Symmetric instability in cross-equatorial western boundary currents

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  • 1 Department of Physics, University of Oxford, Oxford, United Kingdom
  • | 2 Department of Earth Sciences, University of Oxford, Oxford, United Kingdom
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Abstract

The upper limb of the Atlantic Meridional Overturning Circulation draws waters with negative potential vorticity from the southern hemisphere into the northern hemisphere. The North Brazil Current is one of the cross-equatorial pathways in which this occurs: upon crossing the equator, fluid parcels must modify their potential vorticity to render them stable to symmetric instability and to merge smoothly with the ocean interior. In this work a linear stability analysis is performed on an idealized western boundary current, dynamically similar to the North Brazil Current, to identify features which are indicative of symmetric instability. Simple two-dimensional numerical models are used to verify the results of the stability analysis. The two-dimensional models and linear stability theory show that symmetric instability in meridional flows does not change when the non-traditional component of the Coriolis force is included, unlike in zonal flows. Idealized three-dimensional numerical models show anti-cyclonic barotropic eddies being spun off as the western boundary current crosses the equator. These eddies become symmetrically unstable a few degrees north of the equator, and their PV is set to zero through the action of the instability. The instability is found to have a clear fingerprint in the spatial Fourier transform of the vertical kinetic energy. An analysis of the water mass formation rates suggest that symmetric instability has a minimal effect on water mass transformation in the model calculations; however, this may be the result of unresolved dynamics, such as secondary Kelvin Helmholtz instabilities, which are important in diabatic transformation.

Corresponding author: Fraser W. Goldsworth, frasergocean@gmail.com

Oxford NERC Environmental Research DTP.

Abstract

The upper limb of the Atlantic Meridional Overturning Circulation draws waters with negative potential vorticity from the southern hemisphere into the northern hemisphere. The North Brazil Current is one of the cross-equatorial pathways in which this occurs: upon crossing the equator, fluid parcels must modify their potential vorticity to render them stable to symmetric instability and to merge smoothly with the ocean interior. In this work a linear stability analysis is performed on an idealized western boundary current, dynamically similar to the North Brazil Current, to identify features which are indicative of symmetric instability. Simple two-dimensional numerical models are used to verify the results of the stability analysis. The two-dimensional models and linear stability theory show that symmetric instability in meridional flows does not change when the non-traditional component of the Coriolis force is included, unlike in zonal flows. Idealized three-dimensional numerical models show anti-cyclonic barotropic eddies being spun off as the western boundary current crosses the equator. These eddies become symmetrically unstable a few degrees north of the equator, and their PV is set to zero through the action of the instability. The instability is found to have a clear fingerprint in the spatial Fourier transform of the vertical kinetic energy. An analysis of the water mass formation rates suggest that symmetric instability has a minimal effect on water mass transformation in the model calculations; however, this may be the result of unresolved dynamics, such as secondary Kelvin Helmholtz instabilities, which are important in diabatic transformation.

Corresponding author: Fraser W. Goldsworth, frasergocean@gmail.com

Oxford NERC Environmental Research DTP.

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