Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-28T21:13:02.880Z Has data issue: false hasContentIssue false
  • English
  • Français

The long-term circulation driven by density currents in a two-layer stratified basin

Published online by Cambridge University Press:  23 January 2007

M. G. WELLS  and
J. S. WETTLAUFER
M. G. WELLS
Affiliation:
Department of Geology and Geophysics, Yale University, New Haven, CT 06520-8109, USA
J. S. WETTLAUFER
Affiliation:
Department of Geology and Geophysics, Yale University, New Haven, CT 06520-8109, USA Department of Physics, Yale University, New Haven, CT 06520-8109, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

Experimentation and theory are used to study the long-term dynamics of a two-dimensional density current flowing into a two-layer stratified basin. When the initial Richardson number, , characterizing the ratio of the background stratification to the buoyancy flux of the density current, is less than the critical value of , it is found that the density current penetrates the stratified interface. This result is ostensibly independent of slope for angles between 30° and 90°. If the current does not initially penetrate the interface, then it slowly increases the density of the top layer until the interfacial density difference is reduced sufficiently to drive penetration. The time scale for this to occur, , is explicitly a function of the buoyancy flux B and the length of the basin L. The initial Richardson number, , is a function of depth, the initial reduced gravity of the interface and a weak function of slope angle. In the absence of initial penetration for very steep slopes of 75° and 90°, we observe that penetrative convection at the interface leads to significant local entrainment. In consequence, the top layer thickens and the interfacial entrainment rate increases as the fifth power of the interfacial Froude number. In contrast, such a process is not observed at comparable interfacial Froude numbers on lower slopes of 30°, 45° and 60°, thereby demonstrating the important role of impact angle on penetrative convection. We attribute the increased interfacial entrainment by the steep density currents as the result of the transition from an undular bore to a turbulent hydraulic jump at the point where the density current intrudes. We discuss the applicability of the observed circulation to the stability of the Arctic halocline where we find years for a range of contemporary oceanographic conditions.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 572 , February 2007 , pp. 37 - 58
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

Aagaard, K. & Greisman, P. 1975 Toward new mass and heat budgets for the Arctic Ocean. J. Geophys. Res. 80, 3821–3827.CrossRefGoogle Scholar
Aagaard, K., Coachman, L. K. & Carmack, E. C. 1981 On the halocline of the Arctic Ocean. Deep-Sea Res. 28, 529–545.CrossRefGoogle Scholar
Baines, P. G. 1995 Topographic effects in fluids. Cambridge University Press.Google 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. 2005 Mixing regimes for the flow of dense fluid down slopes into stratified environments. J. Fluid Mech. 538, 245–267.CrossRefGoogle Scholar
Baines, W. D. 1975 Entrainment by a plume or jet at a density interface. J. Fluid Mech. 68, 309–320.CrossRefGoogle Scholar
