Quasi-geostrophic turbulence and generalized scale invariance, a theoretical reply - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Atmospheric Chemistry and Physics Année : 2012

Quasi-geostrophic turbulence and generalized scale invariance, a theoretical reply

(1) , (1) , (2) , (1)


Lindborg et al. (2010) claim that the apparent spectrum power law E(k) approximate to 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 + H-z (0 <= H-z <= 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 + H-z)-D turbulence (with 0 < H-z < 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.
Fichier principal
Vignette du fichier
acp-12-327-2012.pdf (288.65 Ko) Télécharger le fichier
Origine : Fichiers éditeurs autorisés sur une archive ouverte

Dates et versions

hal-00697578 , version 1 (22-05-2012)



D Schertzer, Ioulia Tchiguirinskaia, S. Lovejoy, A. F. Tuck. Quasi-geostrophic turbulence and generalized scale invariance, a theoretical reply. Atmospheric Chemistry and Physics, 2012, 12 (1), pp.327-336. ⟨10.5194/acp-12-327-2012⟩. ⟨hal-00697578⟩
158 Consultations
346 Téléchargements



Gmail Facebook Twitter LinkedIn More