A Barotropic Stability Study of Free and Forced Planetary Waves

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  • 1 Department of Meteorology, McGill University, Montreal, Quebec, Canada H3A 2K6
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Abstract

The stability of free and forced planetary waves in a β plane channel is investigated with a barotropic model. The equilibrium flows that are considered have the gravest possible scale in the meridional direction and a zonal wavenumber of either 1 or 2. The equilibrium-forced waves are the result of the interaction of a constant mean zonal wind over finite-amplitude surface orography.

The frequency of all possible small-amplitude perturbations to the equilibrium flows are calculated as a function of the strength of the mean zonal wind and of the amplitude of the orography. The forced zonal-wavenumber-1 flow is found to have three major regions of instability in parameter space, two of which have stationary growing perturbations. The free Rossby wave of that scale is stable for all amplitudes. The forced zonal-wavenumber-2 wave has two adjacent instability domains one on each side of the resonant mean zonal wind. The free wave becomes unstable for sufficiently large amplitudes. The results are interpreted through the use of a severely truncated spectral model and are related to those of previous studies with infinite β-planes. We also report the existence of a traveling subresonant topographic instability, which seems to have gone unnoticed in previous studies.

Abstract

The stability of free and forced planetary waves in a β plane channel is investigated with a barotropic model. The equilibrium flows that are considered have the gravest possible scale in the meridional direction and a zonal wavenumber of either 1 or 2. The equilibrium-forced waves are the result of the interaction of a constant mean zonal wind over finite-amplitude surface orography.

The frequency of all possible small-amplitude perturbations to the equilibrium flows are calculated as a function of the strength of the mean zonal wind and of the amplitude of the orography. The forced zonal-wavenumber-1 flow is found to have three major regions of instability in parameter space, two of which have stationary growing perturbations. The free Rossby wave of that scale is stable for all amplitudes. The forced zonal-wavenumber-2 wave has two adjacent instability domains one on each side of the resonant mean zonal wind. The free wave becomes unstable for sufficiently large amplitudes. The results are interpreted through the use of a severely truncated spectral model and are related to those of previous studies with infinite β-planes. We also report the existence of a traveling subresonant topographic instability, which seems to have gone unnoticed in previous studies.

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