Journal cover Journal topic
Atmospheric Chemistry and Physics An interactive open-access journal of the European Geosciences Union
Atmos. Chem. Phys., 12, 327-336, 2012
© Author(s) 2012. This work is distributed under
the Creative Commons Attribution 3.0 License.
Peer-reviewed comment
05 Jan 2012
Quasi-geostrophic turbulence and generalized scale invariance, a theoretical reply
D. Schertzer1, I. Tchiguirinskaia1, S. Lovejoy2, and A. F. Tuck1 1Université Paris-Est, Ecole des Ponts ParisTech, LEESU, Marne-la-Vallée, France
2McGill U., Physics dept, Montreal, Canada
Abstract. Lindborg et al. (2010) claim that the apparent spectrum power law E(k) ≈ k−3 on scales ≥600 km obtained with the help of commercial jetliner trajectory deviations (GASP and Mozaic databases) could not be brought into question (Lovejoy et al., 2009a), because this spectrum corresponds to "a well known theory of quasi-geostrophic turbulence developed by Charney (1971)". Lindborg et al. (2010) also claim that "limitations [of this theory] have been relaxed in many of the modern models of atmospheric turbulence". We show that both claims are irrelevant and that generalized scale invariance (GSI) is indispensable to go beyond the quasi-geostrophic limitations, to go in fact from scale analysis to scaling analysis in order to derive better analytical models. In this direction, we derive vorticity equations in a space of (fractal) dimension D=2+Hz (0 ≤ Hz ≤ 1), which corresponds to a first step in the derivation of a dynamical alternative to the quasi-geostrophic approximation and turbulence. The corresponding precise definition of fractional dimensional turbulence already demonstrates that the classical 2-D and 3-D turbulence are not the main options to understand atmospheric dynamics. Although (2 + Hz)-D turbulence (with 0 < Hz < 1) has more common features with 3-D turbulence than with 2-D turbulence, it has nevertheless very distinctive features: its scaling anisotropy is in agreement with the layered pancake structure, which is typical of rotating and stratified turbulence but not of the classical 3-D turbulence.

Citation: Schertzer, D., Tchiguirinskaia, I., Lovejoy, S., and Tuck, A. F.: Quasi-geostrophic turbulence and generalized scale invariance, a theoretical reply, Atmos. Chem. Phys., 12, 327-336,, 2012.
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