What does it mean to take the mean? The effect of the averaging scale on the characterization of interstellar turbulence

In studies of the interstellar medium (ISM), defining an ordered and a random velocity or magnetic field extends beyond the scope of simple thought experiments. It often plays a crucial role in interpreting the dynamics of turbulence, both in simulations and in observations. We investigate how the choice of an averaging scale affects the measurement and characterization of magnetic and kinetic turbulence in Milky Way-sized disk galaxies with different initial magnetic morphologies. We analyzed two magnetohydrodynamic (MHD) simulations of isolated disk galaxies: one initialized with a toroidal magnetic field (model T) and the other with a random field (model R). Using a spherical filtering method, we decomposed the magnetic and velocity fields into mean and fluctuating components, while varying the averaging scale. We examined their energy ratios and power spectra as functions of time and the averaging radius. Both models develop ordered and turbulent magnetic structures, whose relative strengths vary strongly with the averaging radius. The power spectra of the velocity and magnetic mean fields steepen with an increasing smoothing scale, tracing the transition from coherent to turbulent regimes. The turbulent kinetic energy dominates over the magnetic counterpart, although the latter remains dynamically significant. Importantly, we find that these ratios depend more strongly on the averaging radius than on the initial conditions of the magnetic field. The characterization of turbulence as strong or weak, meaning whether or not fluctuations dominate over the mean depends sensitively on the chosen averaging scale, rather than being an intrinsic property of the system. The strong dependence of the turbulent fractions on the averaging scale has direct implications for magnetic field estimates obtained from observational methods such as the Davis-Chandrasekhar-Fermi technique. A careful consideration of scale is therefore essential when interpreting magnetic and kinetic turbulence in galaxies.