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Breaking surface waves generate drops of a broad range of sizes that have a significant influence on regional and global climates, as well as the identification of ship movements. Characterizing these phenomena requires a fundamental understanding of the underlying mechanisms behind drop production. The interscale nature of these mechanisms also influences the development of models that enable cost-effective computation of large-scale waves. Interscale locality implies the universality of small scales and the suitability of generic subgrid-scale (SGS) models, while interscale nonlocality points to the potential dependence of the small scales on larger-scale geometry configurations and the corresponding need for tailored SGS models instead. A recently developed analysis toolkit combining theoretical population balance models, multiphase numerical simulations, and structure-tracking algorithms is used to probe the nature of drop production and its corresponding interscale mass-transfer characteristics above the surface of breaking waves. The results from the application of this toolkit suggest that while drop breakup is a somewhat scale-nonlocal process, its interscale transfer signature suggests that it is likely capillary-dominated and thus sensitive not to the specific nature of large-scale wave breaking, but rather to the specific geometry of the parent drops.

Knowledge of bubble and drop size distributions in two-phase flows is important for characterizing a wide range of phenomena, including combustor ignition, sonar communication, and cloud formation. The physical mechanisms driving the background flow also drive the time evolution of these distributions. Accurate and robust identification and tracking algorithms for the dispersed phase are necessary to reliably measure this evolution and thereby quantify the underlying mechanisms in interface-resolving flow simulations. The identification of individual bubbles and drops traditionally relies on an algorithm used to identify connected regions. This traditional algorithm can be sensitive to the presence of spurious structures. A cost-effective refinement is proposed to maximize volume accuracy while minimizing the identification of spurious bubbles and drops. An accurate identification scheme is crucial for distinguishing bubble and drop pairs with large size ratios. The identified bubbles and drops need to be tracked in time to obtain breakup and coalescence statistics that characterize the evolution of the size distribution, including breakup and coalescence frequencies, and the probability distributions of parent and child bubble and drop sizes. An algorithm based on mass conservation is proposed to construct bubble and drop lineages using simulation snapshots that are not necessarily from consecutive time-steps. These lineages are then used to detect breakup and coalescence events, and obtain the desired statistics. Accurate identification of large-size-ratio bubble and drop pairs enables accurate detection of breakup and coalescence events over a large size range. Together, these algorithms enable insights into the mechanisms behind bubble and drop formation and evolution in flows of practical importance., Comment: Under review for the Journal of Computational Physics

Breaking waves generate a distribution of bubble sizes that evolves over time. Knowledge of how this distribution evolves is of practical importance for maritime and climate studies. The analytical framework developed in Part 1 examined how this evolution is governed by the bubble-mass flux from large to small bubble sizes, which depends on the rate of break-up events and the distribution of child bubble sizes. These statistics are measured in Part 2 as ensemble-averaged functions of time by simulating ensembles of breaking waves, and identifying and tracking individual bubbles and their break-up events. The break-up dynamics are seen to be statistically unsteady, and two intervals with distinct characteristics were identified. In the first interval, the dissipation rate and bubble-mass flux are quasi-steady, and the theoretical analysis of Part 1 is supported by all observed statistics, including the expected -10/3 power-law exponent for the super-Hinze-scale size distribution. Strong locality is observed in the corresponding bubble-mass flux, supporting the presence of a super-Hinze-scale break-up cascade. In the second interval, the dissipation rate decays, and the bubble-mass flux increases as small- and intermediate-sized bubbles become more populous. This flux remains strongly local with cascade-like behaviour, but the dominant power-law exponent for the size distribution increases to -8/3 as small bubbles are also depleted more quickly. This suggests the emergence of different physical mechanisms during different phases of the breaking-wave evolution, although size-local break-up remains a dominant theme. Parts 1 and 2 present an analytical toolkit for population balance analysis in two-phase flows., Comment: Under review for the Journal of Fluid Mechanics. Several figure placements were affected by arXiv's processing; contact authors for the original submitted manuscript

