Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-11-23T12:53:36.237Z Has data issue: false hasContentIssue false
  • English
  • Français

Thermohaline staircase formation in the diffusive convection regime: a theory based upon stratified turbulence asymptotics

Published online by Cambridge University Press:  22 November 2021

Yuchen Ma Open the ORCID record for Yuchen Ma [Opens in a new window]  and
W.R. Peltier
Yuchen Ma*
Affiliation:
Department of Physics, University of Toronto, 60 St George Street, Toronto, ON M5R 2M8, Canada
W.R. Peltier
Affiliation:
Department of Physics, University of Toronto, 60 St George Street, Toronto, ON M5R 2M8, Canada
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We describe a mechanism that leads to the spontaneous formation of a thermohaline staircase in the high-latitude oceans. Our analysis of this mechanism is based upon a model in which uniform gradients of temperature and salinity are assumed and is applied to a simplified mean-field model of stratified turbulence. Detailed analysis employs a parametrization of turbulent diapycnal diffusivities (Bouffard & Boegman, Dyn. Atmos. Oceans, vol. 61, 2013, pp. 14–34). This parametrization is apparently unique in that it distinguishes between the diapycnal diffusivities for heat and salt on the basis of their Prandtl (Schmidt) numbers. Our model predicts that the temperature and salinity profiles will be susceptible to linear instability if the buoyancy Reynolds number lies in the range 0.18–91, and a nonlinear mean-field model simulation demonstrates that it evolves into a well-defined thermohaline staircase that matches the characteristics of those found in the high-latitude oceans. The criterion for initial instability is furthermore shown to be consistent with the observed regional variability of staircase occurrence in the Arctic Ocean as determined by the most recent observational datasets.

JFM classification

Geophysical and Geological Flows: Stratified flows Instability: Nonlinear instability Mixing: Turbulent mixing
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 931 , 25 January 2022 , R4
Check for updates
Copyright
© The Author(s), 2021. Published by 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

