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The Relative Influence of Diapycnal Mixing and Hydrologic Forcing on the Stability of the Thermohaline Circulation

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  • 1 MIT/WHOI Joint Program, Massachusetts Institute of Technology, Cambridge, Massachusetts
  • | 2 Department of Physical Oceanography, Woods Hole Oceanographic Institution, Woods Hole, Massachusetts
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Abstract

Scaling analysis of the oceanic thermohaline circulation has been done under two types of surface boundary conditions: (i) Under “relaxation” conditions (sea surface temperature and salinity are relaxed to prescribed values), there is a two-thirds power law dependence of the meridional overturning (and the poleward heat transport) on the diapycnal diffusivity. For any given external forcing, there is only one equilibrium state for the thermohaline circulation. (ii) Under “mixed” boundary conditions (temperature is relaxed to prescribed values and a virtual salt flux condition is used for salinity), multiple equilibria become possible. For a given thermal forcing, the existence of multiple equilibria depends on the relative contributions of diapycnal diffusivity and the hydrologic forcing: for each diapycnal diffusivity K, there is a threshold freshwater flux Ec = CK2/3 (C is a constant) below which three modes are possible with one stable thermal mode, one unstable thermal mode, and a stable haline mode and above which only one stable haline mode can exist.

Numerical experiments are also implemented to test the above scaling arguments. Consistent results have been obtained under the two types of boundary conditions. The relationship derived here focuses attention on the need to better understand both the diapycnal mixing in the ocean and the strength of the hydrologic forcing at its surface.

Present affiliation: The North Bridge Group, Lincoln, Massachusetts.

Corresponding author address: Raymond W. Schmitt, MS21, Department of Physical Oceanography, Woods Hole Oceanographic Institution, Woods Hole, MA.

Email: rschmitt@whoi.edu

Abstract

Scaling analysis of the oceanic thermohaline circulation has been done under two types of surface boundary conditions: (i) Under “relaxation” conditions (sea surface temperature and salinity are relaxed to prescribed values), there is a two-thirds power law dependence of the meridional overturning (and the poleward heat transport) on the diapycnal diffusivity. For any given external forcing, there is only one equilibrium state for the thermohaline circulation. (ii) Under “mixed” boundary conditions (temperature is relaxed to prescribed values and a virtual salt flux condition is used for salinity), multiple equilibria become possible. For a given thermal forcing, the existence of multiple equilibria depends on the relative contributions of diapycnal diffusivity and the hydrologic forcing: for each diapycnal diffusivity K, there is a threshold freshwater flux Ec = CK2/3 (C is a constant) below which three modes are possible with one stable thermal mode, one unstable thermal mode, and a stable haline mode and above which only one stable haline mode can exist.

Numerical experiments are also implemented to test the above scaling arguments. Consistent results have been obtained under the two types of boundary conditions. The relationship derived here focuses attention on the need to better understand both the diapycnal mixing in the ocean and the strength of the hydrologic forcing at its surface.

Present affiliation: The North Bridge Group, Lincoln, Massachusetts.

Corresponding author address: Raymond W. Schmitt, MS21, Department of Physical Oceanography, Woods Hole Oceanographic Institution, Woods Hole, MA.

Email: rschmitt@whoi.edu

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