title: Symmetries, invariants, and cascades in a shell model of turbulence
abstract: Reduced wave number models of turbulence, namely shell models, show cascade processes and anomalous scaling of correlators which might be analogous to what is observed in Navier-Stokes (NS) turbulence. The scaling properties of the shell models depend on the specific symmetries and invariants of the models. A shell model is investigated. It is argued that this model might have a closer resemblance than the standard Gledzer-Ohkitani-Yamada model to the NS turbulence. The shell model investigated here coincides with the Sabra model proposed by L'vov et al. [Phys. Rev. E. 58, 1811 (1998)] for a specific choice of the free parameters of their model. For this choice of parameters, besides the energy and the "helicity," the model has a cubic inviscid invariant.
authors.affiliation: The Niels Bohr Institute, University of Copenhagen, Juliane Maries Vej 30, DK-2100 Copenhagen O, Denmark.
authors.initials: PD
authors.lastname: Ditlevsen