Institut de Recherche sur les Phénomènes Hors Équilibre

We first study the impact of a liquid drop of low viscosity on a super-hydrophobic surface. Denoting the drop size and speed as $D_{0}$ and $U_{0}$ , we find that the maximal spreading $D_{\hbox{\scriptsize\it max}}$ scales as $D_{0}\hbox{\it We}^{1/4}$ where We is the Weber number associated with the shock ( $\hbox{\it We}\,{\equiv}\,\rho U_{0}^2 D_{0}/\sigma$ , where $\rho$ and $\sigma$ are the liquid density and surface tension). This law is also observed to hold on partially wettable surfaces, provided that liquids of low viscosity (such as water) are used. The law is interpreted as resulting from the effective acceleration experienced by the drop during its impact. Viscous drops are also analysed, allowing us to propose a criterion for predicting if the spreading is limited by capillarity, or by viscosity.

Quantum ESPRESSO is an integrated suite of computer codes for electronic-structure calculations and materials modeling, based on density-functional theory, plane waves, and pseudopotentials (norm-conserving, ultrasoft, and projector-augmented wave). Quantum ESPRESSO stands for "opEn Source Package for Research in Electronic Structure, Simulation, and Optimization". It is freely available to researchers around the world under the terms of the GNU General Public License. Quantum ESPRESSO builds upon newly-restructured electronic-structure codes that have been developed and tested by some of the original authors of novel electronic-structure algorithms and applied in the last twenty years by some of the leading materials modeling groups worldwide. Innovation and efficiency are still its main focus, with special attention paid to massively-parallel architectures, and a great effort being devoted to user friendliness. Quantum ESPRESSO is evolving towards a distribution of independent and inter-operable codes in the spirit of an open-source project, where researchers active in the field of electronic-structure calculations are encouraged to participate in the project by contributing their own codes or by implementing their own ideas into existing codes.

Suspensions of aerobic bacteria often develop flows from the interplay of chemotaxis and buoyancy. We find in sessile drops that flows related to those in the Boycott effect of sedimentation carry bioconvective plumes down the slanted meniscus and concentrate cells at the drop edge, while in pendant drops such self-concentration occurs at the bottom. On scales much larger than a cell, concentrated regions in both geometries exhibit transient, reconstituting, high-speed jets straddled by vortex streets. A mechanism for large-scale coherence is proposed based on hydrodynamic interactions between swimming cells.

We depict and analyse the successive steps of atomization of a liquid jet when a fast gas stream blows parallel to its surface. Experiments performed with various liquids in a fast air flow show that the liquid destabilization proceeds from a two-stage mechanism: a shear instability first forms waves on the liquid. The transient acceleration experienced by the liquid suggests that a Rayleigh–Taylor type of instability is triggered at the wave crests, producing liquid ligaments which further stretch in the air stream and break into droplets. The primary wavelength $\lambda\,{\sim}\,\delta (\rho_{1}/\rho_{2})^{1/2}$ is set by the vorticity thickness $\delta$ , in the fast air stream and the liquid/gas density ratio $\rho_{1}/\rho_{2}$ . The transverse corrugations of the crests have a size $\lperp\,{\sim}\,\delta {\We_{\delta}}^{-1/3} (\rho_{1}/\rho_{2})^{1/3}$ , where $\We_{\delta}\,{=}\,\rho_{2}u_{2}^{2}\delta/\sigma$ is the Weber number constructed on the gas velocity $u_{2}$ and liquid surface tension $\sigma$ . The ligament dynamics gives rise, after break-up, to a well-defined droplet size distribution whose mean is given by $\lperp$ . This distribution bears an exponential tail characteristic of the broad size statistics in airblast sprays.

A Leidenfrost drop forms when a volatile liquid is brought in contact with a very hot solid. Then, a vapor film comes in between the solid and the drop, giving to the latter the appearance of a liquid pearl. After a brief description of the shape of a Leidenfrost drop, we show that its size cannot exceed a certain value. Then, we describe the characteristics of the vapor layer on which it floats. We show how it is related to the drop size, and how both vary with time, as evaporation takes place. We finally deduce scaling laws for the lifetime of these drops.

