• Alexakis, A., 2005: On Holmboe’s instability for smooth shear and density profiles. Phys. Fluids, 17, 084103, https://doi.org/10.1063/1.2001567.

  • Baines, P. G. G., and A. E. Gill, 1969: On thermohaline convection with linear gradients. J. Fluid Mech., 37, 289306, https://doi.org/10.1017/S0022112069000553.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bebieva, Y., and M.-L. Timmermans, 2017: The relationship between double-diffusive intrusions and staircases in the Arctic Ocean. J. Phys. Oceanogr., 47, 867878, https://doi.org/10.1175/JPO-D-16-0265.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bebieva, Y., and M.-L. Timmermans, 2019: Double-diffusive layering in the Canada basin: An explanation of along-layer temperature and salinity gradients. J. Geophys. Res. Oceans, 124, 723735, https://doi.org/10.1029/2018JC014368.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Blass, A., X. Zhu, R. Verzicco, D. Lohse, and R. J. A. M. Stevens, 2019: Flow organization and heat transfer in turbulent wall sheared thermal convection. J. Fluid Mech., 897, A22, https://doi.org/10.1017/JFM.2020.378.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Boldrin, A., and S. Rabbitti, 1990: Hydrography of the brines in the Bannock and Tyro anoxic basins (eastern Mediterranean). Mar. Chem., 31, 2133, https://doi.org/10.1016/0304-4203(90)90029-C.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Brown, J. M., and T. Radko, 2019: Initiation of diffusive layering by time-dependent shear. J. Fluid Mech., 858, 588608, https://doi.org/10.1017/jfm.2018.790.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Canuto, C., M. Y. Hussaini, A. Quarteroni, and T. A. Zang, 2007: Spectral Methods: Evolution to Complex Geometries and Applications to Fluid Dynamics. Springer, 596 pp.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Carpenter, J. R., and M.-L. Timmermans, 2014: Does rotation influence double-diffusive fluxes in polar oceans? J. Phys. Oceanogr., 44, 289296, https://doi.org/10.1175/JPO-D-13-098.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 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, https://doi.org/10.1017/jfm.2012.399.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Cole, S. T., M.-L. Timmermans, J. M. Toole, R. A. Krishfield, and F. T. Thwaites, 2014: Ekman veering, internal waves, and turbulence observed under Arctic Sea ice. J. Phys. Oceanogr., 44, 13061328, https://doi.org/10.1175/JPO-D-12-0191.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Flanagan, J. D., A. S. Lefler, and T. Radko, 2013: Heat transport through diffusive interfaces. Geophys. Res. Lett., 40, 24662470, https://doi.org/10.1002/grl.50440.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Foster, T. D., and E. C. Carmack, 1976: Temperature and salinity structure in the Weddell Sea. J. Phys. Oceanogr., 6, 3644, https://doi.org/10.1175/1520-0485(1976)006<0036:TASSIT>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Guthrie, J. D., I. Fer, and J. H. Morison, 2017: Thermohaline staircases in the Amundsen Basin: Possible disruption by shear and mixing. J. Geophys. Res. Oceans, 122, 77677782, https://doi.org/10.1002/2017JC012993.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Holmboe, J., 1962: On the behavior of symmetric waves in stratified shear layers. Geofys. Publ., 24, 67 113.

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

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kelley, D. E., H. J. S. Fernando, A. E. Gargett, J. Tanny, and E. Özsoy, 2003: The diffusive regime of double-diffusive convection. Prog. Oceanogr., 56, 461481, https://doi.org/10.1016/S0079-6611(03)00026-0.

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

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Konopliv, N., L. Lesshafft, and E. Meiburg, 2018: The influence of shear on double-diffusive and settling-driven instabilities. J. Fluid Mech., 849, 902926, https://doi.org/10.1017/jfm.2018.432.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kwok, R., and N. Untersteiner, 2011: The thinning of Arctic Sea ice. Phys. Today, 64, 3641, https://doi.org/10.1063/1.3580491.

