  Exploring the ICM power spectrum can help us to probe the physics of galaxy
clusters. Using high-resolution 3D plasma simulations, we study the statistics
of the velocity field and its relation with the thermodynamic perturbations.
The normalization of the ICM spectrum (density, entropy, or pressure) is
linearly tied to the level of large-scale motions, which excite both gravity
and sound waves due to stratification. For low 3D Mach number M~0.25, gravity
waves mainly drive entropy perturbations, traced by preferentially tangential
turbulence. For M>0.5, sound waves start to significantly contribute, passing
the leading role to compressive pressure fluctuations, associated with
isotropic (or slightly radial) turbulence. Density and temperature fluctuations
are then characterized by the dominant process: isobaric (low M), adiabatic
(high M), or isothermal (strong conduction). Most clusters reside in the
intermediate regime, showing a mixture of gravity and sound waves, hence
drifting towards isotropic velocities. Remarkably, regardless of the regime,
the variance of density perturbations is comparable to the 1D Mach number. This
linear relation allows to easily convert between gas motions and ICM
perturbations, which can be exploited by Chandra, XMM data and by the
forthcoming Astro-H. At intermediate and small scales (10-100 kpc), the
turbulent velocities develop a Kolmogorov cascade. The thermodynamic
perturbations act as effective tracers of the velocity field, broadly
consistent with the Kolmogorov-Obukhov-Corrsin advection theory. Thermal
conduction acts to damp the gas fluctuations, washing out the filamentary
structures and steepening the spectrum, while leaving unaltered the velocity
cascade. The ratio of the velocity and density spectrum thus inverts the
downtrend shown by the non-diffusive models, allowing to probe the presence of
significant conductivity in the ICM.
