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We present experiments on large air cavities spanning a wide range of sizes relative to the Hinze scale 
$d_{H}$, the scale at which turbulent stresses are balanced by surface tension, disintegrating in turbulence. For cavities with initial sizes 
$d_0$ much larger than 
$d_{H}$ (probing up to 
$d_0/d_{H} = 8.3$), the size distribution of bubbles smaller than 
$d_{H}$ follows 
$N(d) \propto d^{-3/2}$, with 
$d$ the bubble diameter. The capillary instability of ligaments involved in the deformation of the large bubbles is shown visually to be responsible for the creation of the small bubbles. Turning to dynamical, three-dimensional measurements of individual break-up events, we describe the break-up child size distribution and the number of child bubbles formed as a function of 
$d_0/d_{H}$. Then, to model the evolution of a population of bubbles produced by turbulent bubble break-up, we propose a population balance framework in which break-up involves two physical processes: an inertial deformation to the parent bubble that sets the size of large child bubbles, and a capillary instability that sets the size of small child bubbles. A Monte Carlo approach is used to construct the child size distribution, with simulated stochastic break-ups constrained by our experimental measurements and the understanding of the role of capillarity in small bubble production. This approach reproduces the experimental time evolution of the bubble size distribution during the disintegration of large air cavities in turbulence.
We investigate how turbulence in liquid affects the rising speed of gas bubbles within the inertial range. Experimentally, we employ stereoscopic tracking of bubbles rising through water turbulence created by the convergence of turbulent jets and characterized with particle image velocimetry performed throughout the measurement volume. We use the spatially varying, time-averaged mean water velocity field to consider the physically relevant bubble slip velocity relative to the mean flow. Over a range of bubble sizes within the inertial range, we find that the bubble mean rise velocity 
$\left \langle v_z \right \rangle$ decreases with the intensity of the turbulence as characterized by its root-mean-square fluctuation velocity, 
$u'$. Non-dimensionalized by the quiescent rise velocity 
$v_{q}$, the average rise speed follows 
$\left \langle v_z \right \rangle /v_{q}\propto 1/{\textit {Fr}}$ at high 
${\textit {Fr}}$, where 
${\textit {Fr}}=u'/\sqrt {dg}$ is a Froude number comparing the intensity of the turbulence to the bubble buoyancy, with 
$d$ the bubble diameter and 
$g$ the acceleration due to gravity. We complement these results by performing numerical integration of the Maxey–Riley equation for a point bubble experiencing nonlinear drag in three-dimensional, homogeneous and isotropic turbulence. These simulations reproduce the slowdown observed experimentally, and show that the mean magnitude of the slip velocity is proportional to the large-scale fluctuations of the flow velocity. Combining the numerical estimate of the slip velocity magnitude with a simple theoretical model, we show that the scaling 
$\left \langle v_z \right \rangle /v_{q}\propto 1/{\textit {Fr}}$ originates from a combination of the nonlinear drag and the nearly isotropic behaviour of the slip velocity at large 
${\textit {Fr}}$ that drastically reduces the mean rise speed.
