Frontal Instability in a Sheared Basic State

Douglas M. Sinton San Jose State University, San Jose, California

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William D. Heise San Jose State University, San Jose, California

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Abstract

A two-layer frontal model is adapted to investigate the stability of fronts in the presence of potential vorticity (PV) anomalies corresponding to cross-front shear of the mean alongfront flow. Introducing shear modifies the unstable baroclinic modes that exist in the original unsheared model. In addition, the shear produces two new unstable ageostrophic modes. One of these new modes is characterized by barotropic instability, while the other is a shallow mode characterized by a mixed barotropic–baroclinic instability. The alongfront scale of the most unstable mode in both cases is determined by the scale of the anomaly.

The barotropic mode requires some PV anomaly in both layers, whereas the mixed mode can exist with an anomaly confined to the lower layer only. The maximum growth rate of the barotropic mode is independent of the scale of the PV anomaly and the Richardson number of the flow. Anomalies in the basic-state relative vorticity of 10−4 s−1 produce growth rates of 1.45 day−1. The mixed mode is moderately destabilized for anomalies on the scale of the Rossby radius of deformation with a maximum growth rate of 1 day−1.

A baroclinic frontal mode that exists for the unsheared case has its growth rate tripled to 1.82 day−1 when a mean vorticity anomaly of 10−4 s−1 is introduced on the scale of the Rossby radius of deformation. This has implications for rapid cyclogenesis.

Abstract

A two-layer frontal model is adapted to investigate the stability of fronts in the presence of potential vorticity (PV) anomalies corresponding to cross-front shear of the mean alongfront flow. Introducing shear modifies the unstable baroclinic modes that exist in the original unsheared model. In addition, the shear produces two new unstable ageostrophic modes. One of these new modes is characterized by barotropic instability, while the other is a shallow mode characterized by a mixed barotropic–baroclinic instability. The alongfront scale of the most unstable mode in both cases is determined by the scale of the anomaly.

The barotropic mode requires some PV anomaly in both layers, whereas the mixed mode can exist with an anomaly confined to the lower layer only. The maximum growth rate of the barotropic mode is independent of the scale of the PV anomaly and the Richardson number of the flow. Anomalies in the basic-state relative vorticity of 10−4 s−1 produce growth rates of 1.45 day−1. The mixed mode is moderately destabilized for anomalies on the scale of the Rossby radius of deformation with a maximum growth rate of 1 day−1.

A baroclinic frontal mode that exists for the unsheared case has its growth rate tripled to 1.82 day−1 when a mean vorticity anomaly of 10−4 s−1 is introduced on the scale of the Rossby radius of deformation. This has implications for rapid cyclogenesis.

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