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

  • Lipps, F. B., 1971: Two-dimensional numerical experiments in thermal convection with vertical shear. J. Atmos. Sci., 28, 319, https://doi.org/10.1175/1520-0469(1971)028<0003:TDNEIT>2.0.CO;2.

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

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

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

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Noguchi, T., and H. Niino, 2010: Multi-layered diffusive convection. Part I. Spontaneous layer formation. J. Fluid Mech., 651, 443464, https://doi.org/10.1017/S0022112009994150.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Orszag, S. A., 1969: Numerical methods for the simulation of turbulence. Phys. Fluids, 12, II–250, https://doi.org/10.1063/1.1692445.

  • Padman, L., 1994: Momentum fluxes through sheared oceanic thermohaline steps. J. Geophys. Res., 99, 22 49122 499, https://doi.org/10.1029/94JC01741.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Polyakov, I. V., L. Padman, Y. D. Lenn, A. Pnyushkov, R. Rember, and V. V. Ivanov, 2019: Eastern Arctic Ocean diapycnal heat fluxes through large double-diffusive steps. J. Phys. Oceanogr., 49, 227246, https://doi.org/10.1175/JPO-D-18-0080.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Radko, T., 2013: Double-Diffusive Convection. Cambridge University Press, 342 pp.

  • Radko, T., 2016: Thermohaline layering in dynamically and diffusively stable shear flows. J. Fluid Mech., 805, 147170, https://doi.org/10.1017/jfm.2016.547.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Radko, T., 2019: Thermohaline-shear instability. Geophys. Res. Lett., 46, 822832, https://doi.org/10.1029/2018GL081009.

  • Rogallo, R. S., 1981: Numerical experiments in homogeneous turbulence. NASA Tech. Memo. 81315, 91 pp., https://ntrs.nasa.gov/api/citations/19810022965/downloads/19810022965.pdf.

  • Shibley, N. C., M.-L. Timmermans, J. R. Carpenter, and J. M. Toole, 2017: Spatial variability of the Arctic Ocean’s double-diffusive staircase. J. Geophys. Res. Oceans, 122, 980994, https://doi.org/10.1002/2016JC012419.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Simpson, J. H., M. R. Howe, N. C. G. Morris, and J. Stratford, 1979: Velocity shear in the steps below the Mediterranean outflow. Deep Sea Res., 26A, 13811386, https://doi.org/10.1016/0198-0149(79)90005-0.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Smyth, W. D., and S. Kimura, 2007: Instability and diapycnal momentum transport in a double-diffusive, stratified shear layer. J. Phys. Oceanogr., 37, 15511565, https://doi.org/10.1175/JPO3070.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Smyth, W. D., and J. R. Carpenter, 2019: Instability in Geophysical Flows. Cambridge University Press, 328 pp.

  • Sommer, T., J. Carpenter, M. Schmid, R. Lueck, M. Schurter, and A. Wuest, 2013: Interface structure and flux laws in a natural double-diffusive layering. J. Geophys. Res. Oceans, 118, 60926106, https://doi.org/10.1002/2013JC009166.

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

  • Stranne, C., and et al. , 2017: Acoustic mapping of thermohaline staircases in the Arctic Ocean. Sci. Rep., 7, 15192, https://doi.org/10.1038/s41598-017-15486-3.

    • Crossref
    • 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 thermocline. J. Geophys. Res., 113, C00A02, https://doi.org/10.1029/2008JC004829.

