Analytical theory of forced rotating sheared turbulence. The Parallel case

TL;DR

This paper analyzes how parallel rotation and shear flow influence turbulence, transport, and energy cascade, revealing that rotation impacts turbulence amplitude mainly at rapid rotation rates and affects particle transport under similar conditions.

Contribution

It provides a theoretical analysis of the parallel rotation-shear case, complementing previous work on perpendicular configurations, and clarifies the effects on turbulence and transport properties.

Findings

Rotation affects turbulence amplitude only at very rapid rotation rates.

Rotation influences particle transport mainly during rapid rotation.

Rotation reduces anisotropy slightly at high rotation speeds.

Abstract

Forced turbulence combined with the effect of rotation and shear flow is studied. In a previous paper [Leprovost and Kim, PRE in press (2008)], we considered the case where the shear and the rotation are perpendicular. Here, we consider the complementary case of parallel rotation and shear, elucidating how rotation and flow shear influence the generation of shear flow (e.g. the direction of energy cascade), turbulence level, transport of particles and momentum. In contrast with the case where rotation and shear are perpendicular, we found that rotation affects turbulence amplitude only for very rapid rotation ($\Omega \gg \A$) where it reduces slightly the anisotropy due to shear flow. Also, concerning the transport properties of turbulence, we find that rotation affects only the transport of particle and only for rapid rotation, leading to an almost isotropic transport (whereas, in the case of perpendicular rotation and shear, rotation favors isotropic transport even for slow rotation).