Abstract. Many astrophysical fluids are in turbulent state. To maintain turbulence, energy must be injected into the fluid. In turbulence simulations, it is customary to drive the fluids on a scale comparable to the size of the computational domain. In this paper, we show how some statistics of turbulence, especially turbulence statistics projected on the plane of the sky, is changed when we do not follow the conventional approach. As an example of such a statistics, we discuss in detail how the Chandrasekhar-Fermi method is affected by the small-scale driving, which is a simple and powerful technique for estimating the strength of the mean magnetic field projected on the plane of the sky.
IntroductionDriving is required to initiate and maintain turbulence. When hydrodynamic turbulence is driven on a scale L f , the injected energy cascades down to small scales and, when the energy cascade reaches the dissipation scale L d , the energy is lost through viscous damping. The energy spectrum of turbulence peaks at the driving wavenumber k f and shows a power-law scaling in the range between k f and the dissipation wave number k d . The spectrum drops rapidly for wavenumbers larger than k d .In turbulence simulations, the driving scale L f is usually very close to the computational box size L sys . The reason for this is to maximize the inertial range. Let us assume L sys = 2π throughout the paper. In most turbulence simulations, the dissipation wavenumber k d is determined by the numerical resolution: k d is slightly smaller than the maximum wavenumber N x /2, where N x is the number of grid points in one direction. Therefore, in order to maximize the inertial range, it is necessary to drive turbulence near k ∼ 1, which means k f ∼ 1 andIn astronomy, observed quantities are usually integrated along the line-of-sight (LOS). Since observed quantities are two-dimensional (2D) data, obtaining three-dimensional (3D) quantities from observations is not easy. Nevertheless, there are techniques developed to derive 3D turbulence properties from 2D observations. However, those techniques have an intrinsic shortcoming: it is difficult to verify them. To overcome this difficulty, people use computer simulation data to verify their techniques.One such example is the Chandrasekhar-Fermi (CF) method [1], which is a powerful technique for estimating the strength of the plane-of-the-sky component of the mean magnetic field, B 0,sky . The CF method makes use of polarized emission from magnetically aligned dust grains. In the