Laboratoire d'Hydrodynamique de l'École polytechnique

The description of coherent features of fluid flow is essential to our understanding of fluid-dynamical and transport processes. A method is introduced that is able to extract dynamic information from flow fields that are either generated by a (direct) numerical simulation or visualized/measured in a physical experiment. The extracted dynamic modes, which can be interpreted as a generalization of global stability modes, can be used to describe the underlying physical mechanisms captured in the data sequence or to project large-scale problems onto a dynamical system of significantly fewer degrees of freedom. The concentration on subdomains of the flow field where relevant dynamics is expected allows the dissection of a complex flow into regions of localized instability phenomena and further illustrates the flexibility of the method, as does the description of the dynamics within a spatial framework. Demonstrations of the method are presented consisting of a plane channel flow, flow over a two-dimensional cavity, wake flow behind a flexible membrane and a jet passing between two cylinders.

This critical review discusses the current understanding of the formation, transport, and merging of drops in microfluidics. We focus on the physical ingredients which determine the flow of drops in microchannels and recall classical results of fluid dynamics which help explain the observed behaviour. We begin by introducing the main physical ingredients that differentiate droplet microfluidics from single-phase microfluidics, namely the modifications to the flow and pressure fields that are introduced by the presence of interfacial tension. Then three practical aspects are studied in detail: (i) The formation of drops and the dominant interactions depending on the geometry in which they are formed. (ii) The transport of drops, namely the evaluation of drop velocity, the pressure-velocity relationships, and the flow field induced by the presence of the drop. (iii) The fusion of two drops, including different methods of bridging the liquid film between them which enables their merging.

Hydrodynamic stability theory has recently seen a great deal of development. After being dominated by modal (eigenvalue) analysis for many decades, a different perspective has emerged that allows the quantitative description of short-term disturbance behavior. A general formulation based on the linear initial-value problem, thus circumventing the normal-mode approach, yields an efficient framework for stability calculations that is easily extendable to incorporate time-dependent flows, spatially varying configurations, stochastic influences, nonlinear effects, and flows in complex geometries.

Dynamic mode decomposition (DMD) represents an effective means for capturing the essential features of numerically or experimentally generated flow fields. In order to achieve a desirable tradeoff between the quality of approximation and the number of modes that are used to approximate the given fields, we develop a sparsity-promoting variant of the standard DMD algorithm. Sparsity is induced by regularizing the least-squares deviation between the matrix of snapshots and the linear combination of DMD modes with an additional term that penalizes the ℓ1-norm of the vector of DMD amplitudes. The globally optimal solution of the resulting regularized convex optimization problem is computed using the alternating direction method of multipliers, an algorithm well-suited for large problems. Several examples of flow fields resulting from numerical simulations and physical experiments are used to illustrate the effectiveness of the developed method.

The allohexaploid bread wheat genome consists of three closely related subgenomes (A, B, and D), but a clear understanding of their phylogenetic history has been lacking. We used genome assemblies of bread wheat and five diploid relatives to analyze genome-wide samples of gene trees, as well as to estimate evolutionary relatedness and divergence times. We show that the A and B genomes diverged from a common ancestor ~7 million years ago and that these genomes gave rise to the D genome through homoploid hybrid speciation 1 to 2 million years later. Our findings imply that the present-day bread wheat genome is a product of multiple rounds of hybrid speciation (homoploid and polyploid) and lay the foundation for a new framework for understanding the wheat genome as a multilevel phylogenetic mosaic.

*Laboratoire de Recherches sur l'Histodynamique Osseuse, Chaire d'Hydrologie Therepeutique, Faculte de Medecine, 8 Av. Rockfeller, 69. Lyon (8e), France. †Reaserch Assistant, Mineral Metabolism Unit (Dr. B.E.C. Nordin), General Infirmary, Leeds 1, England.

In this paper, new scaling properties for granular flows down rough inclined planes are presented. In the dense steady uniform flow regime, we have systematically measured the mean velocity of the flow as a function of the inclination of the surface θ and of the thickness h of the layer. The results obtained for different systems of beads corresponding to different surface roughness conditions are shown to collapse into a single curve when properly scaled. The scaling is based on the measurement of the minimum thickness hstop(θ) necessary to observe a steady uniform flow at inclination θ. From this experimental observation an empirical description for granular flows down inclined planes is proposed in terms of a dynamic friction coefficient.

