Kolmogorov scaling, its extensions,and two-dimensional turbulence - Turbulence in the Atmosphere - page 167

Figure 7.6 Spectra of horizontal velocity components and temperature in the upper
atmosphere. From Nastrom and Gage ( 1985 ).

7.5.5 Atmospheric observations
Perhaps the most complete observations of velocity spectra above the boundary
layer are those reported by Nastrom and Gage ( 1985 ). Their results, which are
based on measurements made during more than 6000 commercial aircraft flights,
are summarized in Figure 7.6 . At the smaller wavenumbers the spectra fall as κ − 3
for perhaps a half-decade, and at larger wavenumbers they show an extended κ − 5 / 3
range. According to Vallis ( 2006 )the

3 range may be associated with a forward
enstrophy cascade, but the origin of the κ − 5 / 3 range at smaller scales is not clear.
But Gage ( 1979 ) has hypothesized that two-dimensional turbulence can exhibit a
κ − 5 / 3 range due to an inverse energy cascade, and Gage and Nastrom ( 1986 ) state
that it seems reasonable to assume that “breaking waves” are an important part of
its small-scale energy source. Lilly ( 1989 ) shows that turbulence closure models
indicate that such forward enstrophy and inverse energy cascades can coexist in
two-dimensional turbulence with energy sources at both large and small scales.

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