REFERENCES

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.CrossRefGoogle Scholar
Bouffard, D. & Boegman, L. 2013 A diapycnal diffusivity model for stratified environmental flows. Dyn. Atmos. Oceans 61, 14–34.CrossRefGoogle Scholar
Brown, J.M. & Radko, T. 2019 Initiation of diffusive layering by time-dependent shear. J. Fluid Mech. 858, 588–608.CrossRefGoogle 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.CrossRefGoogle Scholar
Caulfield, C.P. 2021 Layering, instabilities, and mixing in turbulent stratified flows. Annu. Rev. Fluid Mech. 53, 113–145.CrossRefGoogle Scholar
Chanona, M., Waterman, S. & Gratton, Y. 2018 Variability of internal wave-driven mixing and stratification in Canadian arctic shelf and shelf-slope waters. J. Geophys. Res.: Oceans 123 (12), 9178–9195.CrossRefGoogle Scholar
Dosser, H.V., Chanona, M., Waterman, S., Shibley, N.C. & Timmermans, M.-L. 2021 Changes in internal wave-driven mixing across the Arctic Ocean: finescale estimates from an 18-year pan-arctic record. Geophys. Res. Lett. 48 (8), e2020GL091747.CrossRefGoogle Scholar
Gregg, M.C., D'Asaro, E.A., Riley, J.J. & Kunze, E. 2018 Mixing efficiency in the ocean. Ann. Rev. Mar. Sci. 10, 443–473.CrossRefGoogle ScholarPubMed
Guthrie, J.D., Fer, I. & Morison, J.H. 2017 Thermohaline staircases in the Amundsen Basin: possible disruption by shear and mixing. J. Geophys. Res.: Oceans 122 (10), 7767–7782.CrossRefGoogle Scholar
Jackson, P.R. & Rehmann, C.R. 2003 Laboratory measurements of differential diffusion in a diffusively stable, turbulent flow. J. Phys. Oceanogr. 33 (8), 1592–1603.CrossRefGoogle Scholar
Kelley, D.E., Fernando, H.J.S., Gargett, A.E., Tanny, J. & Özsoy, E. 2003 The diffusive regime of double-diffusive convection. Prog. Oceanogr. 56 (3–4), 461–481.CrossRefGoogle Scholar
Krishfield, R., Toole, J., Proshutinsky, A. & Timmermans, M.-L. 2008 Automated Ice-Tethered Profilers for seawater observations under pack ice in all seasons. J. Atmos. Ocean. Technol. 25 (11), 2091–2105.CrossRefGoogle Scholar
Linden, P.F. & Shirtcliffe, T.G.L. 1978 The diffusive interface in double-diffusive convection. J. Fluid Mech. 87 (3), 417–432.CrossRefGoogle Scholar
Ma, Y. & Peltier, W.R. 2021 a Gamma instability in an inhomogeneous environment and salt-fingering staircase trapping: determining the step size. Phys. Rev. Fluids 6 (3), 033903.CrossRefGoogle Scholar
Ma, Y. & Peltier, W.R. 2021 b Parametrization of irreversible diapycnal diffusivity in salt-fingering turbulence using DNS. J. Fluid Mech. 911, A9.CrossRefGoogle Scholar
Merryfield, W.J. 2000 Origin of thermohaline staircases. J. Phys. Oceanogr. 30 (5), 1046–1068.2.0.CO;2>CrossRefGoogle Scholar
Neal, V.T., Neshyba, S. & Denner, W. 1969 Thermal stratification in the Arctic Ocean. Science 166 (3903), 373–374.CrossRefGoogle ScholarPubMed
Osborn, T.R. 1980 Estimates of the local rate of vertical diffusion from dissipation measurements. J. Phys. Oceanogr. 10 (1), 83–89.2.0.CO;2>CrossRefGoogle Scholar
Padman, L. & Dillon, T.M. 1987 Vertical heat fluxes through the Beaufort Sea thermohaline staircase. J. Geophys. Res.: Oceans 92 (C10), 10799–10806.CrossRefGoogle Scholar
Peltier, W.R. & Caulfield, C.P. 2003 Mixing efficiency in stratified shear flows. Annu. Rev. Fluid Mech. 35 (1), 135–167.CrossRefGoogle Scholar
Phillips, O.M. 1972 Turbulence in a strongly stratified fluid—is it unstable? In Deep Sea Research and Oceanographic Abstracts, vol. 19, pp. 79–81. Elsevier.CrossRefGoogle Scholar
Polzin, K.L., Toole, J.M. & Schmitt, R.W. 1995 Finescale parameterizations of turbulent dissipation. J. Phys. Oceanogr. 25 (3), 306–328.2.0.CO;2>CrossRefGoogle Scholar
Radko, T. 2003 A mechanism for layer formation in a double-diffusive fluid. J. Fluid Mech. 497, 365–380.CrossRefGoogle Scholar
Radko, T. 2005 What determines the thickness of layers in a thermohaline staircase? J. Fluid Mech. 523, 79–98.CrossRefGoogle Scholar
Radko, T. 2007 Mechanics of merging events for a series of layers in a stratified turbulent fluid. J. Fluid Mech. 577, 251–273.CrossRefGoogle Scholar
Radko, T. 2013 Double-Diffusive Convection. Cambridge University Press.CrossRefGoogle Scholar
Radko, T. 2016 Thermohaline layering in dynamically and diffusively stable shear flows. J. Fluid Mech. 805, 147–170.CrossRefGoogle Scholar
Radko, T. 2019 a Thermohaline layering on the microscale. J. Fluid Mech. 862, 672–695.CrossRefGoogle Scholar
Radko, T. 2019 b Thermohaline-shear instability. Geophys. Res. Lett. 46 (2), 822–832.CrossRefGoogle Scholar
Rehmann, C.R. & Koseff, J.R. 2004 Mean potential energy change in stratified grid turbulence. Dyn. Atmos. Oceans 37 (4), 271–294.CrossRefGoogle Scholar
Salehipour, H., Peltier, W.R., Whalen, C.B. & MacKinnon, J.A. 2016 A new characterization of the turbulent diapycnal diffusivities of mass and momentum in the ocean. Geophys. Res. Lett. 43 (7), 3370–3379.CrossRefGoogle Scholar
Schmitt, R.W. 1994 Double diffusion in oceanography. Annu. Rev. Fluid Mech. 26 (1), 255–285.CrossRefGoogle Scholar
Shaw, W.J. & Stanton, T.P. 2014 Vertical diffusivity of the Western Arctic Ocean halocline. J. Geophys. Res.: Oceans 119 (8), 5017–5038.CrossRefGoogle Scholar
Shibley, N.C. & Timmermans, M.-L. 2019 The formation of double-diffusive layers in a weakly turbulent environment. J. Geophys. Res.: Oceans 124 (3), 1445–1458.CrossRefGoogle 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.CrossRefGoogle Scholar
Shih, L.H., Koseff, J.R., Ivey, G.N. & Ferziger, J.H. 2005 Parameterization of turbulent fluxes and scales using homogeneous sheared stably stratified turbulence simulations. J. Fluid Mech. 525, 193–214.CrossRefGoogle Scholar
Smyth, W.D., Nash, J.D. & Moum, J.N. 2005 Differential diffusion in breaking Kelvin–Helmholtz billows. J. Phys. Oceanogr. 35 (6), 1004–1022.CrossRefGoogle Scholar
Stellmach, S., Traxler, A., Garaud, P., Brummell, N. & Radko, T. 2011 Dynamics of fingering convection. Part 2. The formation of thermohaline staircases. J. Fluid Mech. 677, 554–571.CrossRefGoogle Scholar
Tait, R.I. & Howe, M.R. 1968 Some observations of thermo-haline stratification in the deep ocean. In Deep Sea Research and Oceanographic Abstracts, vol. 15, pp. 275–280. Elsevier.CrossRefGoogle Scholar
Taylor, J.R. & Zhou, Q. 2017 A multi-parameter criterion for layer formation in a stratified shear flow using sorted buoyancy coordinates. J. Fluid Mech. 823, R5.CrossRefGoogle 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.: Oceans 113 (C1).CrossRefGoogle Scholar
Toole, J.M., Krishfield, R.A., Timmermans, M.-L. & Proshutinsky, A. 2011 The Ice-Tethered Profiler: Argo of the Arctic. Oceanography 24 (3), 126–135.CrossRefGoogle Scholar
Traxler, A., Stellmach, S., Garaud, P., Radko, T. & Brummell, N. 2011 Dynamics of fingering convection. Part 1. Small-scale fluxes and large-scale instabilities. J. Fluid Mech. 677, 530–553.CrossRefGoogle Scholar
Van Der Boog, C.G., Koetsier, J.O., Dijkstra, H.A., Pietrzak, J.D. & Katsman, C.A. 2021 Global dataset of thermohaline staircases obtained from Argo floats and Ice-Tethered Profilers. Earth Syst. Sci. Data 13 (1), 43–61.CrossRefGoogle Scholar