Stability of a front separating water masses with different stratifications

The linear instability of a narrow current flowing eastward between two semi-infinite water masses of different mean stratification is studied with a multi-mode quasi-geostrophic model. The mean stratification in each domain has an exponential profile. The current is symmetric about the vertical plane separating the two water masses and its vertical profile is determined by the difference between the mean stratification of the two domains, as imposed by the thermal-wind equation. The current so defined is unstable over the entire parameter range we studied. As the ratio between the asymptotic depth of the thermocline in the two domains tends to unity, the current weakens and becomes eventually stable, while the length of the fastest-growing wave increases toward a finite upper limit. Increasing the depth or gradient of the thermocline in both domains by the same ratio also stabilizes the jet. Decreasing the width of the jet destabilizes it, but the length of the most unstable wave is almost independent of current width. The stability results are applied to the Gulf Stream after it has separated from Cape Hatteras, using a realistic stratification. The most unstable wave has a length of 200 km, which is comparable to twice the diameter of warm-core rings. The maximum amplitude of the unstable waves in the cross-stream direction is shifted towards the northern domain. We interpret this shift as inducing formation of warm-core eddies largely to the north of the current axis, while cold-core eddies capture water originally lying almost as much north of the axis as south of it. Anticyclonic eddies in the model would thus tend to exhibit a weaker temperature contrast with the surrounding water mass than the cyclonic ones, as observed in the Gulf-Stream system. The effect of adding a barotropic component to the basic jet depends on the sign and magnitude of this component. For a small westward component or large components of either sign the jet is less stable, while an intermediate range of east- or westward barotropic components reduces the instability. Both the Gulf Stream and Kuroshio are in this latter range, near their respective separation points, so their meandering is mainly induced by baroclinic instability.