Editorial Type:
Article
Article Type:
Research Article

Entrainment in Shallow Rotating Gravity Currents: A Modeling Study

Lars Umlauf Leibniz-Institute for Baltic Sea Research, Warnemünde, Germany

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Lars Arneborg Department of Earth Sciences, University of Gothenburg, Göteborg, Sweden

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Richard Hofmeister Leibniz-Institute for Baltic Sea Research, Warnemünde, Germany

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Hans Burchard Leibniz-Institute for Baltic Sea Research, Warnemünde, Germany

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Print Publication:
01 Aug 2010
DOI:
https://doi.org/10.1175/2010JPO4367.1
Page(s):
1819–1834
Restricted access

Abstract

The physics of shallow gravity currents passing through a rotating channel at subcritical Froude number is investigated here with a series of idealized numerical experiments. It is found that the combined effects of friction and rotation set up a complex transverse circulation that has some crucial implications for the entrainment process. A key component of this secondary circulation is a geostrophically balanced transverse jet in the interface that laterally drains fluid from the interface. This effect is shown to result in a strong cross-channel asymmetry and a spatial separation of the entrainment process: drained interfacial fluid is partly replaced by entrained ambient fluid on the deep side of the gravity current, whereas the downward mixing of buoyant fluid occurs on the shallow side. These results, closely corresponding to recent measurements in a shallow, channelized gravity current in the western Baltic Sea, illustrate that the description of entrainment as a strictly vertical mixing process with the help of local bulk parameters like the Froude number is not generally applicable in rotating gravity currents.

Corresponding author address: Lars Umlauf, Leibniz-Institute for Baltic Sea Research, Seestrasse 15, 18119 Warnemünde, Germany. Email: lars.umlauf@io-warnemuende.de

Abstract

The physics of shallow gravity currents passing through a rotating channel at subcritical Froude number is investigated here with a series of idealized numerical experiments. It is found that the combined effects of friction and rotation set up a complex transverse circulation that has some crucial implications for the entrainment process. A key component of this secondary circulation is a geostrophically balanced transverse jet in the interface that laterally drains fluid from the interface. This effect is shown to result in a strong cross-channel asymmetry and a spatial separation of the entrainment process: drained interfacial fluid is partly replaced by entrained ambient fluid on the deep side of the gravity current, whereas the downward mixing of buoyant fluid occurs on the shallow side. These results, closely corresponding to recent measurements in a shallow, channelized gravity current in the western Baltic Sea, illustrate that the description of entrainment as a strictly vertical mixing process with the help of local bulk parameters like the Froude number is not generally applicable in rotating gravity currents.

Corresponding author address: Lars Umlauf, Leibniz-Institute for Baltic Sea Research, Seestrasse 15, 18119 Warnemünde, Germany. Email: lars.umlauf@io-warnemuende.de

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  • Arneborg, L., V. Fiekas, L. Umlauf, and H. Burchard, 2007: Gravity current dynamics and entrainment: A process study based on observations in the Arkona Basin. J. Phys. Oceanogr., 37 , 2094–2113.

    • Search Google Scholar
    • Export Citation

  • Baringer, M., and J. F. Price, 1997: Mixing and spreading of the Mediterranean outflow. J. Phys. Oceanogr., 27 , 1654–1677.

  • Burchard, H., and H. Baumert, 1995: On the performance of a mixed-layer model based on the k − ϵ turbulence closure. J. Geophys. Res., 100 , (C5). 8523–8540.

    • Search Google Scholar
    • Export Citation

  • Burchard, H., and K. Bolding, 2002: GETM—A general estuarine transport model. Scientific documentation. Tech. Rep. EUR 20253 EN, European Commission, 157 pp.

    • Search Google Scholar
    • Export Citation

  • Burchard, H., and R. D. Hetland, 2010: Quantifying the contributions of tidal straining and gravitational circulation to residual circulation in periodically stratified tidal estuaries. J. Phys. Oceanogr., 40 , 1243–1262.

    • Search Google Scholar
    • Export Citation

  • Burchard, H., F. Janssen, K. Bolding, L. Umlauf, and H. Rennau, 2009: Model simulations of dense bottom currents in the western Baltic Sea. Cont. Shelf Res., 29 , 205–220.

