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A study of Baroclinic Energy Sources for Large-Scale Atmospheric Normal Modes

H. L. TanakaGeophysical Institute, University of Alaska Fairbanks, Fairbanks, Alaska

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Shaojian SunGeophysical Institute, University of Alaska Fairbanks, Fairbanks, Alaska

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Abstract

Observed atmospheric energy peaks in a three-dimensional (3-D) spectral domain are compared with energy peaks predicted by the theory of atmospheric baroclinic instability. The 3-D scale index for global-scale atmospheric motions is represented by the eigenfrequencies of 3-D normal mode functions on a sphere, based on the fact that the eigenfrequencies of Rossby modes are related to the 3-D scale of the waves through the intrinsic wave dispersion relation.

When the observed atmospheric energy level is expressed as a function of the eigenfrequencies, a distinct spectral peak appears in the intermediate value of the eigenfrequencies of Rossby modes. The energy spectrum of atmospheric barotropic components clearly separates a −5/3 power law in the high-frequency range, relative to the energy peak, and a 3 power law in the low-frequency range. The peak may describe a certain energy source for large-scale atmospheric motions. For zonal wavenumber 6, we find that the observed spectral peak coincides with the peak predicted from atmospheric baroclinic instability; the energy peak can be produced by baroclinic instability. For zonal wavenumber 2, we also find that the observed special peak coincides with that predicted from low-frequency baroclinic instability on a sphere. The results suggest that the low-frequency unstable modes of zonal wavenumber 2 contribute a substantial fraction of the observed spectral peak in a manner similar to zonal wavenumber 6.

Abstract

Observed atmospheric energy peaks in a three-dimensional (3-D) spectral domain are compared with energy peaks predicted by the theory of atmospheric baroclinic instability. The 3-D scale index for global-scale atmospheric motions is represented by the eigenfrequencies of 3-D normal mode functions on a sphere, based on the fact that the eigenfrequencies of Rossby modes are related to the 3-D scale of the waves through the intrinsic wave dispersion relation.

When the observed atmospheric energy level is expressed as a function of the eigenfrequencies, a distinct spectral peak appears in the intermediate value of the eigenfrequencies of Rossby modes. The energy spectrum of atmospheric barotropic components clearly separates a −5/3 power law in the high-frequency range, relative to the energy peak, and a 3 power law in the low-frequency range. The peak may describe a certain energy source for large-scale atmospheric motions. For zonal wavenumber 6, we find that the observed spectral peak coincides with the peak predicted from atmospheric baroclinic instability; the energy peak can be produced by baroclinic instability. For zonal wavenumber 2, we also find that the observed special peak coincides with that predicted from low-frequency baroclinic instability on a sphere. The results suggest that the low-frequency unstable modes of zonal wavenumber 2 contribute a substantial fraction of the observed spectral peak in a manner similar to zonal wavenumber 6.

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