Critical “dimension” in shell model turbulence

Anisotropic shell model of turbulence.

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 po...

Shell model for buoyancy-driven turbulence.

In this paper we present a unified shell model for stably stratified and convective turbulence. Numerical simulation of this model for stably stratified flow shows Bolgiano-Obukhbov scaling in which the kinetic energy spectrum varies as k(-11/5). The shell model of convective turbulence yields Kolmogorov's spectrum. These results are consistent with the energy flux and energy feed due to buoyan...

Shell model for quasi-two-dimensional turbulence.

We discuss the possibility to introduce geometrical constraints in shell models of turbulence in order to mimic the turbulent dynamics that takes place in fluid layers with large aspect ratio. By using a scale-dependent set of coupling parameters, we are able to resolve both scales larger and smaller than a geometrical dimension of the flow. The proposed model is able to resolve with high accur...

Anomalous scaling in a shell model of helical turbulence

In a helical flow there is a subrange of the inertial range in which there is a cascade of both energy and helicity. In this range the scaling exponents associated with the cascade of helicity can be defined. These scaling exponents are calculated from a simulation of the GOY shell model. The scaling exponents for even moments are associated with the scaling of the symmetric part of the probabi...

A non-local shell model of hydrodynamic and magnetohydrodynamic turbulence