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STRUCTURE ANISOTROPY IN MHD TURBULENCE SUBJECTED TO MEAN SHEAR AND FRAME ROTATION

Stavros C. Kassinos
Department of Mechanical Engineering Stanford University Stanford, California 94305 USA; Department of Mechanical and Manufacturing Engineering, Computational Sciences Laboratory, UCY-COMPSCI University of Cyprus, Nicosia, Cyprus

A. A. Wray
Center for Turbulence Research NASA Ames Research Center

Abstract

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, τshearm. When τshear << τm, we find that the turbulence structures tend to align preferentially with the streamwise direction irrespective of the magnetic Reynolds number, Rm. When τshear >>τm we find that at low Rm the turbulent eddies become elongated and aligned with the magnetic field, but at moderately high Rm, there is partial streamwise alignment of the eddies. When τshear ~ τm, we find that competing mechanisms tend to produce different structural anisotropics, and small variations in dimensionless parameters can have a strong effect on the structure of the evolving flow. For example, at Rm << 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 Rm ~ 1, the structures are found to be equally aligned in the streamwise and spanwise direction at large times. However, when Rm is moderately high (10 ≤ Rm ≤ 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 τshear ~ τm.