• Caro, G. P., 2009: Direct numerical simulations of diffusive staircases in the Arctic. M.S. thesis, Dept. of Oceanography, Naval Postgraduate School, 61 pp.

  • Carpenter, J. R., , T. Sommer, , and A. Wüest, 2012: Simulations of a double-diffusive interface in the diffusive convection regime. J. Fluid Mech., 711, 411436, doi:10.1017/jfm.2012.399.

    • Search Google Scholar
    • Export Citation
  • Flanagan, J. D., , A. S. Lefler, , and T. Radko, 2013: Heat transport through diffusive interfaces. Geophys. Res. Lett., 40, 2466–2470, doi:10.1002/grl.50440.

    • Search Google Scholar
    • Export Citation
  • Hamilton, J. M., , M. R. Lewis, , and B. R. Ruddick, 1989: Vertical fluxes of nitrate associated with salt fingers in the world’s oceans. J. Geophys. Res., 94, 21372145, doi:10.1029/JC094iC02p02137.

    • Search Google Scholar
    • Export Citation
  • Huppert, H. E., 1971: On the stability of a series of double-diffusive layers. Deep-Sea Res. Oceanogr. Abstr., 18, 10051021, doi:10.1016/0011-7471(71)90005-2.

    • Search Google Scholar
    • Export Citation
  • Kelley, D. E., 1988: Explaining effective diffusivities within diffusive oceanic staircases. Small-Scale Turbulence and Mixing in the Ocean, J. C. J. Nihoul and B. M. Jamart, Eds., Elsevier, 481–502.

  • Kelley, D. E., 1990: Fluxes through diffusive staircases: A new formulation. J. Geophys. Res., 95, 33653371, doi:10.1029/JC095iC03p03365.

    • Search Google Scholar
    • Export Citation
  • Kelley, D. E., , H. J. S. Fernando, , A. E. Gargett, , J. Tanny, , and E. Ozsoy, 2003: The diffusive regime of double-diffusive convection. Prog. Oceanogr., 56, 461481.

    • Search Google Scholar
    • Export Citation
  • Kimura, S., , and W. D. Smyth, 2007: Direct numerical simulation of salt sheets and turbulence in a double-diffusive shear layer. Geophys. Res. Lett., 34, L21610, doi:10.1029/2007GL031935.

    • Search Google Scholar
    • Export Citation
  • Krishfield, R., , J. Toole, , A. Proshutinsky, , and M.-L. Timmermans, 2008: Automated ice-tethered profilers for seawater observations under pack ice in all seasons. J. Atmos. Oceanic Technol., 25, 20912095, doi:10.1175/2008JTECHO587.1.

    • Search Google Scholar
    • Export Citation
  • Kunze, E., 1987: Limits on growing, finite length salt fingers: A Richardson number constraint. J. Mar. Res., 45, 533556, doi:10.1357/002224087788326885.

    • Search Google Scholar
    • Export Citation
  • Kunze, E., 2003: A review of oceanic salt-fingering theory. Prog. Oceanogr., 56, 399417.

  • Linden, P. F., 1974: Salt fingers in a steady shear flow. Geophys. Fluid Dyn., 6, 127, doi:10.1080/03091927409365785.

  • Marmorino, G. O., , and D. R. Caldwell, 1976: Heat and salt transport through a diffusive thermohaline interface. Deep-Sea Res. Oceanogr. Abstr., 23, 5967, doi:10.1016/0011-7471(76)90808-1.

    • Search Google Scholar
    • Export Citation
  • Merryfield, W. J., 2000: Origin of thermohaline staircases. J. Phys. Oceanogr., 30, 10461068, doi:10.1175/1520-0485(2000)030<1046:OOTS>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Morell, J. M., , J. E. Corredor, , and W. J. Merryfield, 2006: Thermohaline staircases in a Caribbean eddy and mechanisms for staircase formation. Deep-Sea Res. II, 53, 128139, doi:10.1016/j.dsr2.2005.09.013.

    • Search Google Scholar
    • Export Citation
  • Neal, V. T., , S. Neshyba, , and W. Denner, 1969: Thermal stratification in the Arctic Ocean. Science, 166, 373374, doi:10.1126/science.166.3903.373.

