Correlations and Cascades in Magnetized Turbulence

Many terrestrial and astrophysical plasmas encompass very large dynamical ranges in space and time, which are not accessible by direct numerical simulations. Thus, idealized subvolumes are often used to study small-scale effects including the dynamics of magnetized turbulence. A significant aspect of magnetized turbulence is the transfer of energy from large to small scales, in part through the operation of a turbulent cascade. In this paper, we present a new shell-to-shell energy transfer analysis framework for understanding energy transfer within magnetized turbulence and in particular, through the cascade. We demonstrate the viability of this framework through application to a series of isothermal subsonic and supersonic simulations of compressible magnetized turbulence and utilize results from this analysis to establish a
nonlinear
benchmark for compressible magnetized turbulence in the subsonic regime. We further study how the autocorrelation time of the driving and its normalization systematically change properties of compressible magnetized turbulence. For example, we find that
$\delta $
-in-time forcing with a constant energy injection leads to a steeper slope in kinetic energy spectrum and less efficient small-scale dynamo action. We examine how these results can impact a range of diagnostics relevant for a range of terrestrial and astrophysical applications.