  The intracluster medium (ICM) in the centers of galaxy clusters is heavily
influenced by the ``feedback'' from supermassive black holes (SMBHs). Feedback
can drive turbulence in the ICM and turbulent dissipation can potentially be an
important source of heating. Due to the limited spatial and spectral
resolutions of X-ray telescopes, direct observations of turbulence in the hot
ICM have been challenging. Recently, we developed a new method to measure
turbulence in the ICM using multiphase filaments as tracers. These filaments
are ubiquitous in cluster centers and can be observed at very high resolution
using optical and radio telescopes. We study the kinematics of the filaments by
measuring their velocity structure functions (VSFs) over a wide range of scales
in the centers of $\sim 10$ galaxy clusters. We find features of the VSFs that
correlate with the SMBHs activities, suggesting that SMBHs are the main driver
of gas motions in the centers of galaxy clusters. In all systems, the VSF is
steeper than the classical Kolmogorov expectation and the slopes vary from
system to system. One theoretical explanation is that the VSFs we have measured
so far mostly reflect the motion of the driver (jets and bubbles) rather than
the cascade of turbulence. We show that in Abell 1795, the VSF of the outer
filaments far from the SMBH flattens on small scales to a Kolmogorov slope,
suggesting that the cascade is only detectable farther out with the current
telescope resolution. The level of turbulent heating computed at small scales
is typically an order of magnitude lower than that estimated at the driving
scale. Even though SMBH feedback heavily influences the kinematics of the ICM
in cluster centers, the level of turbulence it drives is rather low, and
turbulent heating can only offset $\lesssim10\%$ of the cooling loss,
consistent with the findings of numerical simulations.