Breaking waves entrain gas beneath the surface. The wave-breaking process energizes turbulent fluctuations that break bubbles in quick succession to generate a wide range of bubble sizes. Understanding this generation mechanism paves the way towards the development of predictive models for large-scale maritime and climate simulations. Garrett et al. (2000) suggested that super-Hinze-scale turbulent breakup transfers entrained gas from large to small bubble sizes in the manner of a cascade. We provide a theoretical basis for this bubble-mass cascade by appealing to how energy is transferred from large to small scales in the energy cascade central to single-phase turbulence theories. A bubble break-up cascade requires that break-up events predominantly transfer bubble mass from a certain bubble size to a slightly smaller size on average. This property is called locality. In this paper, we analytically quantify locality by extending the population balance equation in conservative form to derive the bubble-mass transfer rate from large to small sizes. Using our proposed measures of locality, we show that scalings relevant to turbulent bubbly flows, including those postulated by Garrett et al. (2000) and observed in breaking-wave experiments and simulations, are consistent with a strongly local transfer rate, where the influence of non-local contributions decays in a power-law fashion. These theoretical predictions are confirmed using numerical simulations in Part 2, revealing key physical aspects of the bubble break-up cascade phenomenology. Locality supports the universality of turbulent small-bubble break-up, which simplifies the development of subgrid-scale models to predict oceanic small-bubble statistics of practical importance., Comment: Under review for the Journal of Fluid Mechanics

Micro-bubbles are of significant interest due to the long-living signature they leave behind naval ships. In order to numerically model and predict these bubbles in naval applications, subgrid-scale models are required because of the extreme separation of length- and time-scales between the macroscopic geometries and the physical processes leading to the formation of these bubbles. Yet, there is much that is unknown about the mechanism behind the entrainment of such bubbles. Furthermore, quantitative information regarding their size distribution and dependence on flow parameters is very limited. Impact events are hypothesized to be the main contributor to the generation of micro-bubbles. This is due to a phenomenon known as Mesler entrainment, which has been observed in the context of the drop-pool impact problem. Namely, when a water droplet with diameter of $\mathcal{O}(1mm)$ impacts a deep water pool with an impact velocity of $\mathcal{O}(1m/s)$, hundreds of air micro-bubbles are entrained into the pool. These bubbles have been found to be remnants of a very thin air film entrapped between the two liquid bodies. These films have extremely high aspect ratios and after being punctured, shed micro-bubbles while retracting on time scales much shorter than the outer flow time scales. This separation of time-scales, along with a lacking of studies on retracting thin gas films has motivated us to study this fundamental problem with numerical simulations in two and three dimensions. Using a diffuse interface method, we perform two-phase simulations of retracting thin gas films in initially static liquid backgrounds to gain understanding regarding this problem and gather statistics that can be potentially used in a subgrid-scale model to predict micro-bubble shedding from a thin gas film. Coupling a model like this to a model that predicts the thin film characteristics ..., Comment: Proceedings of 32nd Symposium on Naval Hydrodynamics, Hamburg, Germany, 5-10 Aug. 2018

The generation of microbubbles upon the collision and interaction of liquid bodies in a gaseous environment is a ubiquitous process in two-phase flows, including large-scale phenomena like ship wakes, breaking waves and rain showers. These collision and interaction events involve the relative approach of pairs of liquid-gas interfaces. As these interfaces approach, the smallest length scales of the system are dynamically reduced. This evolving disparity in length scales is numerically challenging to resolve without the employment of subgrid-scale (SGS) impact and breakup models. In this study, a physics-based impact and breakup model for the generation of these microbubbles is developed and implemented. The objectives of this study are to develop a computational algorithm that identifies interface collision events that contribute to the formation of microbubbles, to formulate a physics-based breakup model that predicts the distribution of microbubble sizes using the characteristics of the originating gas film, and to integrate these modules into a two-phase flow solver that accurately captures the effects of bubbles of all sizes. In these proceedings, an SGS model suitable for the aforementioned problems is proposed, and the steps involved in implementing the proposed SGS model in a macroscale flow solver are outlined. Two aspects of the development of this SGS model are then discussed in detail. First, the formulation and implementation of the first step of the SGS model, the collision detection algorithm, is detailed. Second, preliminary findings of a numerical investigation intended to shed light on breakup processes in turbulent two-phase flows are presented., Comment: This is a low-resolution version submitted to meet the arXiv requirements. For a high-resolution version, please contact the authors directly