Theoretical models for gravity wave horizontal wave number spectra: Effects of wave field anisotropies

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Abstract
Theoretical models are derived for the gravity wave one‐dimensional (1‐D) and 2‐D horizontal wave number spectra which include the effects of wave field anisotropies. The new models are based on the diffusive filtering [Gardner, 1994] and linear instability [Dewan and Good, 1986] wave dissipation paradigms and are generalizations of our earlier models for isotropic spectra. They are derived by making two crucial assumptions, namely, that waves propagating at different azimuth angles are statistically independent because they originate at different locations from different sources, and all waves, including those in the so‐called saturation regime, obey the polarization and dispersion relations. The unambiguous 2‐D spectra can be expressed as functions of (h, ϕ) or (k, l), where k = h sin ϕ is the zonal wave number, l = h cos ϕ is the meridional wave number, h = (k2 + l2)1/2, and ϕ = tan−1k/l is the azimuth angle of propagation. For a given azimuth angle, the unambiguous (h, ϕ) spectrum is simply the 1‐D horizontal wave number spectrum associated with just the waves propagating in the ϕ direction scaled by 2π/h. The diffusive filtering theory spectra are separable in h and ϕ, while the linear instability theory spectra are not. These results can be used to characterize the wave fields generated by realistic source distributions in the lower atmosphere and are particularly useful for developing accurate parameterizations of gravity wave effects in global circulation models.