    • Search Google Scholar
    • Export Citation
  • Traxler, A. L., S. Stellmach, P. Garaud, T. Radko, and N. H. Brummell, 2011: Dynamics of fingering convection. Part I Small-scale fluxes and large-scale instabilities. J. Fluid Mech., 677, 530553, https://doi.org/10.1017/jfm.2011.98.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Turner, J. S., 1968: The behaviour of a stable salinity gradient heated from below. J. Fluid Mech., 33, 183200, https://doi.org/10.1017/S0022112068002442.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Turner, J. S., 2010: The melting of ice in the Arctic Ocean: The influence of double-diffusive transport of heat from below. J. Phys. Oceanogr., 40, 249256, https://doi.org/10.1175/2009JPO4279.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Turner, J. S., and H. Stommel, 1964: A new case of convection in the presence of combined vertical salinity and temperature gradients. Proc. Natl. Acad. Sci. USA., 52, 4953, https://doi.org/10.1073%2FPNAS.52.1.49.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Turner, J. S., and G. Veronis, 2004: The influence of double-diffusive processes on the melting of ice in the Arctic Ocean: Laboratory analogue experiments and their interpretation. J. Mar. Syst., 45, 2137, https://doi.org/10.1016/j.jmarsys.2003.06.002.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Walin, G., 1964: Note on the stability of water stratified by both salt and heat. Tellus, 16A, 389393, https://doi.org/10.1111/j.2153-3490.1964.tb00175.x.

    • Search Google Scholar
    • Export Citation
  • Wells, M. G., R. W. Griffiths, and J. S. Turner, 2001: Generation of density fine structure by salt fingers in a spatially periodic shear. J. Geophys. Res., 106, 70277036, https://doi.org/10.1029/2000JC000620.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Yang, Y., R. Verzicco, and D. Lohse, 2016: Vertically bounded double diffusive convection in the finger regime: Comparing no-slip versus free-slip boundary conditions. Phys. Rev. Lett., 117, 184501, https://doi.org/10.1103/PhysRevLett.117.184501.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zaussinger, F., and F. Kupka, 2018: Layer formation in double-diffusive convection over resting and moving heated plates. Theor. Comput. Fluid Dyn., 33, 383409, https://doi.org/10.1007/s00162-019-00499-7.

    • Crossref
    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 159 159 14
Full Text Views 59 59 5
PDF Downloads 97 97 8

Diffusive Staircases in Shear: Dynamics and Heat Transport

View More View Less
  • 1 a Naval Postgraduate School, Monterey, California
© Get Permissions Rent on DeepDyve
Restricted access

Abstract

Arctic staircases mediate the heat transport from the warm water of Atlantic origin to the cooler waters of the Arctic mixed layer. For this reason, staircases have received much due attention from the community, and their heat transport has been well characterized for systems in the absence of external forcing. However, the ocean is a dynamic environment with large-scale currents and internal waves being omnipresent, even in regions shielded by sea ice. Thus, we have attempted to address the effects of background shear on fully developed staircases using numerical simulations. The code, which is pseudospectral, solves the governing equations for a Boussinesq fluid with temperature and salinity in a shearing coordinate system. We find that—unlike many other double-diffusive systems—the sheared staircase requires three-dimensional simulations to properly capture the dynamics. Our simulations predict shear patterns that are consistent with observations and show that staircases in the presence of external shear should be expected to transport heat and salt at least twice as efficiently as in the corresponding nonsheared systems. These findings may lead to critical improvements in the representation of microscale mixing in global climate models.

For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Justin M. Brown, jmbrown2@nps.edu

Abstract

Arctic staircases mediate the heat transport from the warm water of Atlantic origin to the cooler waters of the Arctic mixed layer. For this reason, staircases have received much due attention from the community, and their heat transport has been well characterized for systems in the absence of external forcing. However, the ocean is a dynamic environment with large-scale currents and internal waves being omnipresent, even in regions shielded by sea ice. Thus, we have attempted to address the effects of background shear on fully developed staircases using numerical simulations. The code, which is pseudospectral, solves the governing equations for a Boussinesq fluid with temperature and salinity in a shearing coordinate system. We find that—unlike many other double-diffusive systems—the sheared staircase requires three-dimensional simulations to properly capture the dynamics. Our simulations predict shear patterns that are consistent with observations and show that staircases in the presence of external shear should be expected to transport heat and salt at least twice as efficiently as in the corresponding nonsheared systems. These findings may lead to critical improvements in the representation of microscale mixing in global climate models.

For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Justin M. Brown, jmbrown2@nps.edu
Save