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Instability of Surface and Upper-Tropospheric Shear Lines

Martin JuckesMeteorologisches Institut der Universität Münich, Munich, Germany

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Abstract

An analytic linear stability analysis is carried out for a shear line associated with a surface temperature anomaly in uniform potential vorticity, quasigeostrophic flow. Previous studies of this type of flow, albeit with more realistic basic states, have relied on numerical solution. The instability can be interpreted as the result of the interaction of counterpropagating edge waves on the two opposing potential temperature gradients that bound the shear line.

The analytic normal mode analysis can easily be extended to investigate nonmodal disturbances. The disturbances defined by maximizing the growth of selected norms over the norms over the normal mode e-folding time generally show similar growth rates to the normal modes. There is weaker scale selectivity and a shift to longer wave-lengths. The enstrophy norm provides an exception to this behavior. This norm is sensitive to small-scale structures and can grow much faster than the large-scale disturbance.

Nonlinear integrations show the instability breaking the shear line into a string of vortices. Narrow secondary shear lines are formed with vorticity values much larger than those of the original shear line. These secondary shear lines are in turn broken up by the same instability mechanism.

Abstract

An analytic linear stability analysis is carried out for a shear line associated with a surface temperature anomaly in uniform potential vorticity, quasigeostrophic flow. Previous studies of this type of flow, albeit with more realistic basic states, have relied on numerical solution. The instability can be interpreted as the result of the interaction of counterpropagating edge waves on the two opposing potential temperature gradients that bound the shear line.

The analytic normal mode analysis can easily be extended to investigate nonmodal disturbances. The disturbances defined by maximizing the growth of selected norms over the norms over the normal mode e-folding time generally show similar growth rates to the normal modes. There is weaker scale selectivity and a shift to longer wave-lengths. The enstrophy norm provides an exception to this behavior. This norm is sensitive to small-scale structures and can grow much faster than the large-scale disturbance.

Nonlinear integrations show the instability breaking the shear line into a string of vortices. Narrow secondary shear lines are formed with vorticity values much larger than those of the original shear line. These secondary shear lines are in turn broken up by the same instability mechanism.

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