Scale Selection and Energy Spectra of Disturbances in Southern Hemisphere Flows

J. S. Frederiksen National Center for Atmospheric Research, Boulder, CO 80307

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Abstract

The growth and nonlinear interaction of initially small-amplitude disturbances, having a complete spectrum of zonal wavenurnbers, with zonally averaged flows characteristic of January and May SouthernHemisphere situations, are studied in a multilevel primitive equation spectral model-incorporating spherical geometry and viscous dissipation. For January, the fastest growing scale has zonal wavenumberm = 9, in close agreement with linear instability theory. However, the contribution from m = 7 subsequently exceeds that of rn = 9 and is largely responsible for the general agreement between model andobserved eddy streamfunctions and fluxes. Although the individual wavenumber contributions, eg,m = 9 and m = 7 undergo vacillation cycles similar to ones found earlier with single zonal wavenumberdisturbances growing on the same zonal flows, the total eddy kinetic energy after the initial growth periodis relatively constant. This appears to be due to the interference between the larger number of waves. ForMay the fastest growing scale has m = 5 and initially grows on the polar jet. As the disturbance maturessecondary growth occurs on the subtropical jet and the disturbance achieves significant amplitude in theupper troposphere in the latitude band between 30 and 60. Unlike previous baroclinic instability results,the nonlinear model and observed eddy fluxes are also in close qualitative agreement.

For January a very long-time viscous integration was carried out and the kinetic energy spectra werestudied at various stages. When zonal wavenumber m = 7 reaches its peak (day 23), the spectrum has anapproximate m-s power law. This. however, is not a statistical quasi-steady state and further integrationout to days 45-SO was needed to reach such a state. Then it was found that the spectra satisfy the m-3power law of classical two-dimensional and quasi-geostrophic turbulence theory.

Abstract

The growth and nonlinear interaction of initially small-amplitude disturbances, having a complete spectrum of zonal wavenurnbers, with zonally averaged flows characteristic of January and May SouthernHemisphere situations, are studied in a multilevel primitive equation spectral model-incorporating spherical geometry and viscous dissipation. For January, the fastest growing scale has zonal wavenumberm = 9, in close agreement with linear instability theory. However, the contribution from m = 7 subsequently exceeds that of rn = 9 and is largely responsible for the general agreement between model andobserved eddy streamfunctions and fluxes. Although the individual wavenumber contributions, eg,m = 9 and m = 7 undergo vacillation cycles similar to ones found earlier with single zonal wavenumberdisturbances growing on the same zonal flows, the total eddy kinetic energy after the initial growth periodis relatively constant. This appears to be due to the interference between the larger number of waves. ForMay the fastest growing scale has m = 5 and initially grows on the polar jet. As the disturbance maturessecondary growth occurs on the subtropical jet and the disturbance achieves significant amplitude in theupper troposphere in the latitude band between 30 and 60. Unlike previous baroclinic instability results,the nonlinear model and observed eddy fluxes are also in close qualitative agreement.

For January a very long-time viscous integration was carried out and the kinetic energy spectra werestudied at various stages. When zonal wavenumber m = 7 reaches its peak (day 23), the spectrum has anapproximate m-s power law. This. however, is not a statistical quasi-steady state and further integrationout to days 45-SO was needed to reach such a state. Then it was found that the spectra satisfy the m-3power law of classical two-dimensional and quasi-geostrophic turbulence theory.

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