A diagnostic Study of Atmospheric Spectral Kinetic Energetics

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  • 1 Atmospheric Environment Service, Environment Canada, Downsview, Ontario M 3H ST4
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Abstract

Wind spectra are obtained from data using expansions in spherical harmonies. Equations governing the tendencies of total kinetic energy of the spectral wind components are derived. Dissipation is obtained diagnostically as a residual. Calculations are performed on a data set for two weeks at eight pressure levels from surface to 100 mb for the Northern Hemisphere. As the data coverage is not global, parity assumptions are necessary for scalar data fields and ate assigned based on observation and the geostrophic wind equations. Results are scaled by the two-dimensional index n (degree of associated Legendre functions Pn1. Expansions are truncated at l=n=24. Data accuracy may be questionable for the higher coefficients considered here.

Some of the results of calculations are as follows:

  1. Kinetic energy above 850 mb is maximum in scales n=2 and 4, with a secondary maximum at n=9. Equipartition of u and v kinetic energy occurs at n=7.

  2. Dissipation residuals are large in every scale, suggesting large fluxes of kinetic. energy between scales n>24 and n<24.

  3. The total nonlinear horizontal transfer of kinetic energy shows sources in scales 4≤n≤10,13≤n≤15,n=18 and =23, with strongest sources in scales n=7 and 9, The source at n=18 is isolated and strong and may be due to the ITCZ. Scales nlt;3 gain kinetic energy in the fashion of the familiar zonal flow in calculations where data are expanded in Fourier series at latitude circles.

  4. The presence of sources of kinetic energy in scales 15<n<24, and the fact that slopes of kinetic energy with scale are generally not close to −3, suggest these scales do not form an inertial subrange.

  5. The contributions of interactions of scales 15<n<24, and the fact that slopes of kinetic energy in each scale 0<n<6,7<14 and 15<n<24 were isolated, and the method is suggested as a means of diagnosing the impact of dissipation and heating parameterizations upon all scales of motion in models of the atmosphere. Interactions involving scales 7<n<14 are quite active, and those involving scales 15<<24 are surprisingly active in view of their small kinetic energy content. Self-interactions in the latter scale range transfer a great deal of kinetic energy into ultra-long scales (n3) and out of n=4 in the upper troposphere, while self-interactions in the 7<n<14 scale range (scale of baroclinic mid-latitude disturbances) transfer much of the kinetic energy out of scales 4<n<9and n=18. Self-interactions in planetary scales 0<n<6 are rather passive in view of the large kinetic energy content involved except in a few scales (n<11). Cross-interactions are active in most scales.

Abstract

Wind spectra are obtained from data using expansions in spherical harmonies. Equations governing the tendencies of total kinetic energy of the spectral wind components are derived. Dissipation is obtained diagnostically as a residual. Calculations are performed on a data set for two weeks at eight pressure levels from surface to 100 mb for the Northern Hemisphere. As the data coverage is not global, parity assumptions are necessary for scalar data fields and ate assigned based on observation and the geostrophic wind equations. Results are scaled by the two-dimensional index n (degree of associated Legendre functions Pn1. Expansions are truncated at l=n=24. Data accuracy may be questionable for the higher coefficients considered here.

Some of the results of calculations are as follows:

  1. Kinetic energy above 850 mb is maximum in scales n=2 and 4, with a secondary maximum at n=9. Equipartition of u and v kinetic energy occurs at n=7.

  2. Dissipation residuals are large in every scale, suggesting large fluxes of kinetic. energy between scales n>24 and n<24.

  3. The total nonlinear horizontal transfer of kinetic energy shows sources in scales 4≤n≤10,13≤n≤15,n=18 and =23, with strongest sources in scales n=7 and 9, The source at n=18 is isolated and strong and may be due to the ITCZ. Scales nlt;3 gain kinetic energy in the fashion of the familiar zonal flow in calculations where data are expanded in Fourier series at latitude circles.

  4. The presence of sources of kinetic energy in scales 15<n<24, and the fact that slopes of kinetic energy with scale are generally not close to −3, suggest these scales do not form an inertial subrange.

  5. The contributions of interactions of scales 15<n<24, and the fact that slopes of kinetic energy in each scale 0<n<6,7<14 and 15<n<24 were isolated, and the method is suggested as a means of diagnosing the impact of dissipation and heating parameterizations upon all scales of motion in models of the atmosphere. Interactions involving scales 7<n<14 are quite active, and those involving scales 15<<24 are surprisingly active in view of their small kinetic energy content. Self-interactions in the latter scale range transfer a great deal of kinetic energy into ultra-long scales (n3) and out of n=4 in the upper troposphere, while self-interactions in the 7<n<14 scale range (scale of baroclinic mid-latitude disturbances) transfer much of the kinetic energy out of scales 4<n<9and n=18. Self-interactions in planetary scales 0<n<6 are rather passive in view of the large kinetic energy content involved except in a few scales (n<11). Cross-interactions are active in most scales.

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