  We report on a investigation of turbulent bubbly flows. Bubbles of a size
larger than the dissipative scale, cannot be treated as point-wise inclusions,
and generate important hydrodynamic fields in the carrier fluid when in motion.
Furthermore, when the volume fraction of bubbles is large enough, the bubble
motion may induce a collective agitation due to hydrodynamic interactions which
display some turbulent-like features. We tackle this complex phenomenon
numerically, performing direct numerical simulations (DNS) with a
Volume-of-fluid (VOF) method. In the first part of the work, we perform both 2D
and 3D tests in order to determine appropriate numerical and physical
parameters.
  We then carry out a highly-resolved simulation of a 3D bubble column, with a
configuration and physical parameters similar to those used in laboratory
experiments. This is the largest simulation attempted for such a configuration
and is possible only thanks to adaptive grid refinement. Results are compared
both with experiments and previous coarse-mesh numerical simulations. In
particular, the one-point Probability Density Function (PDF) of the liquid
velocity fluctuations is in good quantitative agreement with experiments,
notably in the vertical direction, although more extreme events are sampled in
the present configuration. The spectra of the liquid kinetic energy show a
clear $k^{-3}$ scaling.
  The mechanisms underlying the energy transfer and notably the possible
presence of a cascade are unveiled by a local scale-by-scale analysis in the
physical space. The comparison with previous simulations indicate to what
extent simulations not fully resolved may yet give correct results, from a
statistical point of view.
