was comparable to that observed in previous laboratory experiments that exhibited the classic turbulent entrainment behaviour.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 604 , 10 June 2008 , pp. 369 - 388
Copyright
Copyright © Cambridge University Press 2008

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

Aagaard, K., Coachman, L. K. & Carmack, E. C. 1981 On the halocline of the Arctic Ocean Deep-Sea Res. 28, 529–545.CrossRefGoogle Scholar
Alavian, V. 1986 Behavior of density currents on an incline. J. Hydraul. Engg. ASCE 112, 27–42.CrossRefGoogle Scholar
Arneborg, L., Fiekas, V., Umlauf, L. & Burchard, H. 2007 Gravity current dynamics and entrainment – A process study based on observations in the Arkona Basin. J. Phys. Oceanogr. 37, 2094–2113.CrossRefGoogle Scholar
Baines, P. G. 2001 Mixing in flows down gentle slopes into stratified environments. J. Fluid Mech. 443, 237–270.CrossRefGoogle Scholar
Baines, P. G. 2002 Two-dimensional plumes in stratified environments. J. Fluid Mech. 471, 315–337.CrossRefGoogle Scholar
Baines, P. G. 2005 Mixing regimes for the flow of dense fluid down slopes into stratified environments. J. Fluid Mech. 538, 245–267.CrossRefGoogle Scholar
Baringer, M. O. & Price, J. F. 1997 Mixing and spreading of the Mediterranean outflow. J. Phys. Oceanogr. 27, 1654–1677.2.0.CO;2>CrossRefGoogle Scholar
Britter, R. E. & Linden, P. F. 1980 The motion of the front of a gravity current travelling down an incline. J. Fluid Mech. 99, 531–543.CrossRefGoogle Scholar
Cenedese, C., Whitehead, J. A., Ascarelli, T. A. & Ohiwa, M. 2004 A dense current flowing down a sloping bottom in a rotating fluid. J. Phys. Oceanogr. 34, 188–203.2.0.CO;2>CrossRefGoogle Scholar
Dallimore, C. J., Imberger, J. & Ishikawa, T. 2001 Entrainment and turbulence in saline underflow in Lake Ogawara. J. Hydraul. Eng. 127, 937–948.CrossRefGoogle Scholar
Dickson, R. R. & Brown, J. 1994 The production of North Atlantic deep water: sources, rates and pathways. J. Geophys. Res. 99, 12 319–12 341.CrossRefGoogle Scholar
Ellison, T. H. & Turner, J. S. 1959 Turbulent entrainment in stratified flows. J. Fluid Mech. 6, 423–448.CrossRefGoogle Scholar
Etling, D., Gelhardt, F. Schrader, U. Brennecke, F. Kuhn, G. Chabert d'Hieres, G. & Didelle, H. 2000 Experiments with density currents on a sloping bottom on a rotating fluid. Dyn. Atmos. Oceans 31, 139–164.CrossRefGoogle Scholar
Ezer, T. 2005 Entrainment, diapycnal mixing and transport in threedimensional bottom gravity current simulations using the Mellor–Yamada turbulence scheme. Ocean Modell. 9, 151–168.CrossRefGoogle Scholar
Ezer, T. 2006 Topographic influence on overflow dynamics: idealized numerical simulations and the Faroe Bank Channel overflow. J. Geophys. Res. 111 (C02002) doi:10.1029/2005JC003195.Google Scholar
Fleury, M., Mory, M., Hopfinger, E. J. & Auchere, D. 1991 Effects of rotation on turbulent mixing across a density interface. J. Fluid Mech. 223, 165–191.CrossRefGoogle Scholar
Foster, T. D. & Carmack, E. C. 1976 Frontal zone mixing and Antarctic Bottom Water formation in the southern Weddell Sea. Deep-Sea Res. 23, 301–317.Google Scholar
Girton, J. B. & Sanford, T. B. 2003 Descent and modification of the overflow plume in Denmark Strait. J. Phys. Oceanogr. 33, 1351–1364.2.0.CO;2>CrossRefGoogle Scholar
Hughes, G. O. & Griffiths, R. W. 2006 A simple convective model of the global overturning circulation, including effects of entrainment into sinking regions. Ocean Modell. 12, 46–79.CrossRefGoogle Scholar
Ivey, G. N. & Imberger, J. 1991 On the nature of turbulence in a stratified fluid. Part I: The energy of mixing. J. Phys. Oceanogr. 21, 650–658.2.0.CO;2>CrossRefGoogle Scholar
Jackson, L., Hallberg, R. W. & Legg, S. 2008 A parameterisation of shear-driven turbulence for ocean climate models. J. Phys. Oceanogr. (in press).CrossRefGoogle Scholar
Jiang, L. & Garwood, W. J. 1996 Three-dimensional simulations of overflows on continental slopes. J. Phys. Oceanogr. 26, 1224–1233.2.0.CO;2>CrossRefGoogle Scholar
