Turbulent properties of the quiet Sun represent the basic state of surface conditions, and a background for various processes of solar activity. Therefore understanding of properties and dynamics of this `basic state is important for investigation of more complex phenomena, formation and development of observed phenomena in the photosphere and atmosphere. For characterization of the turbulent properties we compare kinetic energy spectra on granular and sub-granular scales obtained from infrared TiO observations with the New Solar Telescope (Big Bear Solar Observatory) and from 3D radiative MHD numerical simulations (SolarBox code). We find that the numerical simulations require a high spatial resolution with 10 - 25 km grid-step in order to reproduce the inertial (Kolmogorov) turbulence range. The observational data require an averaging procedure to remove noise and potential instrumental artifacts. The resulting kinetic energy spectra show a good agreement between the simulations and observations, opening new perspectives for detailed joint analysis of more complex turbulent phenomena on the Sun, and possibly on other stars. In addition, using the simulations and observations we investigate effects of background magnetic field, which is concentrated in self-organized complicated structures in intergranular lanes, and find an increase of the small-scale turbulence energy and its decrease at larger scales due to magnetic field effects.
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