Bag film breakup of droplets in uniform airflows

We present novel numerical simulations investigating the bag breakup of liquid droplets. We first examine the viscous effect on the early-time drop deformation, comparing with theory and experiment. Next, a bag film forms at late time and is susceptible to spurious mesh-induced breakup in numerical simulations, which has prevented previous studies from reaching grid convergence of fragment statistics. We therefore adopt the manifold death (MD) algorithm which artificially perforates thin films once they reach a prescribed critical thickness independent of the grid size, controlled by a numerical parameter Lsig. We show grid convergence of fragment statistics when utilising the MD algorithm, and analyse the fragment behaviour and bag film disintegration mechanisms including ligament breakup, node detachment and rim destabilisation. Our choice of the critical thickness parameter Lsig is limited by numerical constraints and thus has not been matched to experiment or theory; consequently, the current simulations yield critical bag film perforation thicknesses larger than experimentally observed. The influence of the MD algorithm configuration on the bag breakup phenomena and statistics will be investigated in future work. We also study the effects of moderate liquid Ohnesorge number (0.005 ⩽ Oh ⩽ 0.05) on the bag breakup process and fragment statistics, where a non-monotonic dependency of the average diameter of bag film fragments on Oh is found. These results highlight the utility of the MD algorithm in multiphase simulations involving topological changes, and pave the way for physics-based numerical investigations into spume generation at the air-sea interface

Bubble deformation by a turbulent flow

We investigate the modes of deformation of an initially spherical bubble immersed in a homogeneous and isotropic turbulent background flow. We perform direct numerical simulations of the two-phase incompressible Navier-Stokes equations, considering a low-density bubble in the high density turbulent flow at various Weber number (the ratio of turbulent and surface tension forces) using the air-water density ratio. We discuss a theoretical framework for the bubble deformation in a turbulent flow using a spherical harmonic decomposition. We propose, for each mode of bubble deformation, a forcing term given by the statistics of velocity and pressure fluctuations, evaluated on a sphere of the same radius. This approach formally relates the bubble deformation and the background turbulent velocity fluctuations, in the limit of small deformations. The growth of the total surface deformation and of each individual mode is computed from the direct numerical simulations using an appropriate Voronoi decomposition of the bubble surface. We show that two successive temporal regimes occur: the first regime corresponds to deformations driven only by inertial forces, with the interface deformation growing linearly in time, in agreement with the model predictions, whereas the second regime results from a balance between inertial forces and surface tension. The transition time between the two regimes is given by the period of the first Rayleigh mode of bubble oscillation. We discuss how our approach can be used to relate the bubble lifetime to the turbulence statistics and eventually show that at high Weber number, bubble lifetime can be deduced from the statistics of turbulent fluctuations at the bubble scale

Singularity Formation in the Geometry of Perturbed Shocks of General Mach Number

While planar shock waves are known to be stable to small perturbations in the sense that the perturbation amplitude decays over time, it has also been suggested that plane propagating shocks can develop singularities in some derivative of their geometry (Whitham (1974) Linear and nonlinear waves. Wiley, New York) in a nonlinear, wave reinforcement process. We present a spectral-based analysis of the equations of geometrical shock dynamics that predicts the time to singularity formation in the profile of an initially perturbed planar shock for general shock Mach number. We find that following an initially sinusoidal perturbation, the shock shape remains analytic only up to a finite, critical time that is a monotonically decreasing function of the initial perturbation amplitude. At the critical time, the shock profile ceases to be analytic, corresponding physically to the incipient formation of a “shock-shock” or triple point. We present results for gas-dynamic shocks and discuss the potential for extension to shock dynamics of fast MHD shocks

Local Field Effects on Magnetic Suppression of the Converging Richtmyer-Meshkov Instability

We examine how the suppression of the converging shockdriven Richtmyer-Meshkov instability by an applied magnetic field is dependent on the local magnetic field strength and orientation. In particular, we examine whether the extent of suppression can be reasonably predicted by a linear model for the planar case. This is done for cylindrically converging cases with a high perturbation wavenumber and two different initial magnetic field configurations

Clinical characteristics of women captured by extending the definition of severe postpartum haemorrhage with 'refractoriness to treatment': a cohort study

