On two-dimensionalization of three-dimensional turbulence in shell models

TL;DR

This paper uses a modified shell model to study how rotation influences three-dimensional turbulence, revealing spectrum steepening, flux depletion, and inverse cascade phenomena.

Contribution

It introduces a shell model approach to simulate and analyze the two-dimensionalization effects in rotating 3D turbulence.

Findings

Spectrum steepening with increased rotation strength

Depletion of forward energy flux and emergence of inverse cascade

Presence of self-similarity in velocity difference PDFs

Abstract

Applying a modified version of the Gledzer-Ohkitani-Yamada (GOY) shell model, the signatures of so-called two-dimensionalization effect of three-dimensional incompressible, homogeneous, isotropic fully developed unforced turbulence have been studied and reproduced. Within the framework of shell models we have obtained the following results: (i) progressive steepening of the energy spectrum with increased strength of the rotation, and, (ii) depletion in the energy flux of the forward forward cascade, sometimes leading to an inverse cascade. The presence of extended self-similarity and self-similar PDFs for longitudinal velocity differences are also presented for the rotating 3D turbulence case.