Cosmological Fluid Mechanics with Adaptively Refined Large Eddy
  Simulations
  We investigate turbulence generated by cosmological structure formation by
means of large eddy simulations using adaptive mesh refinement. In contrast to
the widely used implicit large eddy simulations, which resolve a limited range
of length scales and treat the effect of turbulent velocity fluctuations below
the grid scale solely by numerical dissipation, we apply a subgrid-scale model
for the numerically unresolved fraction of the turbulence energy. For
simulations with adaptive mesh refinement, we utilize a new methodology that
allows us to adjust the scale-dependent energy variables in such a way that the
sum of resolved and unresolved energies is globally conserved. We test our
approach in simulations of randomly forced turbulence, a gravitationally bound
cloud in a wind, and the Santa Barbara cluster. To treat inhomogeneous
turbulence, we introduce an adaptive Kalman filtering technique that separates
turbulent velocity fluctuations on resolved length scales from the
non-turbulent bulk flow. From the magnitude of the fluctuating component and
the subgrid-scale turbulence energy, a total turbulent velocity dispersion of
several 100 km/s is obtained for the Santa Barbara cluster, while the
low-density gas outside the accretion shocks is nearly devoid of turbulence.
The energy flux through the turbulent cascade and the dissipation rate
predicted by the subgrid-scale model correspond to dynamical time scales around
5 Gyr, independent of numerical resolution.
