Analytical theory of forced rotating sheared turbulence

نویسنده

  • Nicolas Leprovost
چکیده

Rotation and shear flows are ubiquitous features of many astrophysical and geophysical bodies. To understand the origin of large-scale shear flow and its effect on turbulent transport in these systems, we consider a forced turbulence and investigate the combined effect of rotation and shear flow on the turbulence properties. Specifically, we study 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, and the anisotropy in these quantities in the cases where the rotation and the shear are parallel or perpendicular. In all the cases considered, turbulence amplitude is always quenched due to strong shear (ξ = νk y/A ≪ 1, where A is the shearing rate, ν is the molecular viscosity and ky is a characteristic wave-number), with stronger reduction in the direction of the shear than those in the perpendicular directions. Specifically, in the large rotation limit (Ω ≫ A), they scale as A−1 and A−1| ln ξ|, respectively, while in the weak rotation limit (Ω ≪ A), they scale as A−1 and A−2/3, respectively. Thus, flow shear always leads to weak turbulence with an effectively stronger turbulence in the plane perpendicular to shear than in the shear direction, regardless of rotation rate. The anisotropy in turbulence amplitude is however weaker by a factor of ξ1/3| ln ξ| (∝ A−1/3| ln ξ|) in the rapid rotation limit (Ω ≫ A) than that in weak rotation limit (Ω ≪ A) since rotation favours almostisotropic turbulence. Compared to turbulence amplitude, particle transport is found to crucially depend on whether rotation is stronger or weaker than flow shear. When rotation is stronger than flow shear (Ω ≫ A), the transport is inhibited by inertial waves, being quenched inversely proportional to the rotation rate (i.e. ∝ Ω−1) while in the opposite case, it is reduced by shearing as A−1. Furthermore, the anisotropy is found to be very weak in the strong rotation limit (by a factor of 2) while significant in the strong shear limit. The turbulent viscosity is found to be negative with inverse cascade of energy as long as rotation is sufficiently strong compared to flow shear (Ω ≫ A) while positive in the opposite limit of weak rotation (Ω ≪ A). Even if the eddy viscosity is negative for strong rotation (Ω ≫ A), flow shear, which transfers energy to small scales, has an interesting effect by slowing down the rate of inverse cascade with the value of negative eddy viscosity decreasing as |νT | ∝ A−2 for strong shear. Furthermore, the interaction between the shear and the rotation is shown to give rise to a novel non-diffusive flux of angular momentum (Λ-effect), even in the absence of external sources of anisotropy. This effect provides a mechanism alternative to negative turbulent viscosity for the existence of shearing structures in astrophysical and geophysical systems.

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تاریخ انتشار 2007