Fragmentation phenomena are reviewed with a particular emphasis on processes that give rise to drops—in the broad sense, the process of atomization. Various observations are brought together to give a unified picture of the overall transition between a compact macroscopic liquid volume and its subsequent dispersion into stable drops. In liquids, primary instabilities always give birth to more or less corrugated ligaments whose breakup determines the shape of the drop-size distribution in the resulting spray. Examples examined here include fragmentation of jets and liquid sheets, formation of spume by the wind blowing over a liquid surface, bursting phenomena upon an impact, and raindrops.

Abstract This review is intended to provide a critical and up-to-date survey of the analytical approximate methods that are encountered in scattering from random rough surfaces. The underlying principles of the different methods are evidenced and the functional form of the corresponding scattering amplitude or cross-section is given. The reader is referred to the original papers in order to obtain the explicit expressions of the coefficients and kernels. We have tried to identify the main strengths and weaknesses of the various theories. We provide synthetic tables of their respective performances, according to a dozen important requirements a valuable method should meet. Both scalar acoustic and vector electromagnetic theories are equally addressed.

We consider the critical Weber number ( We c ≡ ρ V 2 0 D /σ) at which the transition from dripping to jetting occurs when a Newtonian liquid of density ρ and surface tension σ is injected with a velocity V 0 through a tube of diameter D downward into stagnant air, under gravity g . We extend Taylor's (1959) model for the recession speed of a free edge, and obtain in the inviscid limit an exact solution which includes gravity and inertia effects. This solution provides a criterion for the transition which is shown to occur at a critical Weber number formula here where Bo and Bo o are the Bond numbers ( Bo ≡[ρg D 2 /(2σ)] 1/2 ), respectively based on the inside and outside diameter of the tube, and K is a constant equal to 0.37 for the case of water injected in air. This critical Weber number is shown to be in good agreement with existing experimental values as well as with new measurements performed over a wide range of Bond numbers.

Abstract We depict and analyse the complete evolution of an air bubble formed in a water bulk, from the time it emerges at the liquid surface, up to its fragmentation into dispersed drops. To this end, experiments describing the drainage of the bubble cap film, its puncture and the resulting bursting dynamics determining the aerosol formation are conducted on tapwater bubbles. We discover that the mechanism of marginal pinching at the bubble foot and associated convection motions in the bubble cap, known as marginal regeneration , both drive the bubble cap drainage rate, and are responsible for its puncture. The resulting original film thickness $h$ evolution law in time, supplemented with considerations about the nucleation of holes piercing the film together culminate in a determination of the cap film thickness at bursting ${h}_{b} \propto {R}^{2} / \mathscr{L}$ , where $R$ is the bubble cap radius of curvature, and $\mathscr{L}$ a length which we determine. Subsequent to a hole nucleation event, the cap bursting dynamics conditions the resulting spray. The latter depends both on the bubble shape prescribed by $R/ a$ , where $a$ is the capillary length based on gravity, and on ${h}_{b} $ . The mean drop size $\langle d\rangle \ensuremath{\sim} {R}^{3/ 8} \hspace{0.167em} { h}_{b}^{5/ 8} $ , the number of drops generated per bubble $N\ensuremath{\sim} \mathop{ (R/ a)}\nolimits ^{2} \mathop{ (R/ {h}_{b} )}\nolimits ^{7/ 8} $ and the drop size distribution $P(d)$ are derived, comparing well with measurements. Combined with known bubble production rates over the ocean, our findings offer an adjustable parameter-free prediction for the aerosol flux and spray structure caused by bubble bursting in this precise context.

This article reviews the characteristics and behavior of counter-rotating and corotating vortex pairs, which are seemingly simple flow configurations yet immensely rich in phenomena. Since the reviews in this journal by We discuss two-dimensional dynamics, including the merging of same-sign vortices and the interaction with the mutually induced strain, as well as three-dimensional displacement and core instabilities resulting from this interaction. Flows subject to combined instabilities are also considered, in particular the impingement of opposite-sign vortices on a ground plane. We emphasize the physical mechanisms responsible for the flow phenomena and clearly present the key results that are useful to the reader for predicting the dynamics and instabilities of parallel vortices.

