title: Logarithmic discretization and systematic derivation of shell models in two-dimensional turbulence.
abstract: A detailed systematic derivation of a logarithmically discretized model for two-dimensional turbulence is given, starting from the basic fluid equations and proceeding with a particular form of discretization of the wave-number space. We show that it is possible to keep all or a subset of the interactions, either local or disparate scale, and recover various limiting forms of shell models used in plasma and geophysical turbulence studies. The method makes no use of the conservation laws even though it respects the underlying conservation properties of the fluid equations. It gives a family of models ranging from shell models with nonlocal interactions to anisotropic shell models depending on the way the shells are constructed. Numerical integration of the model shows that energy and enstrophy equipartition seem to dominate over the dual cascade, which is a common problem of two-dimensional shell models.
authors.affiliation: Laboratoire de Physique des Plasmas, Ecole Polytechnique, F-91128 Palaiseau Cedex, France.|CNRS, UMR7648, Laboratoire de Physique des Plasmas, F-91128, Palaiseau, France.|Université Paris-Sud, UMR7648, Laboratoire de Physique des Plasmas, F-91128, Palaiseau, France.|Sorbonne Universités, UPMC Univ Paris 06, UMR7648, Laboratoire de Physique des Plasmas, F-91128, Palaiseau, France.
authors.forename: Ö D
authors.initials: ÖD
authors.lastname: Gürcan
authors.affiliation: Laboratoire de Physique des Plasmas, Ecole Polytechnique, F-91128 Palaiseau Cedex, France.|CNRS, UMR7648, Laboratoire de Physique des Plasmas, F-91128, Palaiseau, France.|Université Paris-Sud, UMR7648, Laboratoire de Physique des Plasmas, F-91128, Palaiseau, France.|Sorbonne Universités, UPMC Univ Paris 06, UMR7648, Laboratoire de Physique des Plasmas, F-91128, Palaiseau, France.
authors.forename: P
authors.initials: P
authors.lastname: Morel
authors.affiliation: Laboratoire de Physique des Plasmas, Ecole Polytechnique, F-91128 Palaiseau Cedex, France.|CNRS, UMR7648, Laboratoire de Physique des Plasmas, F-91128, Palaiseau, France.
authors.forename: S
authors.initials: S
authors.lastname: Kobayashi
authors.affiliation: Laboratoire de Physique des Plasmas, Ecole Polytechnique, F-91128 Palaiseau Cedex, France.|CNRS, UMR7648, Laboratoire de Physique des Plasmas, F-91128, Palaiseau, France.
authors.forename: Rameswar
authors.initials: R
authors.lastname: Singh
authors.affiliation: Laboratoire de Physique des Plasmas, Ecole Polytechnique, F-91128 Palaiseau Cedex, France.|Université Paris-Sud, UMR7648, Laboratoire de Physique des Plasmas, F-91128, Palaiseau, France.
authors.forename: S
authors.initials: S
authors.lastname: Xu
authors.affiliation: CASS and Department of Physics, University of California San Diego, La Jolla, California 92093-0424, USA.
authors.forename: P H
authors.initials: PH
authors.lastname: Diamond