  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.