    • Search Google Scholar
    • Export Citation

  • Canuto, V. M., A. Howard, Y. Cheng, and M. S. Dubovikov, 2001: Ocean turbulence. Part I: One-point closure model—Momentum and heat vertical diffusivities. J. Phys. Oceanogr., 31 , 1413–1426.

    • Search Google Scholar
    • Export Citation

  • Cenedese, C., and C. Adduce, 2008: Mixing in density-driven current flowing down a slope in a rotating fluid. J. Fluid Mech., 604 , 369–388.

    • Search Google Scholar
    • Export Citation

  • Chapman, D. C., and G. Gawarkiewicz, 1995: Offshore transport of dense shelf water in the presence of a submarine canyon. J. Geophys. Res., 100 , (C7). 13373–13387.

    • Search Google Scholar
    • Export Citation

  • Davies, P. A., A. K. WÃ¥hlin, and Y. Guo, 2006: Laboratory and analytical model studies of the Faroe Bank Channel deep-water overflow. J. Phys. Oceanogr., 36 , 1348–1364.

    • Search Google Scholar
    • Export Citation

  • Ellison, T. H., and J. S. Turner, 1959: Turbulent entrainment in stratified flows. J. Fluid Mech., 6 , 423–448.

  • 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.

    • Search Google Scholar
    • Export Citation

  • Fer, I., G. Voet, K. S. Seim, and B. Rudels, 2010: Intense mixing of the Faroe Bank Channel overflow. Geophys. Res. Lett., 37 , L02604. doi:10.1029/2009GL041924.

    • Search Google Scholar
    • Export Citation

  • Galperin, B., L. H. Kantha, S. Hassid, and A. Rosati, 1988: A quasi-equilibrium turbulent energy model for geophysical flows. J. Atmos. Sci., 45 , 55–62.

    • Search Google Scholar
    • Export Citation

  • Hofmeister, R., H. Burchard, and J-M. Beckers, 2010: Non-uniform adaptive vertical grids for 3D numerical ocean models. Ocean Modell., 33 , 70–86.

    • Search Google Scholar
    • Export Citation

  • Hogg, N. G., 1983: Hydraulic control and flow separation in a multi-layered fluid with applications to the Vema Channel. J. Phys. Oceanogr., 13 , 695–708.

    • Search Google Scholar
    • Export Citation

  • Hughes, G. O., and R. W. Griffiths, 2006: A simple convective model of the global overturning circulation including effects of entrainment into sinking regions. Ocean Modell., 12 , 46–79.

    • Search Google Scholar
    • Export Citation

  • Ilicak, M., T. M. Özgökmen, H. Peters, H. Z. Baumert, and M. Iskandarani, 2008: Performance of two-equation turbulence closures in three-dimensional simulations of the Red Sea overflow. Ocean Modell., 24 , 122–139.

    • Search Google Scholar
    • Export Citation

  • Johnson, G. C., and T. B. Sanford, 1992: Secondary circulation in the Faroe Bank channel outflow. J. Phys. Oceanogr., 22 , 927–933.

    • Search Google Scholar
    • Export Citation

  • Johnson, G. C., and D. R. Ohlson, 1994: Frictionally modified rotating hydraulic channel exchange and ocean outflows. J. Phys. Oceanogr., 24 , 66–75.

    • Search Google Scholar
    • Export Citation

  • Jungclaus, J. H., and M. Vanicek, 1999: Fractionally modified flow in a deep ocean channel: Application to the Vema Channel. J. Geophys. Res., 104 , (C9). 21123–21136.

    • Search Google Scholar
    • Export Citation

  • MacCready, P., and P. B. Rhines, 1993: Slippery bottom boundary layers on a slope. J. Phys. Oceanogr., 23 , 5–22.

  • Mauritzen, C., J. Price, T. Sanford, and D. Torres, 2005: Circulation and mixing in the Faroese channels. Deep-Sea Res. I, 52 , 883–913.

    • Search Google Scholar
    • Export Citation

  • Osborn, T. R., 1980: Estimates of the local rate of vertical diffusion from dissipation measurements. J. Phys. Oceanogr., 10 , 83–89.

