Local Baroclinic Instability Induced by Inhomogeneous Stratification

Mankin Mak Department of Atmospheric Sciences, University of Illinois at Urbana—Champaign, Urbana, Illinois

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Abstract

This analysis demonstrates with a linear balance model that a zonally inhomogeneous basic stratification (1 + σ) in the presence of only a horizontally homogeneous baroclinic shear could give rise to local baroclinic instability. Even for the special case of σ = 0, the unstable modes in this model have distinctly different structural properties than those in a quasigeostrophic model.

For a σ relevant to the observed static stability, the growth rate of the most unstable mode for a zonally homogeneous baroclinic flow without a vertical mean component increases by over 50%. The most unstable mode has a highly localized structure in the region where the total static stability is relatively small and has an eastward propagation. The effect of σ greatly increases with its magnitude provided that there is no significant mismatch between its structure and that of the unstable mode in the absence of a σ. The available potential energy associated with the σ field can be released by a normal mode when its structure gives rise to a vertically differential horizontal heat flux that would tend to reduce σ itself.

A substantial vertical mean component in the basic flow would negate the influence of the inhomogeneity in the static stability because a basic strong advection would not be favorable for absolute instability to occur, and thereby only globally instead of locally unstable disturbances could emerge as normal modes.

The results suggest that in considering the local instability in the extratropical atmosphere one should take into account not only the zonal inhomogeneity in the basic shear but also that in the static stability.

Abstract

This analysis demonstrates with a linear balance model that a zonally inhomogeneous basic stratification (1 + σ) in the presence of only a horizontally homogeneous baroclinic shear could give rise to local baroclinic instability. Even for the special case of σ = 0, the unstable modes in this model have distinctly different structural properties than those in a quasigeostrophic model.

For a σ relevant to the observed static stability, the growth rate of the most unstable mode for a zonally homogeneous baroclinic flow without a vertical mean component increases by over 50%. The most unstable mode has a highly localized structure in the region where the total static stability is relatively small and has an eastward propagation. The effect of σ greatly increases with its magnitude provided that there is no significant mismatch between its structure and that of the unstable mode in the absence of a σ. The available potential energy associated with the σ field can be released by a normal mode when its structure gives rise to a vertically differential horizontal heat flux that would tend to reduce σ itself.

A substantial vertical mean component in the basic flow would negate the influence of the inhomogeneity in the static stability because a basic strong advection would not be favorable for absolute instability to occur, and thereby only globally instead of locally unstable disturbances could emerge as normal modes.

The results suggest that in considering the local instability in the extratropical atmosphere one should take into account not only the zonal inhomogeneity in the basic shear but also that in the static stability.

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