▪ Abstract The objective of this review is to critically assess the different approaches developed in recent years to understand the dynamics of open flows such as mixing layers, jets, wakes, separation bubbles, boundary layers, and so on. These complex flows develop in extended domains in which fluid particles are continuously advected downstream. They behave either as noise amplifiers or as oscillators, both of which exhibit strong nonlinearities ( Huerre & Monkewitz 1990 ). The local approach is inherently weakly nonparallel and it assumes that the basic flow varies on a long length scale compared to the wavelength of the instability waves. The dynamics of the flow is then considered as a superposition of linear or nonlinear instability waves that, at leading order, behave at each streamwise station as if the flow were homogeneous in the streamwise direction. In the fully global context, the basic flow and the instabilities do not have to be characterized by widely separated length scales, and the dynamics is then viewed as the result of the interactions between Global modes living in the entire physical domain with the streamwise direction as an eigendirection. This second approach is more and more resorted to as a result of increased computational capability. The earlier review of Huerre & Monkewitz (1990) emphasized how local linear theory can account for the noise amplifier behavior as well as for the onset of a Global mode. The present survey first adopts the opposite point of view by demonstrating how fully global theory accounts for the noise amplifier behavior of open flows. From such a perspective, there is strong emphasis on the very peculiar nonorthogonality of linear Global modes, which in turn allows a novel interpretation of recent numerical simulations and experimental observations. The nonorthogonality of linear Global modes also imposes severe constraints on the extension of linear global theory to the fully nonlinear régime. When the flow is weakly nonparallel, this limitation is so severe that the linear Global mode theory is of little help. It is then much more appropriate to develop a fully nonlinear formulation involving the presence of a front separating the base state region from the bifurcated state region.

Abstract Rainfall variability in the Amazon basin (AB) is analysed for the 1964–2003 period. It is based on 756 pluviometric stations distributed throughout the AB countries. For the first time it includes data from Bolivia, Peru, Ecuador, and Colombia. In particular, the recent availability of rainfall data from the Andean countries makes it possible to complete previous studies. The impact of mountain ranges on rainfall is pointed out. The highest rainfall in the AB is observed in low windward regions, and low rainfall is measured in leeward and elevated stations. Additionally, rainfall regimes are more diversified in the Andean regions than in the lowlands. Rainfall spatio‐temporal variability is studied based on a varimax‐rotated principal component analysis (PCA). Long‐term variability with a decreasing rainfall since the 1980s prevails in June–July–August (JJA) and September–October–November (SON). During the rainiest seasons, i.e. December–January–February (DJF) and March–April–May (MAM), the main variability is at decadal and interannual time scales. Interdecadal variability is related to long‐term changes in the Pacific Ocean, whereas decadal variability, opposing the northwest and the south of the AB, is associated with changes in the strength of the low‐level jet (LLJ) along the Andes. Interannual variability characterizes more specifically the northeast of the basin and the southern tropical Andes. It is related to El Niño‐Southern Oscillation (ENSO) and to the sea surface temperature (SST) gradient over the tropical Atlantic. Mean rainfall in the basin decreases during the 1975–2003 period at an annual rate estimated to be − 0.32%. Break tests show that this decrease has been particularly important since 1982. Further insights into this phenomenon will permit to identify the impact of climate on the hydrology of the AB. Copyright © 2008 Royal Meteorological Society

This review surveys the large variety of mechanical interactions between wind and plants, from plant organs to plant systems. These interactions range from leaf flutter to uprooting and seed dispersal, as well as indirect effects on photosynthesis or insect communication. I first estimate the relevant nondimensional parameters and then discuss turbulence, plant dynamics, and the mechanisms of interaction in this context. Some common features are identified and analyzed in relation to the wind engineering of manmade structures. Strong coupling between plants and wind exists, in which the plant motion modifies the wind dynamics. I also present some related biological issues in which the relation between plant life and wind environment is emphasized. [V]oici la lourde nappe/Et la profonde houle et l’océan des blés [Like a sheet/The deep swell on a sea of wheat] Charles Péguy (1873–1914)

It has been recently shown that the presence of macrotextures on superhydrophobic materials can markedly modify the dynamics of water impacting them, and in particular significantly reduce the contact time of bouncing drops, compared with what is observed on a flat surface. This finding constitutes a significant step in the maximization of water repellency, since it enables to minimize even further the contact between solid and liquid. It also opens a new axis of research on the design of super-structures to induce specific functions such as anti-freezing, liquid fragmentation and/or recomposition, guiding, trapping and so on. Here we show that the contact time of drops bouncing on a repellent macrotexture takes discrete values when varying the impact speed. This allows us to propose a quantitative analysis of the reduction of contact time and thus to understand how and why macrotextures can control the dynamical properties of bouncing drops.

