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We use the Matryoshka run to study the time dependent statistics ofstructure-formation driven turbulence in the intracluster medium of a10$^{15}M_\odot$ galaxy cluster. We investigate the turbulent cascade in theinner Mpc for both compressional and incompressible velocity components. Theflow maintains approximate conditions of fully developed turbulence, withdepartures thereof settling in about an eddy-turnover-time. Turbulent velocitydispersion remains above $700$ km s$^{-1}$ even at low mass accretion rate,with the fraction of compressional energy between 10% and 40%. Normalisationand slope of compressional turbulence is susceptible to large variations onshort time scales, unlike the incompressible counterpart. A major merger occursaround redshift $z\simeq0$ and is accompanied by a long period of enhancedturbulence, ascribed to temporal clustering of mass accretion related tospatial clustering of matter. We test models of stochastic acceleration bycompressional modes for the origin of diffuse radio emission in galaxyclusters. The turbulence simulation model constrains an important unknown ofthis complex problem and brings forth its dependence on the elusivemicro-physics of the intracluster plasma. In particular, the specifics of theplasma collisionality and the dissipation physics of weak shocks affect thecascade of compressional modes with strong impact on the acceleration rates. Inthis context radio halos emerge as complex phenomena in which a hierarchy ofprocesses acting on progressively smaller scales are at work. Stochasticacceleration by compressional modes implies statistical correlation of radiopower and spectral index with merging cores distance, both testable inprinciple with radio surveys.

The Matryoshka Run (II): Time Dependent Turbulence Statistics, Stochastic Particle Acceleration and Microphysics Impact in a Massive Galaxy Cluster