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Instability of Meridional Baroclinic Currents

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  • 1 MIT–WHOI Joint Program, Woods Hole, Massachusetts
  • | 2 Woods Hole Oceanographic Institution, Woods Hole, Massachusetts
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Abstract

The baroclinic instability of a meridional current in a north–south channel is investigated in a two-layer model for the case when the current has no horizontal shear. The vertical shear of the current provides a potential vorticity gradient in the zonal direction while the beta effect provides a potential vorticity gradient in the meridional direction. The normal modes of the two-layer baroclinic flow are found both numerically and analytically.

In contrast to the situation when the current is in the zonal direction there seems to be no minimum shear required for instability in spite of the active presence of the planetary vorticity gradient, β, although the growth rates of the instability are reduced as the shear is weakened. Also, the horizontal structure of the unstable mode is a strong function of the parameters, and weakly growing modes exhibit a boundary layer structure and are compressed to a narrow region near the western edge of the channel. The unstable modes are connected to the neutral Rossby modes that exist in the channel in the absence of shear and an analysis shows how those modes provide information about the long-wave stability threshold of the flow. The short-wave cutoff, which coincides with the Eady cutoff for zero β moves to higher along-channel wavenumber as β increases, thus expanding the range of instability on the short-wave side of the instability interval in wavenumber. For weak shears (or large values of β) the weakly unstable modes are very oscillatory in the zonal direction. Each mode occupies a small interval in meridional wavenumber and a connection to the neutral Rossby mode is inferred. In the special case when the two layers of the model have equal thicknesses, symmetries of the basic equations allow modes with the same growth rate but differing phase speeds and, hence, linear vacillating modes result when two such modes are superposed.

The results of the modal analysis are checked against a direct numerical integration of the initial value problem with excellent agreement and provides a point of contact with earlier numerical calculations by other authors. These findings support the hypothesis that baroclinic instability of midocean flows may represent a significant source of eddy energy.

Corresponding author address: Dr. Joseph Pedlosky, Woods Hole Oceanographic Institution, Clark 363 MS#21, Woods Hole, MA 02543. Email: jpedlosky@whoi.edu

Abstract

The baroclinic instability of a meridional current in a north–south channel is investigated in a two-layer model for the case when the current has no horizontal shear. The vertical shear of the current provides a potential vorticity gradient in the zonal direction while the beta effect provides a potential vorticity gradient in the meridional direction. The normal modes of the two-layer baroclinic flow are found both numerically and analytically.

In contrast to the situation when the current is in the zonal direction there seems to be no minimum shear required for instability in spite of the active presence of the planetary vorticity gradient, β, although the growth rates of the instability are reduced as the shear is weakened. Also, the horizontal structure of the unstable mode is a strong function of the parameters, and weakly growing modes exhibit a boundary layer structure and are compressed to a narrow region near the western edge of the channel. The unstable modes are connected to the neutral Rossby modes that exist in the channel in the absence of shear and an analysis shows how those modes provide information about the long-wave stability threshold of the flow. The short-wave cutoff, which coincides with the Eady cutoff for zero β moves to higher along-channel wavenumber as β increases, thus expanding the range of instability on the short-wave side of the instability interval in wavenumber. For weak shears (or large values of β) the weakly unstable modes are very oscillatory in the zonal direction. Each mode occupies a small interval in meridional wavenumber and a connection to the neutral Rossby mode is inferred. In the special case when the two layers of the model have equal thicknesses, symmetries of the basic equations allow modes with the same growth rate but differing phase speeds and, hence, linear vacillating modes result when two such modes are superposed.

The results of the modal analysis are checked against a direct numerical integration of the initial value problem with excellent agreement and provides a point of contact with earlier numerical calculations by other authors. These findings support the hypothesis that baroclinic instability of midocean flows may represent a significant source of eddy energy.

Corresponding author address: Dr. Joseph Pedlosky, Woods Hole Oceanographic Institution, Clark 363 MS#21, Woods Hole, MA 02543. Email: jpedlosky@whoi.edu

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