The Matryoshka Run: Eulerian Refinement Strategy to Study Statistics of Turbulence in Virialized Cosmic Structures

Abstract: We study the statistical properties of turbulence driven by structure formation in a massive merging galaxy cluster at z=0. The development of turbulence is ensured as the largest eddy turnover time is much shorter than the Hubble time independent of mass and redshift. We achieve a large dynamic range of spatial scales through a novel Eulerian refinement strategy where the cluster volume is refined with progressively finer uniform nested grids during gravitational collapse. This provides an unprecedented resolution of 7.3 h^{-1} kpc across the virial volume. The probability density functions of various velocity derived quantities exhibit the features characteristic of fully developed compressible turbulence observed in dedicated periodic-box simulations. Shocks generate only 60% of the total vorticity within \rvir/3 region and 40% beyond that. We compute second and third order, longitudinal and transverse, structure functions for both solenoidal and compressional components, in the cluster core, virial region and beyond. The structure functions exhibit a well defined inertial range. The injection scale is comparable to the virial radius but increases towards the outskirts. Within \rvir/3, the spectral slope of the solenoidal component is close to Kolmogorov's, but for the compressional component is substantially steeper and close to Burgers'; the flow is mostly solenoidal and statistically rigorously consistent with fully developed, homogeneous and isotropic turbulence. Small scale anisotropy appears due to numerical artifact. Towards the virial region, the flow becomes compressional, the structure functions flatter and modest genuine anisotropy appear. In comparison, mesh adaptivity based on Lagrangian refinement and the same finest resolution, leads to lack of turbulent power on small scale and excess thereof on large scales, and unreliable density weighted structure functions.