Baines, W. D. & Turner, J. S. 1969 Turbulent buoyant convection from a source in a confined region. J. Fluid. Mech. 37, 51–80.CrossRefGoogle Scholar
Baringer, M. O. & Price, J. F. 1999 A review of the physical oceanography of the Mediterranean outflow. Marine Geol. 155, 63–82.CrossRefGoogle Scholar
Björk, G. 1989 A one-dimensional time-dependent model for the vertical stratification of the upper Arctic Ocean. J. Phys. Oceanogr. 19, 52–67.2.0.CO;2>CrossRefGoogle Scholar
Briggs, G. A. 1969 Plume rise. US Atomic Energy Commision Critical Review Series. TID-25075.Google Scholar
Britter, R. F. & 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
Bush, J. W. M. & Woods, A. W. 1999 Vortex generation by line plumes in a rotating stratified fluid. J. Fluid Mech. 388, 289–313.CrossRefGoogle Scholar
Cardoso, S. S. S. & Woods, A. W. 1993 Mixing by a turbulent plume in a confined stratified region. J. Fluid Mech. 250, 277–305.CrossRefGoogle Scholar
Carmack, E. C. 2000 The Arctic Ocean's freshwater budget: sources, sinks and export. In The Freshwater Budget of the Arctic Ocean (ed. Lewis, E. L., Jones, E. P., Lemke, P., Prowse, T. D., & Wadhams, P.), pp. 91–126. Kluwer.CrossRefGoogle Scholar
Carmack, E. C. & Chapman, D. C. 2003 Wind-driven shelf/basin exchange on an Arctic shelf. The joint roles of ice cover extent and shelf-break bathymetry. Geophys. Res. Lett. 30, 1778, doi:10.1029/2003GL017755.CrossRefGoogle Scholar
Caulfield, C. & Woods, A. W. 1998 Turbulent gravitational convection from a point source in a non-uniformly stratified environment. J. Fluid Mech. 360, 229–248.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
Chao, S. Y. & Shaw, P. T. 2003 A numerical study of dense water outflows and halocline anticyclones in an Arctic baroclinic slope current. J. Geophys. Res. 108, 3226, doi:10.1029/2002JC001473.Google Scholar
Chapman, D. C. 1997 A note on isolated convection in a rotating two-layer fluid. J. Fluid Mech. 348, 319–325.CrossRefGoogle Scholar
Ching, C. Y., Fernando, H. J. S. & Noh, Y. 1993 Interaction of a negatively buoyant line plume with a density interface. Dyn. Atmos. ÊOceans 19, 367–388.CrossRefGoogle Scholar
Chow, V. T. 1959 Open-Channel Hydraulics. McGraw–Hill.Google Scholar
Coachman, L. K. & Aagaard, K. 1988 Transports through Bering Strait; annual and inter-annual variability. J. Geophys. Res. 93, 15 535–15 539.CrossRefGoogle Scholar
Cotel, A. J. & Breidenthal, R. E. 1997 Jet detrainment at a stratified interface. J. Geophys. Res. 102, 23 813–23 818.CrossRefGoogle Scholar
Cotel, A. J., Gjestvang, J. A., Ramkhelawan, N. N. & Breidenthal, R. E. 1997 Laboratory experiments of a jet impinging on a stratified interface. Exps. Fluids 23, 155–160.CrossRefGoogle Scholar
Ellison, T. H. & Turner, J. S. 1959 Turbulent entrainment in stratified flows. J. Fluid Mech. 6, 423–448.CrossRefGoogle Scholar
Fischer, H. B., List, E. J., Koh, R. C. Y., Imberger, J. & Brooks, N. H. 1979 Mixing in Coastal and Inland Waters. Academic.Google Scholar
Gascard, J. C., Watson, A. J., Messias, M., Olsson, K. A., Johannessen, T. & Simonsenk, K. 2002 Long-lived vortices as a mode of deep ventilation in the Greenland Sea. Nature 416, 525–527.CrossRefGoogle ScholarPubMed
Gawarkiewicz, G. & Chapman, D. C. 1995 A numerical study of dense water formation and transport on a shallow, sloping continental shelf. J. Geophys. Res. 100, 4489–4507.CrossRefGoogle Scholar
