Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-23T09:27:32.736Z Has data issue: false hasContentIssue false
  • English
  • Français

Initiation of diffusive layering by time-dependent shear

Published online by Cambridge University Press:  06 November 2018

Justin M. Brown Open the ORCID record for Justin M. Brown [Opens in a new window]  and
Timour Radko Open the ORCID record for Timour Radko [Opens in a new window]
Justin M. Brown*
Affiliation:
Department of Oceanography, Naval Postgraduate School, 1 University Circle, Monterey, CA 93943, USA
Timour Radko
Affiliation:
Department of Oceanography, Naval Postgraduate School, 1 University Circle, Monterey, CA 93943, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The Arctic halocline is generally stable to the development of double-diffusive and dynamic instabilities – the two major sources of small-scale mixing in the mid-latitude oceans. Despite this, observations show the abundance of double-diffusive staircases in the Arctic Ocean, which suggests the presence of some destabilizing process facilitating the transition from smooth-gradient to layered stratification. Recent studies have shown that an instability can develop in such circumstances if weak static shear is present even when the flow is dynamically and diffusively stable. However, the impact of oscillating shear, associated with the presence of internal gravity waves, has not yet been addressed for the diffusive case. Through two-dimensional simulations of diffusive convection, we have investigated the impact of the magnitude and frequency of externally forced oscillatory shear on the thermohaline-shear instability. Simulations with stochastic shear – characterized by a continuous spectrum of frequencies from inertial to buoyancy – indicate that thermohaline layering does occur due to the presence of destabilizing modes (oscillations of near the buoyancy frequency). These simulations show that such layers appear as well-defined steps in the temperature and salinity profiles. Thus, the thermohaline-shear instability is a plausible mechanism for staircase formation in the Arctic and merits substantial future study.

JFM classification

Convection: Double diffusive convection Geophysical and Geological Flows: Internal waves Geophysical and Geological Flows: Ocean processes
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 858 , 10 January 2019 , pp. 588 - 608
Check for updates
Copyright
© 2018 Cambridge University Press 

