  We study structure and dynamics of the turbulent photospheric magnetic field
in the active region NOAA 11158 by characterizing the spatial and temporal
scaling properties of the line-of-sight (LOS) component. Using high-resolution
high-cadence LOS magnetograms from SDO/HMI, we measured power-law exponents
$\alpha$ and $\beta$ describing wavenumber- ($k$) and frequency-domain ($f$)
Fourier power spectra, respectively, and investigated their evolution during
the passage of the active region through the field of view of HMI. Flaring
active region NOAA 11158 produces an average one-dimensional spatial power
spectral density that follows approximately a $k^{-2}$ power law -- a spectrum
that suggests parallel MHD fluctuations in an anisotropic turbulent medium. In
addition, we found that values of $\alpha$ capture systematic changes in the
configuration of LOS photospheric magnetic field during flaring activity in the
corona. Position-dependent values of the temporal scaling exponent $\beta$
showed that, on average, the core of the active region scales with $\beta >$ 3
surrounded by a diffusive region with an approximately $f^{-2}$-type spectrum.
Our results indicate that only about 1 - 3 \% of the studied LOS photospheric
magnetic flux displays $\beta\approx\alpha$, implying that Taylor's hypothesis
of frozen-in-flow turbulence is typically invalid for this scalar in presence
of turbulent photospheric flows. In consequence, both spatial and temporal
variations of the plasma and magnetic field must be included in a complete
description of the turbulent evolution of active regions.
