Varieties of scaling regimes in hydromagnetic turbulence

Abstract

We revisit the scaling properties of the energy spectra in fully developed incompressible homogeneous turbulence in forced magnetofluids (MHD) in three dimensions (3D), which are believed to be characterised by {\em universal scaling exponents} in the inertial range. Enumerating these universal scaling exponents that characterise the energy spectra remains a theoretical challenge. To study this, we set up a scaling analysis of the 3D MHD equations, driven by large-scale external forces and with or without a mean magnetic field. We use scaling arguments to bring out various scaling regimes for the energy spectra. We obtain a variety of scaling in the inertial range, ranging from the well-known Kolmogorov spectra in the isotropic 3D ordinary MHD to more complex scaling in the anisotropic cases that depend on the magnitude of the mean magnetic field. We further dwell on the possibility that the energy spectra scales as $k^{-2}$ in the inertial range, where $k$ is a wavevector belonging to the inertial range, and also speculate on unequal scaling by the kinetic and magnetic energy spectra in the inertial range of isotropic 3D ordinary MHD. We predict the possibilities of {\em scale-dependent anisotropy} and intriguing {\em weak dynamic scaling} in the Hall MHD and electron MHD regimes of anisotropic MHD turbulence. Our results can be tested in large scale simulations and relevant laboratory-based and solar wind experiments.