• Bacmeister, J. T., S. D. Eckermann, P. A. Newman, L. Lait, K. R. Chan, M. Loewenstein, M. H. Proffitt, and B. L. Gary, 1996: Stratospheric horizontal wavenumber spectra of winds, potential temperature and atmospheric tracers observed by high-altitude aircraft. J. Geophys. Res., 101 , 94419470.

    • Search Google Scholar
    • Export Citation
  • Bartello, P., 2000: Using low-resolution winds do deduce fine structure in tracers. Atmos.–Ocean, 38 , 303320.

  • Batchelor, G. K., 1953: The Theory of Homogeneous Turbulence. Cambridge University Press.

  • Billant, P., and J-M. Chomaz, 2000a: Experimental evidence for a new instability of a vertical columnar vortex pair in a strongly stratified fluid. J. Fluid Mech., 418 , 167188.

    • Search Google Scholar
    • Export Citation
  • Billant, P., and J-M. Chomaz, 2000b: Three-dimensional stability of a vertical columnar vortex pair in a stratified fluid. J. Fluid Mech., 419 , 6591.

    • Search Google Scholar
    • Export Citation
  • Billant, P., and J. M. Chomaz, 2001: Self-similarity of strongly stratified inviscid flows. Phys. Fluids, 13 , 16451651.

  • Charney, J. G., 1971: Geostrophic turbulence. J. Atmos. Sci., 28 , 10871095.

  • Cho, J. Y. N., and E. Lindborg, 2001: Horizontal velocity structure functions in the upper troposphere and lower stratosphere 1. Observation. J. Geophys. Res., 106 , 1022310232.

    • Search Google Scholar
    • Export Citation
  • Cho, J. Y. N., E. Newell, and J. D. Barrick, 1999: Horizontal wavenumber spectra of winds, temperature and trace gases during the Pacific Exploratory Missions: 2. Gravity waves, quasi-two-dimensional turbulence and vortical modes. J. Geophys. Res., 104 , 1629716308.

    • Search Google Scholar
    • Export Citation
  • Dewan, E. M., 1979: Stratospheric spectra resembling turbulence. Science, 204 , 832835.

  • Dewan, E., 1997: Saturated-cascade similitude theory of gravity wave spectra. J. Geophys. Res., 102 , 2979929817.

  • Frisch, U., 1995: Turbulence. Cambridge University Press.

  • Gage, K. S., 1979: Evidence for a k−5/3 law inertial range in mesoscale two-dimensional turbulence. J. Atmos. Sci., 36 , 19501954.

  • Kitamura, Y., and Y. Matsuda, 2006: The k−3 H and k−5/3 H energy spectra in stratified turbulence. Geophys. Res. Lett., 33 .LO5809, doi: 10.1029/2005GL024996.

    • Search Google Scholar
    • Export Citation
  • Kraichnan, R. H., 1970: Inertial-range transfer in two- and three-dimensional turbulence. J. Fluid Mech., 47 , 525535.

  • Kolmogorov, A. N., 1941: Dissipation of energy in the locally isotropic turbulence. Dokl. Adad. Nauk SSSR, 32, 16–18. [English translation available in Proc. Roy. Soc. London A., 434 (1991), 15–17.].

  • Koshyk, J. N., and K. Hamilton, 2001: The horizontal kinetic energy spectrum and spectral budget simulated by a high-resolution troposphere–stratosphere–mesosphere GCM. J. Atmos. Sci., 58 , 329348.

    • Search Google Scholar
    • Export Citation
  • Lilly, D. K., 1983: Stratified turbulence and the mesoscale variability of the atmosphere. J. Atmos. Sci., 40 , 749761.

  • Lindborg, E., 1995: Kinematics of homogeneous axisymmetric turbulence. J. Fluid Mech., 302 , 179201.

  • Lindborg, E., 1999: Can the atmospheric kinetic energy be explained by two-dimensional turbulence? J. Fluid Mech., 388 , 259288.

  • Lindborg, E., 2005: The effect of rotation on the mesoscale energy cascade in the free atmosphere. Geophys. Res. Lett., 32 .L01809, doi:10.1029/2004GL021319.

    • Search Google Scholar
    • Export Citation
  • Lindborg, E., 2006: The energy cascade in a strongly stratified fluid. J. Fluid Mech., 550 , 207242.

  • Marenco, A., and Coauthors Measurement of ozone and water vapor by airbus in-service aircraft: The MOZAIC airborne program, an overview. J. Geophys. Res., 103 , 2563125642.