Jungclaus, J. H., Hauser, J. & Käse, R. H. 2001 Cyclogenesis in the Denmark Strait overflow plume. J. Phys. Oceanogr. 31, 3214–3229.2.0.CO;2>CrossRefGoogle Scholar
Käse, R. H., Girton, J. B. & Sanford, T. B. 2003 Structure and variability of the Denmark Strait Overflow: model and observations. J. Geophys. Res. 108 (C6), 3181, doi:10.1029/2002JC001548.Google Scholar
Killworth, P. D. 1977 Mixing on the Weddell Sea continental slope. Deep-Sea Res. 24, 427–448.CrossRefGoogle Scholar
Lane-Serff, G. F. & Baines, P. G. 1998 Eddy formation by dense flows on slopes in a rotating fluid. J. Fluid Mech. 363, 229–252.CrossRefGoogle Scholar
Legg, S., Hallberg, R. W. & Girton, J. B. 2006 Comparison of entrainment in overflows simulated by z-coordinate, isopycnal and nonhydrostatic models. Ocean modell. 11, 69–97.CrossRefGoogle Scholar
Mauritzen, C., Price, J., Sanford, T. & Torres, D. 2005 Circulation and mixing in the Faroese Channels. Deep-Sea Res. II 52, 883–913.CrossRefGoogle Scholar
Özgökmen, T. M., Fischer, P. F. & Johns, W. E. 2006 Product water mass formation by turbulent density currents from a high-order nonhydrostatic spectral element model. Ocean Modell. 12, 237–267.CrossRefGoogle Scholar
Price, J. F. & Barringer, M. O. 1994 Outflows and deep water production by marginal seas. Prog. Oceanogr. 33, 161–200.CrossRefGoogle Scholar
Price, J. F., Baringer, M. O., Lueck, R. G., Johnson, G. C., Amabar, I., Parrilla, G., Cantos, A., Kennelly, M. A. & Sanford, T. B. 1993 1993 Mediterranean outflow mixing and dynamics. Science 259, 1277–1282.CrossRefGoogle ScholarPubMed
Princevac, M., Fernando, H. J. S. & Whiteman, D. C. 2005 Turbulent entrainment into natural gravity driven flows. J. Fluid Mech. 533, 259–268.CrossRefGoogle Scholar
Riemenschneider, U. & Legg, S. 2007 Regional simulations of the Faroe Bank Channel overflow in a level model. Ocean Modell. 17, 93–122.CrossRefGoogle Scholar
Saunders, P. M. 1990 Cold outflow from the Faroe Bank Channel. J. Phys. Oceanogr. 20, 29–43.2.0.CO;2>CrossRefGoogle Scholar
Simpson, J. E. 1997 The Anatomy of a Gravity Current. Gravity Currents in the Environment and the Laboratory, 2nd edn, Cambridge University Press pp. 140–163.Google Scholar
Smith, P. C. 1975 A streamtube model for bottom boundary currents in the ocean. Deep-Sea Res. 22, 853–873.Google Scholar
Spall, M. A. & Price, J. F. 1998 Mesoscale variability in Denmark Strait: the PV outflow hypothesis. J. Phys. Oceanogr. 28, 1598–1623.2.0.CO;2>CrossRefGoogle Scholar
Strang, E. J. & Fernando, H. J. S. 2001 Entrainment and mixing in stratified fluis. J. Fluid Mech. 428, 349–386.CrossRefGoogle Scholar
Sutherland, B. R., Nault, J., Yewchuk, K. & Swaters, G. E. 2004 Rotating dense current on a slope. Part-1. Stability. J. Fluid Mech. 508, 241–264.CrossRefGoogle Scholar
Turner, J. S. 1986 Turbulent entrainment: the development of the entrainment assumption and its application to geophysical flows. J. Fluid Mech. 170, 431–471.CrossRefGoogle Scholar
Wåhlin, A. K. & Cenedese, C. 2006 How entraining density currents influence the ocean stratification. Deep-Sea Res. II 53, 172–193.Google Scholar
Wells, M. G. 2007 Influence of Coriolis forces on turbidity currents and their sediment patterns. In Proc. Euromech Colloquium-477.Google Scholar
Wells, M. G. & Wettlaufer, J. S. 2005 Two-dimensional density currents in a confined basin. Geophys. Astrophys. Fluid Dyn. 99, 199–218.CrossRefGoogle Scholar
Whitehead, J. A., Stern, M. Flierl, G. & Klinger, B. 1990 Experimental observations of baroclinic eddies on a sloping bottom. J. Geophys. Res. 95, 9585–9610.CrossRefGoogle Scholar
Xu, X., Chang, Y. S., Peters, H., Özgökmen, T. M. & Chassignet, E. P. 2006 Parameterization of gravity current entrainment for ocean circulation models using a high-order 3D nonhydrostatic spectral element model. Ocean Modell. 14, 19–44.CrossRefGoogle Scholar