Diffusive filtering theory of gravity wave spectra in the atmosphere

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The author presents an alternative to proposed mechanisms explaining horizontal wind gravity wave vertical wavenumber spectra by assuming that the damping effects of molecular viscosity, turbulence, and off-resonance wave-wave interactions can be characterized in terms of a scale-independent diffusivity (D) which increases with altitude. A wave of intrinsic frequency ω and vertical wave number m is assumed to be completely damped when the effective vertical velocity of momentum diffusion (mD) exceeds the vertical phase velocity of the wave (ω/m). Only waves satisfying mD < ω/m, or equivalently m2D < ω and m < ω/D)1/2 are permitted to grow in amplitude as they propagate upward in the atmosphere. If the gravity wave temporal spectrum of horizontal winds varies as ω-p, we show that the vertical wave number spectrum must vary as m-2p+1 and the zonal (or meridional) wave number spectrum must vary as k-(2p+1)/3. The spectra are proportioinal to ω-p, m-3 and k-(3p-1)/(p+1). Because the joint (m, ω) intrinsic spectra for both scale-independent and scale-dependent diffusive filtering are not separable, the theory predicts that the m spectra of vertical winds are proportional to m5-2p for scale-independent diffusion and m(7-3p)/(p-1) for scale-dependent diffusion. -from Author

Original languageEnglish (US)
Pages (from-to)20,601-20,622
JournalJournal of Geophysical Research
Issue numberD10
StatePublished - 1994
Externally publishedYes

ASJC Scopus subject areas

  • Geophysics
  • Forestry
  • Oceanography
  • Aquatic Science
  • Ecology
  • Water Science and Technology
  • Soil Science
  • Geochemistry and Petrology
  • Earth-Surface Processes
  • Atmospheric Science
  • Earth and Planetary Sciences (miscellaneous)
  • Space and Planetary Science
  • Palaeontology


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