Stable and Unstable Near-Resonant States in Multilevel, Severely Truncated, Quasi-Geostrophic Models

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  • 1 Climate Research Group, Scripps Institution of Oceanography, University of California, San Diego, La Jolla 92093
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Abstract

Stationary planetary waves are investigated with severely-truncated quasi-geostrophic models extending from the surface to 100 km. For a typical winter zonal-wind profile, it is shown that large amplitude or resonant planetary waves of intermediate zonal wavenumbers (∼4 or 5) occur with an equivalent barotropic structure. In the presence of Ekman friction and Newtonian damping these stationary waves have associated with them a mountain torque and temperature transport which can influence the zonal flow. In time-dependent calculations it is shown that this wave-zonal flow interaction is stable to small perturbations on the low side of resonance and unstable on the high side of resonance. Here high and low refer to large and small values of the zonal wind.

Resonant zonal wavenumbers of lower wavenumber (∼2 or 3) also occur for the same zonal profile and have a node in the vertical with a small amplitude maximum near the surface and a larger amplitude maximum in the stratosphere; still lower quasi-resonant wavenumbers also occur with two nodes in the vertical. These waves destabilize the wave-zonal flow interaction on both the high and low sides of the resonance peak. This instability depends upon the presence of the orography and the basic asymmetric state as Newtonian damping and surface friction are sufficient to damp the baroclinic instability associated with a linear inviscid model.

Abstract

Stationary planetary waves are investigated with severely-truncated quasi-geostrophic models extending from the surface to 100 km. For a typical winter zonal-wind profile, it is shown that large amplitude or resonant planetary waves of intermediate zonal wavenumbers (∼4 or 5) occur with an equivalent barotropic structure. In the presence of Ekman friction and Newtonian damping these stationary waves have associated with them a mountain torque and temperature transport which can influence the zonal flow. In time-dependent calculations it is shown that this wave-zonal flow interaction is stable to small perturbations on the low side of resonance and unstable on the high side of resonance. Here high and low refer to large and small values of the zonal wind.

Resonant zonal wavenumbers of lower wavenumber (∼2 or 3) also occur for the same zonal profile and have a node in the vertical with a small amplitude maximum near the surface and a larger amplitude maximum in the stratosphere; still lower quasi-resonant wavenumbers also occur with two nodes in the vertical. These waves destabilize the wave-zonal flow interaction on both the high and low sides of the resonance peak. This instability depends upon the presence of the orography and the basic asymmetric state as Newtonian damping and surface friction are sufficient to damp the baroclinic instability associated with a linear inviscid model.

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