Air Motions Accompanying the Development of a Planetary Wave Critical Layer

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  • 1 Department of Astrophysical, Planetary, and Atmospheric Sciences, University of Colorado, Boulder, Colorado
  • | 2 Center for Atmospheric Theory and Analysis, University of Colorado, Boulder, Colorado
  • | 3 National Center for Atmospheric Research, Boulder, Colorado
  • | 4 Center for Atmospheric Theory and Analysis, University of Colorado, Boulder, Colorado
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Abstract

Horizontal air motions accompanying the development of a planetary wave critical layer are investigated on the sphere in the equivalent barotropic framework. For small wave amplitude or strong shear in the neighborhood of the zero wind line, the critical region is confined laterally to a narrow zone adjacent to the critical latitude. Increasing the wave amplitude or reducing the zonal shear near the zero wind line expands the critical region poleward. Stirring within the critical region is controlled by a competition between wave advection, which promotes instability by rearranging potential vorticity, and dissipation, which limits the steepening of gradients and damps instability. Eddy advection strains bodies of air inside the critical region down to small dimensions, until eventually dissipation becomes efficient and anomalies in potential vorticity and other tracers “dissolve.”

For a narrow critical region, eddy stirring tends to homogenize potential vorticity near the zero wind line. The reduced gradient of potential vorticity resulting under weakly damped conditions lead to reflection of wave activity that suppresses wave generation and allows the flow to approach equilibrium. For a wide critical region, the flow can adjust nonlinearly directly at the forcing, making eddy stirring at low latitudes less important. The picture in that case is one of “global-scale entrainment,” where material lines fold across much of the hemisphere initially in westerlies. Air injected into the polar cap spins up anticyclonically, sweeping easterlies across mid-latitudes that shield the critical line from wave activity. Once this occurs, the eddy field at low latitudes collapses and easterlies advance over the forcing to suppress wave generation and restore equilibrium.

The preliminary development of the critical region resembles the familiar “wave breaking” signature in stratospheric potential vorticity maps and is reproduced quite well in linear and quasi-linear restrictions of the complete system. Although the nonlinear planetary wave critical layer captures a number of observed features, this paradigm of stratospheric air motions breaks down quickly with realistic wave amplitudes. Without a restoring mechanism to counteract the disruptive influence of eddy advection, the vortex is seriously compromised after only a month.

Abstract

Horizontal air motions accompanying the development of a planetary wave critical layer are investigated on the sphere in the equivalent barotropic framework. For small wave amplitude or strong shear in the neighborhood of the zero wind line, the critical region is confined laterally to a narrow zone adjacent to the critical latitude. Increasing the wave amplitude or reducing the zonal shear near the zero wind line expands the critical region poleward. Stirring within the critical region is controlled by a competition between wave advection, which promotes instability by rearranging potential vorticity, and dissipation, which limits the steepening of gradients and damps instability. Eddy advection strains bodies of air inside the critical region down to small dimensions, until eventually dissipation becomes efficient and anomalies in potential vorticity and other tracers “dissolve.”

For a narrow critical region, eddy stirring tends to homogenize potential vorticity near the zero wind line. The reduced gradient of potential vorticity resulting under weakly damped conditions lead to reflection of wave activity that suppresses wave generation and allows the flow to approach equilibrium. For a wide critical region, the flow can adjust nonlinearly directly at the forcing, making eddy stirring at low latitudes less important. The picture in that case is one of “global-scale entrainment,” where material lines fold across much of the hemisphere initially in westerlies. Air injected into the polar cap spins up anticyclonically, sweeping easterlies across mid-latitudes that shield the critical line from wave activity. Once this occurs, the eddy field at low latitudes collapses and easterlies advance over the forcing to suppress wave generation and restore equilibrium.

The preliminary development of the critical region resembles the familiar “wave breaking” signature in stratospheric potential vorticity maps and is reproduced quite well in linear and quasi-linear restrictions of the complete system. Although the nonlinear planetary wave critical layer captures a number of observed features, this paradigm of stratospheric air motions breaks down quickly with realistic wave amplitudes. Without a restoring mechanism to counteract the disruptive influence of eddy advection, the vortex is seriously compromised after only a month.

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