    • Search Google Scholar
    • Export Citation
  • Monin, A. S., and A. M. Yaglom, 1975: Statistical Fluid Mechanics: Mechanics of Turbulence. Vol. 2, The MIT Press.

  • Nastrom, G. D., and K. S. Gage, 1985: A climatology of atmospheric wavenumber spectra of wind and temperature observed by commercial aircraft. J. Atmos. Sci., 42 , 950960.

    • Search Google Scholar
    • Export Citation
  • Riley, J. J., and S. T. DeBruynKops, 2003: Dynamics of turbulence strongly influenced by buoyancy. Phys. Fluids, 15 , 20472059.

  • Skamarock, W. C., 2004: Evaluating mesoscale NWP models using kinetic energy spectra. Mon. Wea. Rev., 132 , 30193032.

  • Smith, K. S., 2004: Comments on “The k−3 and k−5/3 energy spectrum of atmospheric turbulence: Quasigeostrophic two-level model simulation”. J. Atmos. Sci., 61 , 937942.

    • Search Google Scholar
    • Export Citation
  • Tung, K. K., and W. W. Orlando, 2003: The k−3 and k−5/3 energy spectrum of atmospheric turbulence: Quasigeostrophic two-level simulation. J. Atmos. Sci., 60 , 824835.

    • Search Google Scholar
    • Export Citation
  • Tung, K. K., and W. W. Orlando, 2004: “The k−3 and k−5/3 energy spectrum of atmospheric turbulence: Quasigeostrophic two-level simulation”—Reply. J. Atmos. Sci., 61 , 943948.

    • Search Google Scholar
    • Export Citation
  • VanZandt, T. E., 1982: A universal spectrum of buoyancy waves in the atmosphere. Geophys. Res. Lett., 9 , 575578.

  • Vinnichenko, V. K., 1970: The kinetic energy spectrum in the free atmosphere—1 second to 5 years. Tellus, 22 , 158166.

  • Waite, M. L., and P. Bartello, 2004: Stratified turbulence dominated by vortical motion. J. Fluid Mech., 517 , 281308.

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Horizontal Wavenumber Spectra of Vertical Vorticity and Horizontal Divergence in the Upper Troposphere and Lower Stratosphere

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  • 1 Linné Flow Centre, Department of Mechanics, KTH, Stockholm, Sweden
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Abstract

The author shows that the horizontal two-point correlations of vertical vorticity and the associated vorticity wavenumber spectrum can be constructed from previously measured velocity structure functions in the upper troposphere and lower stratosphere. The spectrum has a minimum around k = 10−2 cycles per kilometer (cpkm) corresponding to wavelengths of 100 km. For smaller wavenumbers it displays a k−1 range and for higher wavenumbers, corresponding to mesoscale motions, it grows as k1/3. The two-point correlation of horizontal divergence of horizontal velocity and the associated horizontal spectrum is also constructed. The horizontal divergence spectrum is of the same order of magnitude as the vorticity spectrum in the mesoscale range and show similar inertial range scaling. It is argued that these results show that the mesoscale motions are not dominated by internal gravity waves. Instead, the author suggests that the dynamic origin of the k1/3 range is stratified turbulence. However, in contrast to Lilly, the author finds that stratified turbulence is not a phenomenon associated with an upscale energy cascade, but with a downscale energy cascade.

Corresponding author address: Erik Lindborg, Linné Flow Centre, Department of Mechanics, KTH S-100 44 Stockholm, Sweden. Email: erikl@mech.kth.se

Abstract

The author shows that the horizontal two-point correlations of vertical vorticity and the associated vorticity wavenumber spectrum can be constructed from previously measured velocity structure functions in the upper troposphere and lower stratosphere. The spectrum has a minimum around k = 10−2 cycles per kilometer (cpkm) corresponding to wavelengths of 100 km. For smaller wavenumbers it displays a k−1 range and for higher wavenumbers, corresponding to mesoscale motions, it grows as k1/3. The two-point correlation of horizontal divergence of horizontal velocity and the associated horizontal spectrum is also constructed. The horizontal divergence spectrum is of the same order of magnitude as the vorticity spectrum in the mesoscale range and show similar inertial range scaling. It is argued that these results show that the mesoscale motions are not dominated by internal gravity waves. Instead, the author suggests that the dynamic origin of the k1/3 range is stratified turbulence. However, in contrast to Lilly, the author finds that stratified turbulence is not a phenomenon associated with an upscale energy cascade, but with a downscale energy cascade.

Corresponding author address: Erik Lindborg, Linné Flow Centre, Department of Mechanics, KTH S-100 44 Stockholm, Sweden. Email: erikl@mech.kth.se

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