Hamblin, P. F. & Carmack, E. C. 1978 River induced currents in a Fjord lake. J. Geophys. Res. 83, 885–899. ÊCrossRefGoogle Scholar
Hebbert, B., Imberger, J., Loh, I. & Patterson, J. 1979 Collie river underflow into the Wellington reservoir. J. Hydraul. Div. ASCE 105, 533–545.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 Model. 12, 46–79.CrossRefGoogle Scholar
Hunkins, K. & Whitehead, J. A. 1992 Laboratory simulation of exchange through Fram Strait. J. Geophys. Res. 97, 11 299–11 321.CrossRefGoogle Scholar
Imberger, J. & Hamblin, P. F. 1982 Dynamics of lakes, reservoirs, and cooling ponds. Annu. Rev. Fluid. Mech. 14, 153–187.CrossRefGoogle Scholar
Kikuchi, T., Hatakeyama, K. & Morison, J. H. 2004 Distribution of convective Lower Halocline Water in the eastern Arctic Ocean. J. Geophys. Res. 109, C12030, doi:10.1029/2003JC002223.CrossRefGoogle Scholar
Killworth, P. D. 1977 Mixing on the Weddell Sea continential slope. Deep-Sea Res. 24, 427–448.CrossRefGoogle Scholar
Killworth, P. D. & Carmack, E. C. 1979 A filling box model of river dominated lakes. Limnol. Oceanogr. 24, 201–217.CrossRefGoogle Scholar
Kneller, B. C., Bennett, S. J. & McCaffrey, W. D. 1999 Velocity structure, turbulence and fluid stresses in experimental gravity currents. J. Geophys. Res 104, 5381–5391.CrossRefGoogle Scholar
Kulkarni, A. C., Murphy, F. & Manohar, S. S. 1993 Interaction of buoyant plumes with two-layer stably stratified media. Expl Thermal Fluid Sci. 7, 241–248.CrossRefGoogle Scholar
Kumagai, M. 1984 Turbulent buoyant convection from a source in a confined two-layered region. J. Fluid Mech. 147, 105–131.CrossRefGoogle Scholar
Manins, P. C. & Turner, J. S. 1978 The relation between flux ratio and energy ratio in convectively mixed-layers. Q. J. R. Met. Soc. 104, 39–44.CrossRefGoogle Scholar
Marino, B. M., Thomas, L. P. & Linden, P. F. 2005 The front condition for gravity currents. J. Fluid Mech. 536, 49–78.CrossRefGoogle Scholar
Maxworthy, T. & Narimousa, S. 1994 Unsteady, turbulent convection into a homogeneous, rotating fluid, with oceanographic applications. J. Phys. Oceanogr. 24, 865–887.2.0.CO;2>CrossRefGoogle Scholar
Melling, H. & Lewis, E. L. 1982 Shelf drainage flows in the Beaufort Sea and their effect on the Arctic Ocean pycnocline. Deep-Sea Res. 29, 967–985.CrossRefGoogle Scholar
Monaghan, J. J., Cas, R. A. F., Kos, A. M. & Hallworth, M. A. 1999 Gravity currents descending a ramp in a stratified tank. J. Fluid Mech. 379, 39–70.CrossRefGoogle Scholar
Morison, J. H., Aagaard, K. & Steele, M. 2000 Recent environmental changes in the Arctic: a review. Arctic 53, 359–371.CrossRefGoogle Scholar
Morton, B. R., Taylor, G. I. & Turner, J. S. 1956 Turbulent gravitational convection from maintained and instantaneous sources. Proc. R. Soc. Lon. A 234, 1–32.Google Scholar
Narimousa, S. 1996 Penetrative turbulent convection into a rotating two-layer fluid. J. Fluid Mech. 321, 299–313.CrossRefGoogle Scholar
Noh, Y., Fernando, H. J. S. & Ching, C. Y. 1992 Flows induced by the impingement of a two-dimensional thermal on a density Êinterface. J. Phys. Oceanogr. 22, 1207–1222.2.0.CO;2>CrossRefGoogle Scholar
Polyakov, I., Walsh, D., Dmitrenko, I., Colony, R. & Timokhov, L. A. 2003 Arctic Ocean variability derived from historical observations. Geophys. Res. Lett. 30, doi:10.1029/2001GL016441.CrossRefGoogle Scholar
