An essential parameter for models of coronal heating and fast solar wind acceleration that rely on the dissipation of MHD turbulence is the characteristic energy-containing length $lambda_{bot}$ of the squared velocity and magnetic field fluctuations
($u^2$ and $b^2$) transverse to the mean magnetic field inside a coronal hole (CH) at the base of the corona. The characteristic length scale defines directly the heating rate. We use a time series analysis of solar granulation and magnetic field measurements inside two CHs obtained with the New Solar Telescope (NST) at Big Bear Solar Observatory. A data set for transverse magnetic fields obtained with the Solar Optical Telescope/Spectro-Polarimeter (SOT/SP) aboard {it Hinode} spacecraft was utilized to analyze the squared transverse magnetic field fluctuations $b_t^2$. Local correlation tracking (LCT) was applied to derive the squared transverse velocity fluctuations $u^2$. We find that for $u^2$-structures, Batchelor integral scale $lambda$ varies in a range of 1800 - 2100 km, whereas the correlation length $varsigma$ and the $e$-folding length $L$ vary between 660 and 1460 km. Structures for $b_t^2$ yield $lambda approx 1600$ km, $varsigma approx 640$ km, and $L approx 620$ km. An averaged (over $lambda, varsigma$, and $L$) value of the characteristic length of $u^2$-fluctuations is 1260$pm$500 km, and that of $b_t^2$ is 950$pm$560 km. The characteristic length scale in the photosphere is approximately 1.5-50 times smaller than that adopted in previous models (3-30$times10^3$ km). Our results provide a critical input parameter for current models of coronal heating and should yield an improved understanding of fast solar wind acceleration.
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.