The Okinawa Trough, lying to the east of China, is a back arc basin formed by extension within continental lithosphere behind the Ryukyu trench‐arc system. Middle to late Miocene uplift, associated with normal faulting of the initially adjacent Ryukyu nonvolcanic arc and the Taiwan‐Sinzi folded belt, corresponds to the first rifting phase. The timing of rifting is supported by the presence of marine sediments of corresponding age drilled in the northern Okinawa Trough. The rifting occurred after a major early Miocene change in the motion of the Philippine plate with respect to Eurasia and ceased during the Pliocene. A second rifting phase started about 2 m.y. ago, at the Plio‐Pleistocene boundary and has continued until the present time. It has proceeded to a more advanced stage in the middle and southern Okinawa Trough than it has farther north. Detailed bathymetric (Sea Beam), seismic reflection, and magnetics data collected during the POP 1 cruise of the R/V Jean Charcot reveal the principal features of the extensional processes. The back arc spreading phase started very recently in the southern and middle Okinawa Trough, as exemplified by several en échelon and, in some cases, overlapping active, central graben oriented N70°E–N80°E. Some of these depressions are intruded by volcanic ridges of fresh back arc basalt with associated large magnetic anomalies. Transform faults between these en échelon active rifts are not obvious. We suggest that the major part of the southern Okinawa Trough is underlain by a thinned continental crust and that except for the system of en échelon rifts of the southern Okinawa Trough, the back arc basin oceanic domain is limited to a width of a few tens of kilometers or less in the axial portion of the trough. The system of axial back arc volcanic ridges that occur in the rifts ends at the latitude of Okinawa Island whereas active volcanoes in the Ryukyu arc occur only north of Okinawa Island. We refer to this transition between active arc and back arc volcanism as the volcanic arc‐rift migration phenomenon (VAMP). Globally, back arc volcanism propagated from the southern Okinawa Trough to the Okinawa VAMP area. Rifting continues to occur in the northern Okinawa Trough but is not yet accompanied by associated volcanism. The Okinawa VAMP area is characterized by a series of parallel basaltic ridges oriented N75°E with associated linear magnetic anomalies characteristic of dyke intrusions. We suggest that the formation of the back arc oceanic domain took place along the axial back arc extensional zone trending N75°E and that this zone presently ends at the southern extremity of the active volcanic chain. The initial phase of formation of back arc basin oceanic crust is non‐steady state and is characterized by the lack of a developed fracture zone pattern. The termination of the VAMP area in the direction of the volcanic zone of the arc is consistent with the suggestion of Molnar and Atwater that the volcanic arc is a fundamental line of weakness which determines where initial back arc spreading occurs. Apparently, back arc extension initially occurred within the continental lithosphere located westward of the Ryukyu arc, along its whole length, but the subsequent back arc volcanism was initiated in the southernmost portion of the region and then moved northward. This migration was accompanied by the shutting down of volcanic activity along the abandoned portions of the arc. It is this transfer of volcanism that we call the VAMP process. Thus arc and back arc basin volcanism seem to be associated in such a manner that spreading tends to migrate simultaneously with a cessation in volcanic activity along the arc. This interplay of arc and back arc activity is probably linked to changes in the parameters of plate convergence. Since the plate motion in the Phillippine sea is oblique to the trench at least in the southern part of the Okinawa Trough, we suggest that the oblique resisting force applied to the edge of the overriding plate engenders the development of en échelon extensional features within and behind the arc. The motion of the Ryukyu platelet with respect to Eurasia is consequently an extensional strike‐slip motion trending roughly parallel to the Okinawa Trough.

