Quasi-linear theory of forced rotating sheared turbulence
نویسنده
چکیده
Rotation and shear flows are an ubiquitous features of many astrophysical and geophysical bodies, playing a crucial role in turbulent transport. To understand the complex dynamics in these systems, 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 (turbulent viscosity and diffusivity), taking into account the effect of shear and rotation on turbulence. We focus on the two cases where the rotation is perpendicular and parallel to the plane of the shear flow. 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 when it is perpendicular to the shear but does not have much effect when it is parallel to the shear. The interaction between the shear and the rotation is shown to give rise to a novel nondiffusive flux of angular momentum (Λ-effect), providing a mechanism for the permanence of shearing structure in astrophysical and geophysical systems. Eddy viscosity tends to become negative for fast rotation and strong shear. Anisotropic transport reduction is also found in turbulent mixing of passive scalars, largely due to shear flow.
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