The single-domain Darcy–Brinkman model is applied to some analytically tractable flows through adjacent porous and pure-fluid domains and is compared systematically with the multiple-domain Stokes–Darcy model. In particular, we focus on the interaction between flow and solidification within the mushy layer during binary alloy solidification in a corner flow and on the effects of the chosen mathematical description on the resulting macrosegregation patterns. Large-scale results provided by the multiple-domain formulation depend strongly on the microscopic interfacial conditions. No satisfactory agreement between the single- and multiple-domain approaches is obtained when using previously suggested conditions written directly at the interface between the liquid and the porous medium. Rather, we define a viscous transition zone inside the porous domain, where the Stokes equation still applies, and we impose continuity of pressure and velocities across it. This new condition provides good agreement between the two formulations of solidification problems when there is a continuous variation of porosity across the interface between a partially solidified region (mushy zone) and the melt.

In this paper, we investigate the three-dimensional instability of a counter-rotating vortex pair to short waves, which are of the order of the vortex core size, and less than the inter-vortex spacing. Our experiments involve detailed visualizations and velocimetry to reveal the spatial structure of the instability for a vortex pair, which is generated underwater by two rotating plates. We discover, in this work, a symmetry-breaking phase relationship between the two vortices, which we show to be consistent with a kinematic matching condition for the disturbances evolving on each vortex. In this sense, the instabilities in each vortex evolve in a coupled, or ‘cooperative’, manner. Further results demonstrate that this instability is a manifestation of an elliptic instability of the vortex cores, which is here identified clearly for the first time in a real open flow. We establish a relationship between elliptic instability and other theoretical instability studies involving Kelvin modes. In particular, we note that the perturbation shape near the vortex centres is unaffected by the finite size of the cores. We find that the long-term evolution of the flow involves the inception of secondary transverse vortex pairs, which develop near the leading stagnation point of the pair. The interaction of these short-wavelength structures with the long-wavelength Crow instability is studied, and we observe significant modifications in the longevity of large vortical structures.

A drop of low viscosity hitting a solid may bounce, provided that the material is highly hydrophobic. As a model of such a situation, we consider here the case of a very hot solid. Then, as discovered by Leidenfrost, a thin layer of vapour sustains the drop, preventing any contact with the substrate. On hitting such a solid, a drop rebounds, and we discuss here the elasticity of the shock. Two very different cases are described: at a large velocity, the weaker the impact velocity, the weaker the elasticity; at a small velocity, a quasi-elastic regime is found. The boundary between the two domains is set by a Weber number, which compares the kinetic and surface energies of the drop, of order unity.

We study the collapse of a transient cavity of air in water created by the impact of a solid body. Experimentally, we characterize the dynamics of the cavity from its creation ( t = 0) until it collapses ( t = τ) in the limit where inertia dominates viscous and capillary effects. Theoretically, we find in this regime an approximate analytical solution which describes the time evolution of the shape of the cavity. This theoretical solution predicts the existence of two different types of cavities that we also observe experimentally.

▪ Abstract This review deals primarily with the bifurcation, stability, and evolution of gravity and capillary-gravity waves. Recent results on the bifurcation of various types of capillary-gravity waves, including two-dimensional solitary waves at the minimum of the dispersion curve, are reviewed. A survey of various mechanisms (including the most recent ones) to explain the frequency downshift phenomenon is provided. Recent significant results are given on “horseshoe” patterns, which are three-dimensional structures observable on the sea surface under the action of wind or in wave tank experiments. The so-called short-crested waves are then discussed. Finally, the importance of surface tension effects on steep waves is studied.

The stability of a helical vortex filament of finite core and infinite extent to small sinusoidal displacements of its centre-line is considered. The influence of the entire perturbed filament on the self-induced motion of each element is taken into account. The effect of the details of the vorticity distribution within the finite vortex core on the self-induced motion due to the bending of its axis is calculated using the results obtained previously by Widnall, Bliss & Zalay (1970). In this previous work, an application of the method of matched asymptotic expansions resulted in a general solution for the self-induced motion resulting from the bending of a slender vortex filament with an arbitrary distribution of vorticity and axial velocity within the core. The results of the stability calculations presented in this paper show that the helical vortex filament has three modes of instability: a very short-wave instability which probably exists on all curved filaments, a long-wave mode which is also found to be unstable by the local-induction model and a mutual-inductance mode which appears as the pitch of the helix decreases and the neighbouring turns of the filament begin to interact strongly. Increasing the vortex core size is found to reduce the amplification rate of the long-wave instability, to increase the amplification rate of the mutual-inductance instability and to decrease the wavenumber of the short-wave instability.

