Analytical theory of forced rotating sheared turbulence. I. Perpendicular case

Abstract

We provide a consistent theory of turbulence in the presence of shear and rotation. Starting from a quasi-linear equation for the fluctuating fields, we derive turbulence amplitude and turbulent transport coefficients, taking into account the effect of shear and rotation on turbulence. We show that the shear reduces both turbulence amplitude and transport, more strongly in the direction parallel to the shear than in the perpendicular one, effectively inducing an anisotropic turbulence. The rotation further reduces turbulence amplitude and transport. The interaction between the shear and the rotation is shown to give rise to a novel non-diffusive flux of angular momentum ($Λ$-effect), providing a mechanism for the permanence of shearing structure in astrophysical and geophysical systems.