Proshutinsky, A., Bourke, R. H. & McLaughlin, F. A. 2002 The role of the Beaufort Gyre in Arctic climate variability: seasonal to decadal climate scales. Geophys. Res. Lett. 29, doi:10.1029/2001GL015847.CrossRefGoogle Scholar
Roach, A. T., Aagaard, K. & Carsey, F. D. 1993 Coupled ice-ocean variability in the Greenland Sea. Atmos.-Ocean 31, 319–337.CrossRefGoogle Scholar
Rudels, B., Anderson, L. & Jones, E. 1996 Formation and evolution of the surface mixed-layer and Halocline of the Arctic Ocean. J. Geophys. Res. 101, 8807–8822.CrossRefGoogle Scholar
Shin, J. O., Dalziel, S. B. & Linden, P. F. 2004 Gravity currents produced by lock exchange. J. Fluid Mech. 521, 1–34.CrossRefGoogle Scholar
Steele, M. & Boyd, T. 1998 Retreat of the cold halocline layer in the Arctic Ocean. J. Geophys. Res. 103, 10 419–10 435.CrossRefGoogle Scholar
Stigebrandt, A. 1981 A model for the thickness and salinity of the upper layer in the Arctic Ocean and the relationship between the ice thickness and some external parameters. J. Phys. Oceanogr. 11, 1407–1422.2.0.CO;2>CrossRefGoogle Scholar
Stommel, H. 1958 The abyssal circulation. Deep-Sea Res. 5, 80–82.Google Scholar
Sukru, B., Ozsoy, E. & Unluata, U. 1993 Filling of the Marmara Sea by the Dardanelles lower layer inflow. Deep-Sea Res. 40, 1815–1838.Google Scholar
Taylor, G. I. 1948 Dynamics of a mass of hot gas rising in air. USAEC Rep. MDDC-919 (LADC-276), Los Alamos Scientific Laboratory, National Technical Information Service, Springfield, VA.Google Scholar
Turner, J. S. 1973 Buoyancy Effects in Fluids. Cambridge University Press.CrossRefGoogle Scholar
Turner, J. S. 1986 Turbulent entrainment – the developement of the entrainment assumption and its application to geophysical flows. J. Fluid. Mech. 173, 431–471.CrossRefGoogle Scholar
Untersteiner, N. 1988 On the ice and heat balance in Fram Strait. J. Geophys. Res. 93, 527–531.CrossRefGoogle Scholar
Wahlin, A. K. & Cenedese, C. 2006 How entraining density currents influence the ocean stratification in aone-dimensional ocean basin. Deep-Sea Res. II 53, 172–193.Google Scholar
Wallace, R. B. & Sheff, B. 1987 Two-dimensional buoyant-jets in two-layer ambient fluid. J. Hydraulic Engng ASCE 113, 992–1005.CrossRefGoogle Scholar
Wells, M. G. & Sherman, B. 2001 Stratification produced by surface cooling in lakes with significant shallow regions. Limnol. Oceanogr. 46, 1747–1759.CrossRefGoogle Scholar
Wells, M. G. & Wettlaufer, J. S. 2005 Two-dimensional density currents in confined basins. Geophys. Astrophys. Fluid Dyn. 99, 199–218.CrossRefGoogle Scholar
Whitehead, J. A. 1993 A laboratory model of cooling over the continental shelf. J. Phys. Oceanogr. 23, 2412–2427.2.0.CO;2>CrossRefGoogle Scholar
Worster, M. G. & Huppert, H. E. 1983 Time-dependent density profiles in a filling box. J. Fluid. Mech. 132, 457–466.CrossRefGoogle Scholar
Wright, S. J. & Wallace, R. B. 1979 Two-dimensional buoyant jets in stratified fluid. J. Hydraul. Div. ASCE 105, 1393–1406.CrossRefGoogle Scholar
Yamamoto-Kawai, M., Tanaka, N. & Pivovarov, S. 2005 Freshwater and brine behaviors in the Arctic Ocean deduced from historical data of δO 18 and Alkalinity (1929–2002 ad). J. Geophys. Res. 110, doi:10.1029/2004JC002793.Google Scholar