The goal of this study is to characterize the various breakdown states taking place in a swirling water jet as the swirl ratio S and Reynolds number Re are varied. A pressure-driven water jet discharges into a large tank, swirl being imparted by means of a motor which sets into rotation a honeycomb within a settling chamber. The experiments are conducted for two distinct jet diameters by varying the swirl ratio S while maintaining the Reynolds number Re fixed in the range 300< Re <1200. Breakdown is observed to occur when S reaches a well defined threshold Sc ≈1.3–1.4 which is independent of Re and nozzle diameter used. This critical value is found to be in good agreement with a simple criterion derived in the same spirit as the first stage of Escudier & Keller's (1983) theory. Four distinct forms of vortex breakdown are identified: the well documented bubble state, a new cone configuration in which the vortex takes the form of an open conical sheet, and two associated asymmetric bubble and asymmetric cone states, which are only observed at large Reynolds numbers. The two latter configurations differ from the former by the precession of the stagnation point around the jet axis in a co-rotating direction with respect to the upstream vortex flow. The two flow configurations, bubble or cone, are observed to coexist above the threshold Sc at the same values of the Reynolds number Re and swirl parameter S . The selection of breakdown state is extremely sensitive to small temperature inhomogeneities present in the apparatus. When S reaches Sc , breakdown gradually sets in, a stagnation point appearing in the downstream turbulent region of the flow and slowly moving upstream until it reaches an equilibrium location. In an intermediate range of Reynolds numbers, the breakdown threshold displays hysteresis lying in the ability of the breakdown state to remain stable for S < Sc once it has taken place. Below the onset of breakdown, i.e. when 0< S < Sc , the swirling jet is highly asymmetric and takes the shape of a steady helix. By contrast above breakdown onset, cross-section visualizations indicate that the cone and the bubble are axisymmetric. The cone is observed to undergo slow oscillations induced by secondary recirculating motions that are independent of confinement effects.

We study via simulation how a lattice breaks if each bond is an elastic beam having longitudinal and flexural breaking thresholds randomly selected according to various probability distributions. We observe scaling of force, displacement, and number of broken beams in the controlled regime. The distribution of local forces just before breaking is characterized by a multifractal spectrum f(\ensuremath{\alpha}).

Direct numerical simulations of stably and strongly stratified turbulent flows with Reynolds number Re ≫ 1 and horizontal Froude number F h ≪ 1 are presented. The results are interpreted on the basis of a scaling analysis of the governing equations. The analysis suggests that there are two different strongly stratified regimes according to the parameter $\mathcal{R} \,{=}\, \hbox{\it Re} F^2_h$ . When $\mathcal{R} \,{\gg}\, 1$ , viscous forces are unimportant and l v scales as l v ∼ U / N ( U is a characteristic horizontal velocity and N is the Brunt–Väisälä frequency) so that the dynamics of the flow is inherently three-dimensional but strongly anisotropic. When $\mathcal{R} \,{\ll}\, 1$ , vertical viscous shearing is important so that $l_v \,{\sim}\, l_h/\hbox{\it Re}^{1/2}$ ( l h is a characteristic horizontal length scale). The parameter $\cal R$ is further shown to be related to the buoyancy Reynolds number and proportional to ( l O /η) 4/3 , where l O is the Ozmidov length scale and η the Kolmogorov length scale. This implies that there are simultaneously two distinct ranges in strongly stratified turbulence when $\mathcal{R} \,{\gg}\, 1$ : the scales larger than l O are strongly influenced by the stratification while those between l O and η are weakly affected by stratification. The direct numerical simulations with forced large-scale horizontal two-dimensional motions and uniform stratification cover a wide Re and F h range and support the main parameter controlling strongly stratified turbulence being $\cal R$ . The numerical results are in good agreement with the scaling laws for the vertical length scale. Thin horizontal layers are observed independently of the value of $\cal R$ but they tend to be smooth for $\cal R$ < 1, while for $\cal R$ > 1 small-scale three-dimensional turbulent disturbances are increasingly superimposed. The dissipation of kinetic energy is mostly due to vertical shearing for $\cal R$ < 1 but tends to isotropy as $\cal R$ increases above unity. When $\mathcal{R}$ < 1, the horizontal and vertical energy spectra are very steep while, when $\cal R$ > 1, the horizontal spectra of kinetic and potential energy exhibit an approximate k −5/3 h -power-law range and a clear forward energy cascade is observed.

We report spontaneous motion in a fully biocompatible system consisting of pure water droplets in an oil-surfactant medium of squalane and monoolein. Water from the droplet is solubilized by the reverse micellar solution, creating a concentration gradient of swollen reverse micelles around each droplet. The strong advection and weak diffusion conditions allow for the first experimental realization of spontaneous motion in a system of isotropic particles at sufficiently large Péclet number according to a straightforward generalization of a recently proposed mechanism [S. Michelin, E. Lauga, and D. Bartolo, Phys. Fluids 25, 061701 (2013); S. Michelin and E. Lauga, J. Fluid Mech. 747, 572 (2014)]. Experiments with a highly concentrated solution of salt instead of water, and tetradecane instead of squalane, confirm the above mechanism. The present swimming droplets are able to carry external bodies such as large colloids, salt crystals, and even cells.

