Anisotropic shell model of turbulence

Abstract

An anisotropic shell model has been proposed for two-dimensional (2D) turbulence. It is similar to the 2D version of the Gledzer-Ohkitani-Yamada model but with the angular variable in wave-number space divided into three distinct directions representing structures elongated in different directions. In the case when the drive is isotropic the usual isotropic solution is recovered as the fixed point of this model. The Hasegawa-Mima limit of the model is considered in particular due to its relevance for 2D anisotropic systems such a quasigeostrophic and plasma turbulence. It is observed from this simple model that the anisotropy diminishes as a function of scale during the cascade process, and the maximum of the energy is not at the node that has maximum drive, but at a nearby node that is directly coupled to that one. © 2011 American Physical Society.