Theoretical study of anisotropic MHD turbulence with low magnetic Reynolds number

Flows of electrically conducting fluids under the action of external magnetic field present an example of strongly anisotropic turbulence. Such flows are not only important for different engineering applications, but also provide an interesting framework for studies of quasi-two-dimensional turbulence with strongly modified transport properties in easily controllable laboratory experiments. We present theoretical results that advance our understanding of magnetohydrodynamic (MHD) flows with low magnetic Reynolds number by treating this phenomenon within the quasi-normal scale elimination (QNSE) theory. Previous applications of the theory to turbulent flows with stable stratification and solid body rotation have demonstrated that QNSE is a powerful tool for studies of anisotropic turbulent flows. We derive expressions for scale-dependent eddy viscosities and eddy diffusivities in the directions parallel and normal to the external magnetic field and investigate progressive anisotropization of turbulent transport of momentum and passive scalar. The theory yields analytical expressions for anisotropic one-dimensional spectra of MHD turbulence. In particular, the theory sheds light upon the modification of the Kolmogorov k(-5/3) spectrum by anisotropic Ohmic (Joule) dissipation.