  We performed numerical simulations of a homogeneous swarm of bubbles rising
at large Reynolds number, Re = 760 with volume fractions ranging from 1% to
10%. We consider a simplified model in which the interfaces are not resolved,
but which allows us to simulate flows with a large number of bubbles and to
emphasize the interactions between bubble wakes. The liquid phase is described
by solving, on an Eulerian grid, the Navier-Stokes equations, including sources
of momentum which model the effect of the bubbles. The dynamics of each bubble
is determined within the Lagrangian framework by solving an equation of motion
involving the hydrodynamic forces exerted by the fluid accounting for the
correction of the fictitious self-interaction of a bubble with its own wake.
The comparison with experiments shows that this coarse-grained simulations
approach can reliably describe the dynamics of the resolved flow scales. We use
conditional averaging to characterize the mean bubble wakes and obtain in
particular the typical shear imposed by the rising bubbles. On the basis of the
spectral decomposition of the energy budget, we observe that the flow is
dominated by production at large scales and by dissipation at small scales and
we rule out the presence of an intermediate range in which the production and
dissipation are locally in balance. We propose that the k-3 subrange of the
energy spectra results from the mean shear rate imposed by the bubbles, which
controls the rate of return to isotropy.