Background: The absence of a uniform and clinically relevant definition of severe postpartum haemorrhage hampers comparative studies and optimization of clinical management. The concept of persistent postpartum haemorrhage, based on refractoriness to initial first-line treatment, was proposed as an alternative to common definitions that are either based on estimations of blood loss or transfused units of packed red blood cells (RBC). We compared characteristics and outcomes of women with severe postpartum haemorrhage captured by these three types of definitions. Methods: In this large retrospective cohort study in 61 hospitals in the Netherlands we included 1391 consecutive women with postpartum haemorrhage who received either ≥4 units of RBC or a multicomponent transfusion. Clinical characteristics and outcomes of women with severe postpartum haemorrhage defined as persistent postpartum haemorrhage were compared to definitions based on estimated blood loss or transfused units of RBC within 24 h following birth. Adverse maternal outcome was a composite of maternal mortality, hysterectomy, arterial embolisation and intensive care unit admission. Results: One thousand two hundred sixty out of 1391 women (90.6%) with postpartum haemorrhage fulfilled the definition of persistent postpartum haemorrhage. The majority, 820/1260 (65.1%), fulfilled this definition within 1 h following birth, compared to 819/1391 (58.7%) applying the definition of ≥1 L blood loss and 37/845 (4.4%) applying the definition of ≥4 units of RBC. The definition persistent postpartum haemorrhage captured 430/471 adverse maternal outcomes (91.3%), compared to 471/471 (100%) for ≥1 L blood loss and 383/471 (81.3%) for ≥4 units of RBC. Persistent postpartum haemorrhage did not capture all adverse outcomes because of missing data on timing of initial, first-line treatment. Conclusion: The definition persistent postpartum haemo

High-resolution direct simulation of deep water breaking waves: transition to turbulence, bubbles and droplet production

[Abridged]We present high-resolution three-dimensional direct numerical simulations of breaking waves solving the two-phase Navier-Stokes equations. We investigate the role of the Reynolds and Bond numbers on the energy, bubble and droplet statistics of strong plunging breakers, and explore the asymptotic regimes at high Reynolds and Bond numbers to be compared with laboratory breaking waves. Energetically, we show that the breaking wave transitions from laminar to three-dimensional turbulent flow on a timescale that depends on the turbulent Reynolds number up to a limiting value of $Re_\lambda \sim 100$, consistent with the mixing transition observed in other canonical turbulent flows. We characterize the role of capillary effects on the impacting jet and ingested main cavity shape and subsequent fragmentation process. We confirm two distinct power-law regimes in the bubble size distribution, separated by the Hinze scale $r_H$. We also confirm the interplay between the generation of bubbles with the turbulent dissipation rate and extend the buoyant-energetic scaling of Deike et al. (2016) to account for further Bond number effects. We show resolved bubbles up to one order of magnitude below the Hinze scale and observe a good collapse of the numerical data, both above and below the Hinze scale, compared to laboratory breaking wave Deane and Stokes (2002). We resolve droplet statistics and our data show good agreement with recent experiments (Erinin et al., 2009) in various statistics. We present velocity distributions for the droplets, finding ejection velocities up to four times the phase speed of the wave, which are produced during the most intense splashing events of the breaking process. This study paves the way for future integrated studies of the statistics of energetics, bubbles and droplets and their interdependences in breaking ocean waves and multiphase turbulent flows.Comment: 54 pages, 31 figure

Energy Dissipation in Shallow Water Breaking Waves

We present numerical results of energy dissipation in two-dimensional shallow water breaking waves. Using a two-phase DNS approach, we seek a fundamental energy dissipation model and classification scheme for breaking type and mechanism. A solitary wave of amplitude a 0 is initialized over a region of uniform depth h and propagated onto a beach with a uniformly sloping bathymetry of gradient α. We discuss the various types of resulting breakers as a function of these parameters, including plunging, spilling, and surging types. The breaker dissipates kinetic and gravitational potential energy in the wave before it runs up onto the beach. We discuss the energy dissipation and wave run-up in terms of the control parameters and propose a model for energy dissipation adapted from the inertial scaling model for deep water breakers

Inertial Energy Dissipation in Shallow-Water Breaking Waves

We present direct numerical simulations of breaking solitary waves in shallow water to quantify the energy dissipation during the active breaking time. We find that this dissipation can be predicted by an inertial model based on Taylor\u27s hypothesis as a function of the local wave height, depth and the beach slope. We obtain a relationship that gives the dissipation rate of a breaking wave on a shallow slope as a function of local breaking parameters. Next, we use empirical relations to relate the local wave parameters to the offshore conditions. This enables the energy dissipation to be predicted in terms of the initial conditions. We obtain good collapse of the numerical data with respect to the theoretical scaling