    • Search Google Scholar
    • Export Citation
  • Neshyba, S., , V. T. Neal, , and W. W. Denner, 1971: Temperature and conductivity measurements under ice island T-3. J. Geophys. Res., 76, 81078120, doi:10.1029/JC076i033p08107.

    • Search Google Scholar
    • Export Citation
  • Padman, L., , and T. M. Dillon, 1987: Vertical heat fluxes through the Beaufort Sea thermohaline staircase. J. Geophys. Res., 92, 10 79910 806, doi:10.1029/JC092iC10p10799.

    • Search Google Scholar
    • Export Citation
  • Park, Y.-G., , J. A. Whitehead, , and A. Gnanadeskian, 1994: Turbulent mixing in stratified fluids: Layer formation and energetics. J. Fluid Mech., 279, 279311, doi:10.1017/S0022112094003915.

    • Search Google Scholar
    • Export Citation
  • Radko, T., 2003: A mechanism for layer formation in a double-diffusive fluid. J. Fluid Mech., 497, 365380, doi:10.1017/S0022112003006785.

    • Search Google Scholar
    • Export Citation
  • Radko, T., 2005: What determines the thickness of layers in a thermohaline staircase? J. Fluid Mech., 523, 7998, doi:10.1017/S0022112004002290.

    • Search Google Scholar
    • Export Citation
  • Radko, T., 2007: Mechanics of merging events for a series of layers in a stratified turbulent fluid. J. Fluid Mech., 577, 251273, doi:10.1017/S0022112007004703.

    • Search Google Scholar
    • Export Citation
  • Radko, T., 2008: The double-diffusive modon. J. Fluid Mech., 609, 5985, doi:10.1017/S0022112008002127.

  • Radko, T., 2013: Double-Diffusive Convection. Cambridge University Press, 344 pp.

  • Radko, T., , and D. P. Smith, 2012: Equilibrium transport in double-diffusive convection. J. Fluid Mech., 692, 527, doi:10.1017/jfm.2011.343.

    • Search Google Scholar
    • Export Citation
  • Radko, T., , A. Bulters, , J. Flanagan, , and J.-M. Campin, 2014: Double-diffusive recipes. Part I: Large-scale dynamics of thermohaline staircases. J. Phys. Oceanogr.,44, 1269–1284, doi:10.1175/JPO-D-13-0155.1.

    • Search Google Scholar
    • Export Citation
  • Ruddick, B. R., , T. J. McDougall, , and J. S. Turner, 1989: The formation of layers in a uniformly stirred density gradient. Deep-Sea Res., 36, 597609, doi:10.1016/0198-0149(89)90009-5.

    • Search Google Scholar
    • Export Citation
  • Schmitt, R. W., 1979a: Flux measurements on salt fingers at an interface. J. Mar. Res., 37, 419436.

  • Schmitt, R. W., 1979b: Flux measurements in an interface. J. Mar. Res., 37, 419436.

  • Schmitt, R. W., 1994: Double diffusion in oceanography. Annu. Rev. Fluid Mech., 26, 255285, doi:10.1146/annurev.fl.26.010194.001351.

  • Stellmach, S., , A. Traxler, , P. Garaud, , N. Brummell, , and T. Radko, 2011: Dynamics of fingering convection. Part 2: The formation of thermohaline staircases. J. Fluid Mech., 677, 554571, doi:10.1017/jfm.2011.99.

    • Search Google Scholar
    • Export Citation
  • Stern, M. E., 1969: Collective instability of salt fingers. J. Fluid Mech., 35, 209218, doi:10.1017/S0022112069001066.

  • Stern, M. E., , T. Radko, , and J. Simeonov, 2001: 3D salt fingers in an unbounded thermocline with application to the central ocean. J. Mar. Res., 59, 355390, doi:10.1357/002224001762842244.

    • Search Google Scholar
    • Export Citation
  • Timmermans, M.-L., , J. Toole, , R. Krishfield, , and P. Winsor, 2008: Ice-tethered profiler observations of the double-diffusive staircase in the Canada Basin thermohaline. J. Geophys. Res., 113, C00A02, doi:10.1029/2008JC004829.

    • Search Google Scholar
    • Export Citation
  • Toole, J. M., , R. A. Krishfield, , M.-L. Timmermans, , and A. Proshutinsky, 2011: The ice-tethered profiler: Argo of the Arctic. Oceanography, 24, 126135, doi:10.5670/oceanog.2011.64.

