Statistical measures of structural anisotropy in MHD turbulence subjected to mean shear and frame rotation

We consider homogeneous turbulence in a conducting fluid that is exposed to a uniform external magnetic field while being sheared in fixed and rotating frames. We take both the frame-rotation axis and the applied magnetic field to be aligned in the direction normal to the plane of the mean shear. We find that a key parameter determining the structural morphology of the flow is the ratio of the time scale of the mean shear to the Joule time, τ_shear/τ _m . When τ_shear ≪ τ _m , we find that the turbulence structures tend to align preferentially with the streamwise direction irrespective of the magnetic Reynolds number, R _m . When τ_shear ≫ τ _m , we find that at low R _m the turbulent eddies become elongated and aligned with the magnetic field, but at moderately high R _m , there is partial streamwise alignment of the eddies. When τ_shear≈ τ _m , we find that competing mechanisms tend to produce different structural anisotropies, and small variations in dimensionless parameters can have a strong effect on the structure of the evolving flow. For example, at R _m ≪ 1, a preferential alignment of structures in the direction of the magnetic field emerges as the flow evolves, consistent with the predictions of the quasi-static approach. For R _m ∼ 1, the structures are found to be equally aligned in the streamwise and spanwise direction at large times. However, when R _m is moderately high (10 ≲ R _m ≲ 50) this strong spanwise alignment is replaced by a preferential alignment of structures in the streamwise direction. Counter to intuition, we found evidence that strong rotation in combination with a spanwise magnetic field tends to promote a streamwise alignment of the eddies, at least when τ_shear≈ τ _m .