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

Baines, P. G. G. & Gill, A. E. 1969 On thermohaline convection with linear gradients. J. Fluid Mech. 37 (02), 289–306.Google Scholar
Bebieva, Y. & Timmermans, M.-L. 2017 The relationship between double-diffusive intrusions and staircases in the arctic ocean. J. Phys. Oceanogr. 47 (4), 867–878.Google Scholar
Carpenter, J. R., Sommer, T. & Wüest, A. 2012 Simulations of a double-diffusive interface in the diffusive convection regime. J. Fluid Mech. 711, 411–436.Google Scholar
Cole, S. T., Timmermans, M.-L., Toole, J. M., Krishfield, R. A. & Thwaites, F. T. 2014 Ekman veering, internal waves, and turbulence observed under arctic sea ice. J. Phys. Oceanogr. 44 (5), 1306–1328.Google Scholar
Crapper, P. F. 1976 Fluxes of heat and salt across a diffusive interface in the presence of grid generated turbulence. Intl J. Heat Mass Transfer 19 (12), 1371–1378.Google Scholar
Flanagan, J. D., Lefler, A. S. & Radko, T. 2013 Heat transport through diffusive interfaces. Geophys. Res. Lett. 40 (10), 2466–2470.Google Scholar
Flanagan, J. D., Radko, T., Shaw, W. J. & Stanton, T. P. 2014 Dynamic and double-diffusive instabilities in a weak pycnocline. Part II. Direct numerical simulations and flux laws. J. Phys. Oceanogr. 44 (8), 1992–2012.Google Scholar
Garaud, P. 2017 The formation of diffusive staircases. J. Fluid Mech. 812, 1–4.Google Scholar
Garrett, C. & Munk, W. 1972 Space–time scales of internal waves. Geophys. Astrophys. Fluid Dyn. 3 (1), 225–264.Google Scholar
Guthrie, J. D., Morison, J. H. & Fer, I. 2013 Revisiting internal waves and mixing in the Arctic Ocean. J. Geophys. Res. Oceans 118 (8), 3966–3977.Google Scholar
Huppert, H. E. 1971 On the stability of a series of double-diffusive layers. Deep-Sea Res. Oceanogr. Abstr. 18 (10), 1005–1021.Google Scholar
Huppert, H. E. & Linden, P. F. 1979 On heating a stable salinity gradient from below. J. Fluid Mech. 95 (03), 431–464.Google Scholar
Levine, M. D., Paulson, C. A. & Morison, J. H. 1987 Observations of internal gravity waves under the Arctic pack ice. J. Geophys. Res. Oceans 92 (C), 779–782.Google Scholar
Malkus, W. V. R. 1954 The heat transport and spectrum of thermal turbulence. Proc. R. Soc. Lond. A 225 (1161), 196–212.Google Scholar
Merryfield, W. J. 2000 Origin of thermohaline staircases. J. Phys. Oceanogr. 30 (5), 1046–1068.Google Scholar
Molemaker, M. J. & Dijkstra, H. A. 1997 The formation and evolution of a diffusive interface. J. Fluid Mech. 331, 199–229.Google Scholar
Neal, V. T., Neshyba, S. & Denner, W. 1969 Thermal stratification in the arctic ocean. Science 166 (3903), 373–374.Google Scholar
Neshyba, S., Neal, V. T. & Denner, W. 1971 Temperature and conductivity measurements under Ice Island T-3. J. Geophys. Res. 76 (3), 8107–8120.Google Scholar
Noguchi, T. & Niino, H. 2010 Multi-layered diffusive convection. Part 2. Dynamics of layer evolution. J. Fluid Mech. 651, 443–464.Google Scholar
Osborn, T. R. & Cox, C. S. 1972 Oceanic fine structure. Geophys. Astrophys. Fluid Dyn. 3 (1), 321–345.Google Scholar
Perkin, R. G. & Lewis, E. L. 1984 Mixing in the West spitsbergen current. Am. Meteorol. Soc. 14 (8), 1315–1325.Google Scholar
Radko, T. 2003 A mechanism for layer formation in a double-diffusive fluid. J. Fluid Mech. 497, 365–380.Google Scholar
Radko, T. 2005 What determines the thickness of layers in a thermohaline staircase? J. Fluid Mech. 523, 79–98.Google Scholar
Radko, T. 2013 Double-diffusive Convection. Cambridge University Press.Google Scholar
Radko, T. 2016 Thermohaline layering in dynamically and diffusively stable shear flows. J. Fluid Mech. 805, 147–170.Google Scholar
Radko, T., Ball, J., Colosi, J. & Flanagan, J. D. 2015 Double-diffusive convection in a stochastic shear. J. Phys. Oceanogr. 45 (12), 3155–3167.Google Scholar
Rudels, B., Kuzmina, N., Schauer, U. E., Stipa, T. & Zhurbas, V. 2009 Double-diffusive convection and interleaving in the arctic ocean – distribution and importance. Geophysica 45 (1–2), 199–213.Google Scholar
Shibley, N. C., Timmermans, M.-L., Carpenter, J. R. & Toole, J. M. 2017 Spatial variability of the Arctic Ocean’s double-diffusive staircase. J. Geophys. Res. Oceans 122 (2), 980–994.Google Scholar
Shraiman, B. I. & Siggia, E. D. 1990 Heat transport in high-Rayleigh-number convection. Phys. Rev. A 42 (6), 3650–3653.Google Scholar
Stern, M. E. 1960 The ‘Salt-Fountain’ and thermohaline convection. Tellus A 12 (2), 172–175.Google Scholar
Timmermans, M.-L., Garrett, C. & Carmack, E. 2003 The thermohaline structure and evolution of the deep waters in the Canada Basin, Arctic Ocean. Deep Sea Res. 50 (10–11), 1305–1321.Google Scholar
Timmermans, M.-L., Toole, J., Krishfield, R. & Winsor, P. 2008 Ice-Tethered Profiler observations of the double-diffusive staircase in the Canada Basin thermocline. J. Geophys. Res. 113 (C7), C00A02.Google Scholar
Traxler, A. L., Stellmach, S., Garaud, P., Radko, T. & Brummell, N. H. 2011 Dynamics of fingering convection. Part 1 Small-scale fluxes and large-scale instabilities. J. Fluid Mech. 677, 530–553.Google Scholar
Turner, J. S. 1965 The coupled turbulent transports of salt and and heat across a sharp density interface. Intl J. Heat Mass Transfer 8 (5), 759–767.Google Scholar
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 (1), 249–256.Google Scholar
Turner, J. S. & Stommel, H. 1964 A new case of convection in the presence of combined vertical salinity and temperature gradients. Proc. Nat. Acad. Sci. 52 (1), 49–53.Google Scholar
Walin, G. 1964 Note on the stability of water stratified by both salt and heat. Tellus A 16 (3), 389–393.Google Scholar