Resonance of Topographically Forced Waves in a Quasi-Geostrophic Model

Herschel L. Mitchell Recherche en Prévision Numérique, Atmospheric Environment Service, Dorval, Québec, H9b IJ3, Canada

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Jacques Derome Department of Meteorology, McGill University, Montréal, Québec, H3A 2K6, Canada

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Abstract

The resonance of stationary waves forced by topography is examined using a quasi-geostrophic model on a beta-plane channel. It is shown analytically that among the factors favoring the resonance of large, rather than synoptic or small, scale waves is the fact that the sensitivity of the large resonant responses to a change of zonal wind decreases as the scale of the resonant wave increases. A numerical model is used to examine resonance in the presence of topography having zonal wavenumber 2 with zonal flows having horizontal and vertical shear and including the effects of damping and nonlinear interactions. Although the effects of resonance are found to be important even in the presence of damping mechanisms, linear experiments with topographical forcing of reasonable amplitude indicate that a period or several weeks is required for a resonant internal mode to achieve large amplitude in the troposphere. However, as the structure of the resonant mode is such that it has much larger amplitudes in the upper atmosphere than in the troposphere, the interaction between this growing resonant mode and the mean flow which occurs when nonlinear effects are permitted triggers a stratospheric warming and zonal wind reversal. These events, which drive the system off resonance, occur long before large wave amplitudes are achieved in the lower atmosphere. The barotropic mode of zonal wavenumber 2 is shown not to resonate for reasonable values of our mean zonal wind primarily because the latter has the same (sinusoidal) meridional structure as the topography.

Abstract

The resonance of stationary waves forced by topography is examined using a quasi-geostrophic model on a beta-plane channel. It is shown analytically that among the factors favoring the resonance of large, rather than synoptic or small, scale waves is the fact that the sensitivity of the large resonant responses to a change of zonal wind decreases as the scale of the resonant wave increases. A numerical model is used to examine resonance in the presence of topography having zonal wavenumber 2 with zonal flows having horizontal and vertical shear and including the effects of damping and nonlinear interactions. Although the effects of resonance are found to be important even in the presence of damping mechanisms, linear experiments with topographical forcing of reasonable amplitude indicate that a period or several weeks is required for a resonant internal mode to achieve large amplitude in the troposphere. However, as the structure of the resonant mode is such that it has much larger amplitudes in the upper atmosphere than in the troposphere, the interaction between this growing resonant mode and the mean flow which occurs when nonlinear effects are permitted triggers a stratospheric warming and zonal wind reversal. These events, which drive the system off resonance, occur long before large wave amplitudes are achieved in the lower atmosphere. The barotropic mode of zonal wavenumber 2 is shown not to resonate for reasonable values of our mean zonal wind primarily because the latter has the same (sinusoidal) meridional structure as the topography.

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