Rapidly sheared homogeneous MHD turbulence in a rotating frame

Abstract

© 2011 International Symposium on Turbulence and Shear Flow Phenomena, TSFP07. All rights reserved. Rapid distortion theory is applied to magneto-hydrodynamic turbulence that is sheared in a rotating frame. We describe analytically the modification of the three-dimensional velocity spectra due to the presence of an external magnetic field, using the quasi-static approximation. Using this analytical solution, we investigate the effect of the frame rotation in the evolution of one-point statistics, under the linear theory. For initial fields that are two-dimensional (but three-componential), with the axis of independence aligned with the flow direction, we derive analytically one-point statistics, such as the Reynolds stresses and the structure dimensionality tensor in physical space. The analytical results are compared with the linear three-dimensional exact numerical solution for initially isotropic homogeneous turbulence, and they show remarkable agreement. They describe accurately the tendencies in the morphology of the turbulent structures that develop as a result of the two competitive mechanisms of the frame rotation and the Joule dissipation. These results are in qualitative agreement with existing non-linear DNS results.