We study bubble break-up in homogeneous and isotropic turbulence by direct numerical
simulations of the two-phase incompressible Navier–Stokes equations. We create the
turbulence by forcing in physical space and introduce the bubble once a statistically
stationary state is reached. We perform a large ensemble of simulations to investigate the
effect of the Weber number (the ratio of turbulent and surface tension forces) on bubble
break-up dynamics and statistics, including the child bubble size distribution, and discuss
the numerical requirements to obtain results independent of grid size. We characterize
the critical Weber number below which no break-up occurs and the associated Hinze
scale dh. At Weber number close to stable conditions (initial bubble sizes d0 ≈ dh), we
observe binary and tertiary break-ups, leading to bubbles mostly between 0.5dh and dh,
a signature of a production process local in scale. For large Weber numbers (d0 > 3dh),
we observe the creation of a wide range of bubble radii, with numerous child bubbles
between 0.1dh and 0.3dh, an order of magnitude smaller than the parent bubble. The
separation of scales between the parent and child bubble is a signature of a production
process non-local in scale. The formation mechanism of these sub-Hinze scale bubbles
relates to rapid large deformation and successive break-ups: the first break-up in a sequence
leaves highly deformed bubbles which will break again, without recovering a spherical
shape and creating an array of much smaller bubbles. We discuss the application of this
scenario to the production of sub-Hinze bubbles under breaking waves.