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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, threedimensional measurements of individual breakup events, we describe the breakup 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 breakup, we propose a population balance framework in which breakup 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 breakups 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.more » « lessFree, publiclyaccessible full text available November 25, 2023

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, timeaveraged 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 rootmeansquare fluctuation velocity, $u'$ . Nondimensionalized 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 threedimensional, 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 largescale 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.more » « less

Three‐Dimensional Measurements of Air Entrainment and Enhanced Bubble Transport During Wave Breaking
Abstract We experimentally investigate the depth distributions and dynamics of air bubbles entrained by breaking waves in a wind‐wave channel over a range of breaking wave conditions using high‐resolution imaging and three‐dimensional bubble tracking. Below the wave troughs, the bubble concentration decays exponentially with depth. Patches of entrained bubbles are identified for each breaking wave, and statistics describing the horizontal and vertical transport are presented. Aggregating our results, we find a stream‐wise transport faster than the associated Stokes drift and modified Stokes drift for buoyant particles, which is an effect not accounted for in current models of bubble transport. This enhancement in transport is attributed to the flow field induced by the breaking waves and is relevant for the transport of bubbles, oil droplets, and microplastics at the ocean surface.

Although bubble pinchoff is an archetype of a dynamical system evolving toward a singularity, it has always been described in idealized theoretical and experimental conditions. Here, we consider bubble pinchoff in a turbulent flow representative of natural conditions in the presence of strong and random perturbations, combining laboratory experiments, numerical simulations, and theoretical modeling. We show that the turbulence sets the initial conditions for pinchoff, namely the initial bubble shape and flow field, but after the pinchoff starts, the turbulent time at the neck scale becomes much slower than the pinching dynamics: The turbulence freezes. We show that the average neck size, d ¯ , can be described by d ¯ ∼ ( t − t 0 ) α , where t 0 is the pinchoff or singularity time and α ≈ 0.5 , in close agreement with the axisymmetric theory with no initial flow. While frozen, the turbulence can influence the pinchoff through the initial conditions. Neck shape oscillations described by a quasi–2dimensional (quasi2D) linear perturbation model are observed as are persistent eccentricities of the neck, which are related to the complex flow field induced by the deformed bubble shape. When turbulent stresses are less able to be counteracted by surface tension, a 3dimensional (3D) kinklike structure develops in the neck, causing d ¯ to escape its selfsimilar decrease. We identify the geometric controlling parameter that governs the appearance of these kinklike interfacial structures, which drive the collapse out of the selfsimilar route, governing both the likelihood of escaping the selfsimilar process and the time and length scale at which it occurs.more » « less