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Atmos. Chem. Phys. Discuss., 11, 3301-3320, 2011
www.atmos-chem-phys-discuss.net/11/3301/2011/ doi:10.5194/acpd-11-3301-2011 © Author(s) 2011. This work is distributed under the Creative Commons Attribution 3.0 License. |
Quasi-geostrophic turbulence and generalized scale invariance, a theoretical reply
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 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. This enables us to derive vorticity equations in a space of (fractional) dimension D=2+Hz (0 ≤ Hz ≤1), which seem to be an interesting dynamical alternative to the quasi-geostrophic approximation and turbulence.
Citation: Schertzer, D., Tchiguirinskaia, I., Lovejoy, S., and Tuck, A.: Quasi-geostrophic turbulence and generalized scale invariance, a theoretical reply, Atmos. Chem. Phys. Discuss., 11, 3301-3320, doi:10.5194/acpd-11-3301-2011, 2011.