Stellar nucleosynthesis of heavy elements such as carbon allowed the formation of organic molecules in space, which appear to be widespread in our Galaxy. The physical and chemical conditions—including density, temperature, ultraviolet (UV) radiation and energetic particles—determine reaction pathways and the complexity of organic molecules in different space environments. Dense interstellar clouds are the birth sites of stars of all masses and their planetary systems. During the protostellar collapse, interstellar organic molecules in gaseous and solid phases are integrated into protostellar disks from which planets and smaller solar system bodies form. After the formation of the planets 4.6 billion years ago, our solar system, including the Earth, was subjected to frequent impacts for several hundred million years. Life on Earth may have emerged during or shortly after this heavy bombardment phase, perhaps as early as 3.90–3.85 billion years ago, but the exact timing remains uncertain. A prebiotic reducing atmosphere, if present, predicts that building blocks of biopolymers—such as amino acids, sugars, purines and pyrimidines—would be formed in abundance. Recent modelling of the Earth's early atmosphere suggests, in contrast, more neutral conditions (e.g. H2O, N2, CO2), thus, precluding the formation of significant concentrations of prebiotic organic compounds. Moreover, even if the Earth's atmosphere were reducing, the presence of UV photons would readily destroy organic compounds unless they were quickly sequestered away in rocks or in the prebiotic ocean. Other possible sources of organic compounds would be high temperature vent chemistry, although the stability of such compounds (bases, amino acids) in these environments remains problematic. Finally, organic compounds may have been delivered to the Earth by asteroids, comets and smaller fragments, such as meteorites and interplanetary dust particles.

Development of a 3D printable material system possessing inherent piezoelectric properties to fabricate integrable sensors in a single-step printing process without poling is of importance to the creation of a wide variety of smart structures. Here, we study the effect of addition of barium titanate nanoparticles in nucleating piezoelectric β-polymorph in 3D printable polyvinylidene fluoride (PVDF) and fabrication of the layer-by-layer and self-supporting piezoelectric structures on a micro- to millimeter scale by solvent evaporation-assisted 3D printing at room temperature. The nanocomposite formulation obtained after a comprehensive investigation of composition and processing techniques possesses a piezoelectric coefficient, d31, of 18 pC N–1, which is comparable to that of typical poled and stretched commercial PVDF film sensors. A 3D contact sensor that generates up to 4 V upon gentle finger taps demonstrates the efficacy of the fabrication technique. Our one-step 3D printing of piezoelectric nanocomposites can form ready-to-use, complex-shaped, flexible, and lightweight piezoelectric devices. When combined with other 3D printable materials, they could serve as stand-alone or embedded sensors in aerospace, biomedicine, and robotic applications.

It is well-known that strongly stratified flows are organized into a layered pancake structure in which motions are mostly horizontal but highly variable in the vertical direction. However, what determines the vertical scale of the motion remains an open question. In this paper, we propose a scaling law for this vertical scale Lv when no vertical lengthscales are imposed by initial or boundary conditions and when the fluid is strongly stratified, i.e., when the horizontal Froude number is small: Fh=U/NLh≪1, where U is the magnitude of the horizontal velocity, N the Brunt–Väisälä frequency and Lh the horizontal lengthscale. Specifically, we show that the vertical scale of the motion is Lv=U/N by demonstrating that the inviscid governing equations in the limit Fh→0, without any a priori assumption on the magnitude of Lv, are self-similar with respect to the variable zN/U, where z is the vertical coordinate. This self-similarity fully accounts for the layer characteristics observed in recent studies reporting spontaneous layering from an initially vertically uniform flow. For such a fine vertical scale, vertical gradients are large, O(1/FhLh). Therefore, even if the magnitude of the vertical velocity is small and scales like FhU, the leading order governing equations of these strongly stratified flows are not two-dimensional in contradiction with a previous conjecture. The self-similarity further suggests that the vertical spectrum of horizontal kinetic energy of pancake turbulence should be of the form E(kz)∝N2kz−3, giving an alternative explanation for the observed vertical spectra in the atmosphere and oceans.

Reducing skin friction is important in nature and in many technological applications. This reduction may be achieved by reducing stresses in turbulent boundary layers, for instance tailoring biomimetic rough skins. Here we take a second approach consisting of keeping the boundary layer laminar as long as possible by forcing small optimal perturbations. Because of the highly non-normal nature of the underlying linearized operator, these perturbations are highly amplified and able to modify the mean velocity profiles at leading order. We report results of wind-tunnel experiments in which we implement this concept by using suitably designed roughness elements placed on the skin to enforce nearly optimal perturbations. We show that by using this passive control technique it is possible to sensibly delay transition to turbulence.