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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: yma@physics.utoronto.ca
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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
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

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