http://arxiv.org/abs/1310.2951
We study the statistical properties of turbulence driven by structure formation in a massive merging galaxy cluster at redshift z=0. Turbulence develops as the largest eddy turnover time is much shorter than the Hubble time independent of mass and redshift. To achieve a sufficiently large dynamic range of spatial scales we employ 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 same features characteristic of fully developed compressible turbulence as observed in dedicated periodic-box simulations. We apply Hodge-Helmholtz decomposition to the velocity field and compute second and third order, longitudinal and transverse, structure functions for both solenoidal and compressional components, in the cluster core, virial region and beyond. In general, the structure functions exhibit a well defined inertial range of turbulent cascade. The injection scale is comparable to the virial radius but increases towards the outskirts. In the inner 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’. In addition, 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, however, the flow becomes increasingly compressional, the structure functions flatter and modest genuine anisotropy appears particularly close to the injection scale.
Date added: Mon, 14 Oct 13