On the Stability of Internal Baroclinic Jets in a Rotating Atmosphere

J. G. Charney Massachusetts Institute of Technology

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M. E. Stern Woods Hole Oceanographic Institution

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Abstract

We consider the quasi-geostrophic instability of a circumpolar vortex in which there is available kinetic energy of lateral shear as well as available potential energy due to meridional temperature gradients. Stability criteria are developed for the case of an internal jet, i.e., where the meridional temperature gradients at the ground vanish. The internal jet is stable if the gradient of potential vorticity in isentropic surfaces does not vanish. If it vanishes at a closed isopleth of constant mean zonal vorticity, the jet is unstable.

The special role played by the kinematic and thermodynamic boundary conditions in the theory of baroclinic stability is clarified by re-examining earlier theories in the light of an analogy to two-dimensional shear flow. Simple baroclinic flow with rigid horizontal boundaries is isomorphic to Couette flow with free boundaries. The presence of meridional temperature gradients at boundaries relaxes the constraints on the boundary pressure perturbations and makes possible the release of available potential energy, just as the freeing of the boundary in Couette flow makes possible the release of shear kinetic energy.

The mid-winter breakdown of the polar-night jet may be an example of an instability, but we cannot say whether the concomitant disturbance releases mean kinetic, mean potential energy, or both, of the internal jet type, since the possibility of all of these conversions exists. The apparent downward propagation of the unstable disturbances in the polar-night jet below 30 km may be explained by the prior onset of instability at higher levels.

Abstract

We consider the quasi-geostrophic instability of a circumpolar vortex in which there is available kinetic energy of lateral shear as well as available potential energy due to meridional temperature gradients. Stability criteria are developed for the case of an internal jet, i.e., where the meridional temperature gradients at the ground vanish. The internal jet is stable if the gradient of potential vorticity in isentropic surfaces does not vanish. If it vanishes at a closed isopleth of constant mean zonal vorticity, the jet is unstable.

The special role played by the kinematic and thermodynamic boundary conditions in the theory of baroclinic stability is clarified by re-examining earlier theories in the light of an analogy to two-dimensional shear flow. Simple baroclinic flow with rigid horizontal boundaries is isomorphic to Couette flow with free boundaries. The presence of meridional temperature gradients at boundaries relaxes the constraints on the boundary pressure perturbations and makes possible the release of available potential energy, just as the freeing of the boundary in Couette flow makes possible the release of shear kinetic energy.

The mid-winter breakdown of the polar-night jet may be an example of an instability, but we cannot say whether the concomitant disturbance releases mean kinetic, mean potential energy, or both, of the internal jet type, since the possibility of all of these conversions exists. The apparent downward propagation of the unstable disturbances in the polar-night jet below 30 km may be explained by the prior onset of instability at higher levels.

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