Is isotropic turbulence relevant in the atmosphere?

Abstract

[1] The problem of turbulence is ubiquitous in the Earth sciences, astrophysics and elsewhere. Virtually the only theoretical paradigm that has been seriously considered is strongly isotropic in the sense that scaling exponents are the same in all directions so that any remaining anisotropy is ''trivial.'' Using 235 state-of-the-art drop sonde data sets of the horizontal wind at %5 m resolution in the vertical, we show that the atmosphere is apparently outside the scope of these isotropic frameworks. It suggests that anisotropy may frequently be strong requiring different scaling exponents in the horizontal and vertical directions.

Characterization and Parametrization of Reynolds Stress and Turbulent Heat Flux in the Stably-Stratified Lower Arctic Troposphere Using Aircraft Measurements

“…First, it accounts for the anisotropic nature of turbulence in the troposphere, which is also confirmed by observations of Lovejoy et al (2007). Second, it incorporates term V in the budget equation to predict the observed countergradient heat transport.…”

“…Figure 10 shows the absolute value of the cospectrum of the heat flux for n = 920 spectra on a logarithmic scale and the cospectrum of the heat flux separated into the boundary layer (n = 74) and the free troposphere (n = 846) on a logarithmic-inear scale. The absolute value is used in the logarithmic scale to consolidate all spectra on the same plot in order to observe the regimes associated with the buoyancy flux and the Kolmogorov inertial subrange (Hocking 1999;Pope 2000;Stull 2003;Lovejoy et al 2007). The cospectrum at small scale (inertial subrange) occurs at approximately κ > 0.01 m −1 , while the cospectrum at large scale (buoyancy range) occurs at approximately κ < 0.01 m −1 .…”

The temporal cascade structure of reanalyses and global circulation models

“…A wide-scale range of cascade processes is possible because it appears that the vertical structure of the atmosphere is scaling but with different exponents than in the horizontal structure. This implies that the cascades are anisotropic with structures becoming progressively flatter at larger and larger scales but in a scaling manner (Lovejoy et al, 2007(Lovejoy et al, , 2009a. For a theoretical model based on the (fractional) vorticity equation, see Schertzer et al(2012).…”

Comment on &quot;Reinterpreting aircraft measurement in anisotropic scaling turbulence&quot; by Lovejoy et al. (2009)

“…Although Lovejoy et al (2007) criticized Charney (1971) for using an isothermal lower boundary and for assuming 3-D quasi-isotropy, these limitations have been relaxed in many of the modern models of atmospheric turbulence. Model simulations of anisotropic quasigeostrophic turbulence consistently show a k −3 -spectrum at synoptic scales (e.g.…”

“…According to the argument of Lovejoy et al this small difference causes a dramatic shift of about one order of magnitude in the kinetic energy spectrum and the velocity structure function at scales on the order of 1000 km. Such a large shift is highly unlikely, because the typical change of wind over a vertical distance of 100 m is less than 1 m/s (Alisse and Sidi, 2000;Lovejoy et al, 2007), while the typical change of wind over a horizontal distance of 1000 km is larger than 10 m/s (Cho and Lindborg, 2001). At synoptic scales, the difference between an energy spectrum or a second order structure function measured at an isobar and the same quantity measured at a nearby isoheight can therefore be estimated to be 1% or less.…”