    • Search Google Scholar
    • Export Citation
  • Traxler, A., , S. Stellmach, , P. Garaud, , T. Radko, , and N. Brummel, 2011: Dynamics of fingering convection. Part 1: Small-scale fluxes and large-scale instabilities. J. Fluid Mech., 677, 530553.

    • Search Google Scholar
    • Export Citation
  • Turner, J. S., 1965: The coupled turbulent transports of salt and heat across a sharp density interface. Int. J. Heat Mass Transfer, 8, 759767, doi:10.1016/0017-9310(65)90022-0.

    • Search Google Scholar
    • Export Citation
  • Turner, J. S., 1967: Salt fingers across a density interface. Deep-Sea Res. Oceanogr. Abstr., 14, 599608, doi:10.1016/0011-7471(67)90066-6.

    • Search Google Scholar
    • Export Citation
  • Turner, J. S., 1973: Buoyancy Effects in Fluids. Cambridge University Press, 368 pp.

  • Zodiatis, G., , and G. P. Gasparini, 1996: Thermohaline staircase formations in the Tyrrhenian Sea. Deep-Sea Res., 43, 655678, doi:10.1016/0967-0637(96)00032-5.

    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 67 67 5
PDF Downloads 64 64 0

Double-Diffusive Recipes. Part II: Layer-Merging Events

View More View Less
  • 1 Department of Oceanography, Naval Postgraduate School, Monterey, California
  • | 2 Institut für Geophysik, Westfälische Wilhelms-Universität Münster, Münster, Germany
  • | 3 Department of Geology and Geophysics, Yale University, New Haven, Connecticut
© Get Permissions Rent on DeepDyve
Restricted access

Abstract

This study explores the dynamics of thermohaline staircases: well-defined stepped structures in temperature and salinity profiles, commonly observed in regions of active double diffusion. The evolution of staircases in time is frequently characterized by spontaneous layer-merging events. These phenomena, the authors argue, are essential in regulating the equilibrium layer thickness in fully developed staircases. The pattern and mechanics of merging events are explained using a combination of analytical considerations, direct numerical simulations, and data analysis. The theoretical merger model is based on the stability analysis for a series of identical steps and pertains to both forms of double diffusion: diffusive convection and salt fingering. The conceptual significance of the proposed model lies in its ability to describe merging events without assuming from the outset specific power laws for the vertical transport of heat and salt—the approach adopted by earlier merging models. The analysis of direct numerical simulations indicates that merging models based on the four-thirds flux laws offer adequate qualitative description of the evolutionary patterns but are less accurate than models that do not rely on such laws. Specific examples considered in this paper include the evolution of layers in the diffusive staircase in the Beaufort Gyre of the Arctic Ocean.

Corresponding author address: T. Radko, Department of Oceanography, Naval Postgraduate School, 833 Dyer Road, Bldg. 232, Room 328, Monterey, CA 93943. E-mail: tradko@nps.edu

Abstract

This study explores the dynamics of thermohaline staircases: well-defined stepped structures in temperature and salinity profiles, commonly observed in regions of active double diffusion. The evolution of staircases in time is frequently characterized by spontaneous layer-merging events. These phenomena, the authors argue, are essential in regulating the equilibrium layer thickness in fully developed staircases. The pattern and mechanics of merging events are explained using a combination of analytical considerations, direct numerical simulations, and data analysis. The theoretical merger model is based on the stability analysis for a series of identical steps and pertains to both forms of double diffusion: diffusive convection and salt fingering. The conceptual significance of the proposed model lies in its ability to describe merging events without assuming from the outset specific power laws for the vertical transport of heat and salt—the approach adopted by earlier merging models. The analysis of direct numerical simulations indicates that merging models based on the four-thirds flux laws offer adequate qualitative description of the evolutionary patterns but are less accurate than models that do not rely on such laws. Specific examples considered in this paper include the evolution of layers in the diffusive staircase in the Beaufort Gyre of the Arctic Ocean.

Corresponding author address: T. Radko, Department of Oceanography, Naval Postgraduate School, 833 Dyer Road, Bldg. 232, Room 328, Monterey, CA 93943. E-mail: tradko@nps.edu
Save