    • Search Google Scholar
    • Export Citation

  • Peters, H., and W. E. Johns, 2005: Mixing and entrainment in the Red Sea outflow plume. Part II: Turbulence characteristics. J. Phys. Oceanogr., 35 , 584–600.

    • Search Google Scholar
    • Export Citation

  • Peters, H., W. E. Johns, A. S. Bower, and D. M. Fratantoni, 2005: Mixing and entrainment in the Red Sea outflow plume. Part I: Plume structure. J. Phys. Oceanogr., 35 , 569–583.

    • Search Google Scholar
    • Export Citation

  • Petrén, O., and G. Walin, 1976: Some observations of the deep flow in the Bornholm strait during the period June 1973–December 1974. Tellus, 28 , 74–87.

    • Search Google Scholar
    • Export Citation

  • Sherwin, T. J., 2010: Observations of the velocity profile of a fast and deep oceanic density current constrained in a gully. J. Geophys. Res., 115 , C03013. doi:10.1029/2009JC005557.

    • Search Google Scholar
    • Export Citation

  • Shih, L. H., J. R. Koseff, J. H. Ferziger, and C. R. Rehmann, 2000: Scaling and parameterization of stratified homogeneous turbulent shear flow. J. Fluid Mech., 412 , 1–20.

    • Search Google Scholar
    • Export Citation

  • Shih, L. H., J. R. Koseff, G. N. Ivey, and J. H. Ferziger, 2005: Parameterization of turbulent fluxes and scales using homogenous sheared stably stratified turbulence simulations. J. Fluid Mech., 525 , 193–214.

    • Search Google Scholar
    • Export Citation

  • Turner, J. S., 1986: Turbulent entrainment: the development of the entrainment assumption, and its applications to geophysical flows. J. Fluid Mech., 173 , 431–471.

    • Search Google Scholar
    • Export Citation

  • Umlauf, L., 2009: The description of mixing in stratified layers without shear in large-scale ocean models. J. Phys. Oceanogr., 39 , 3032–3039.

    • Search Google Scholar
    • Export Citation

  • Umlauf, L., and H. Burchard, 2003: A generic length-scale equation for geophysical turbulence models. J. Mar. Res., 61 , 235–265.

  • Umlauf, L., and H. Burchard, 2005: Second-order turbulence closure models for geophysical boundary layers. A review of recent work. Cont. Shelf Res., 25 , 795–827.

    • Search Google Scholar
    • Export Citation

  • Umlauf, L., and L. Arneborg, 2009a: Dynamics of rotating shallow gravity currents passing through a channel. Part I: Observation of transverse structure. J. Phys. Oceanogr., 39 , 2385–2401.

    • Search Google Scholar
    • Export Citation

  • Umlauf, L., and L. Arneborg, 2009b: Dynamics of rotating shallow gravity currents passing through a channel. Part II: Analysis. J. Phys. Oceanogr., 39 , 2402–2416.

    • Search Google Scholar
    • Export Citation

  • Umlauf, L., L. Arneborg, H. Burchard, V. Fiekas, H. U. Lass, V. Mohrholz, and H. Prandke, 2007: Transverse structure of turbulence in a rotating gravity current. Geophys. Res. Lett., 34 , L08601. doi:10.1029/2007GL029521.

    • Search Google Scholar
    • Export Citation

  • WÃ¥hlin, A. K., 2002: Topographic steering of dense currents with application to submarine canyons. Deep-Sea Res. I, 49 , 305–320.

    • Search Google Scholar
    • Export Citation

  • WÃ¥hlin, A. K., 2004: Downward channeling of dense water in topographic corrugations. Deep-Sea Res. I, 51 , 577–590.

  • WÃ¥hlin, A. K., and C. Cenedese, 2006: How entraining density currents influence the stratification in a one-dimensional ocean basin. Deep-Sea Res. II, 53 , 172–193.

    • Search Google Scholar
    • Export Citation

  • WÃ¥hlin, A. K., E. Darelius, C. Cenedese, and G. F. Lane-Serff, 2008: Laboratory observations of enhanced entrainment in dense overflows in the presence of submarine canyons and ridges. Deep-Sea Res. I, 55 , 737–750.

    • Search Google Scholar
    • Export Citation
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