Low-temperature decaying superfluid turbulence is studied using the nonlinear Schr\"odinger equation in the geometry of the Taylor-Green (TG) vortex flow with resolutions up to ${512}^{3}$. The rate of (irreversible) kinetic energy transfer in the superfluid TG vortex is found to be comparable to that of the viscous TG vortex. At the moment of maximum dissipation, the energy spectrum of the superflow has an inertial range compatible with Kolmogorov's scaling. Physical-space visualizations show that the vorticity dynamics of the superflow is similar to that of the viscous flow, including vortex reconnection. The implications to experiments in low-temperature helium are discussed.

This study investigates a fictitious domain model for the numerical solution of various incompressible viscous flows. It is based on the so-called Navier–Stokes/Brinkman and energy equations with discontinuous coefficients all over an auxiliary embedding domain. The solid obstacles or walls are taken into account by a penalty technique. Some volumic control terms are directly introduced in the governing equations in order to prescribe immersed boundary conditions. The implicit numerical scheme, which uses an upwind finite volume method on staggered Cartesian grids, is of second-order accuracy in time and space. A multigrid local mesh refinement is also implemented, using the multi-level Zoom Flux Interface Correction (FIC) method, in order to increase the precision where it is needed in the domain. At each time step, some iterations of the augmented Lagrangian method combined with a preconditioned Krylov algorithm allow the divergence-free velocity and pressure fields be solved for. The tested cases concern external steady or unsteady flows around a circular cylinder, heated or not, and the channel flow behind a backward-facing step. The numerical results are shown in good agreement with other published numerical or experimental data. Copyright © 2000 John Wiley & Sons, Ltd.

We address the flutter instability of a flexible plate immersed in an axial flow. This instability is similar to flag flutter and results from the competition between destabilizing pressure forces and stabilizing bending stiffness. In previous experimental studies, the plates have always appeared much more stable than the predictions of two-dimensional models. This discrepancy is discussed and clarified in this paper by examining experimentally and theoretically the effect of the plate aspect ratio on the instability threshold. We show that the two-dimensional limit cannot be achieved experimentally because hysteretical behaviour and three-dimensional effects appear for plates of large aspect ratio. The nature of the instability bifurcation (sub- or supercritical) is also discussed in the light of recent numerical results.

Abstract. The science guiding the EUREC4A campaign and its measurements is presented. EUREC4A comprised roughly 5 weeks of measurements in the downstream winter trades of the North Atlantic – eastward and southeastward of Barbados. Through its ability to characterize processes operating across a wide range of scales, EUREC4A marked a turning point in our ability to observationally study factors influencing clouds in the trades, how they will respond to warming, and their link to other components of the earth system, such as upper-ocean processes or the life cycle of particulate matter. This characterization was made possible by thousands (2500) of sondes distributed to measure circulations on meso- (200 km) and larger (500 km) scales, roughly 400 h of flight time by four heavily instrumented research aircraft; four global-class research vessels; an advanced ground-based cloud observatory; scores of autonomous observing platforms operating in the upper ocean (nearly 10 000 profiles), lower atmosphere (continuous profiling), and along the air–sea interface; a network of water stable isotopologue measurements; targeted tasking of satellite remote sensing; and modeling with a new generation of weather and climate models. In addition to providing an outline of the novel measurements and their composition into a unified and coordinated campaign, the six distinct scientific facets that EUREC4A explored – from North Brazil Current rings to turbulence-induced clustering of cloud droplets and its influence on warm-rain formation – are presented along with an overview of EUREC4A's outreach activities, environmental impact, and guidelines for scientific practice. Track data for all platforms are standardized and accessible at https://doi.org/10.25326/165 (Stevens, 2021), and a film documenting the campaign is provided as a video supplement.