Institut de Mécanique des Fluides de Toulouse

Immiscible displacements in porous media with both capillary and viscous effects can be characterized by two dimensionless numbers, the capillary number C , which is the ratio of viscous forces to capillary forces, and the ratio M of the two viscosities. For certain values of these numbers, either viscous or capillary forces dominate and displacement takes one of the basic forms: (a) viscous fingering, (b) capillary fingering or (c) stable displacement. We present a study in the simple case of injection of a non-wetting fluid into a two-dimensional porous medium made of interconnected capillaries. The first part of this paper presents the results of network simulators (100 × 100 and 25 × 25 pores) based on the physical rules of the displacement at the pore scale. The second part describes a series of experiments performed in transparent etched networks. Both the computer simulations and the experiments cover a range of several decades in C and M . They clearly show the existence of the three basic domains (capillary fingering, viscous fingering and stable displacement) within which the patterns remain unchanged. The domains of validity of the three different basic mechanisms are mapped onto the plane with axes C and M , and this mapping represents the ‘phase-diagram’ for drainage. In the final section we present three statistical models (percolation, diffusion-limited aggregation (DLA) and anti-DLA) which can be used for describing the three ‘basic’ domains of the phase-diagram.

A subgrid scale model for large eddy simulations of turbulent premixed combustion is developed and validated. The approach is based on the concept of artificially thickened flames, keeping constant the laminar flame speed sl0. This thickening is simply achieved by decreasing the pre-exponential factor of the chemical Arrhenius law whereas the molecular diffusion is enhanced. When the flame is thickened, the combustion–turbulence interaction is affected and must be modeled. This point is investigated here using direct numerical simulations of flame–vortex interactions and an efficiency function E is introduced to incorporate thickening effects in the subgrid scale model. The input parameters in E are related to the subgrid scale turbulence (velocity and length scales). An efficient approach, based on similarity assumptions, is developed to extract these quantities from the resolved velocity field. A specific operator is developed to exclude the dilatational part of the velocity field from the estimation of turbulent fluctuations. The combustion model is then implemented in a compressible parallel finite volume–element solver able to handle hybrid grids to simulate a lateral injections combustor (LIC). Results are in agreement with the available experimental data.

Abstract Marine plastic debris floating on the ocean surface is a major environmental problem. However, its distribution in the ocean is poorly mapped, and most of the plastic waste estimated to have entered the ocean from land is unaccounted for. Better understanding of how plastic debris is transported from coastal and marine sources is crucial to quantify and close the global inventory of marine plastics, which in turn represents critical information for mitigation or policy strategies. At the same time, plastic is a unique tracer that provides an opportunity to learn more about the physics and dynamics of our ocean across multiple scales, from the Ekman convergence in basin-scale gyres to individual waves in the surfzone. In this review, we comprehensively discuss what is known about the different processes that govern the transport of floating marine plastic debris in both the open ocean and the coastal zones, based on the published literature and referring to insights from neighbouring fields such as oil spill dispersion, marine safety recovery, plankton connectivity, and others. We discuss how measurements of marine plastics (both in situ and in the laboratory), remote sensing, and numerical simulations can elucidate these processes and their interactions across spatio-temporal scales.

The mechanisms of displacement of one fluid by another are investigated in an etched network. Experiments show that both fluids are simultaneously present in a duct, the wetting fluid remaining in the extreme corners of the cross-section. Calculation of displacement pressures are in good agreement with experiments for drainage, imbibition and removal of blobs. The results may be related to some flow behaviour exhibited in porous media.

The dynamic characteristics of the pressure and velocity fields of the unsteady incompressible laminar wake behind a circular cylinder are investigated numerically and analysed physically. The governing equations, written in a velocity—pressure formulation and in conservative form, are solved by a predictor—corrector pressure method, a finite-volume second-order-accurate scheme and an alternating-direction-implicit (ADI) procedure. The initiation mechanism for vortex shedding and the evaluation of the unsteady body forces are presented for Reynolds-number values of 100, 200 and 1000. The vortex shedding is generated by a physical perturbation imposed numerically for a short time. The flow transition becomes periodic after a transient time interval. The frequency of the drag and lift oscillations agree well with the experimental data. The study of the interactions of the unsteady pressure and velocity fields shows the phase relations between the pressure and velocity, and the influence of different factors: the strongly rotational viscous region, the convection of the eddies and the almost inviscid flow. The interactions among the different scales of structures in the near wake are also studied, and in particular the time-dependent evolution of the secondary eddies in relation to the fully developed primary ones is analysed.

▪ Abstract Predicting the motion of bubbles in dispersed flows is a key problem in fluid mechanics that has a bearing on a wide range of applications from oceanography to chemical engineering. In this review we synthesize the recent progress made in describing bubble motion in inhomogeneous flow. A trident approach consisting of experimental, analytical, and numerical work has given a clearer description of the hydrodynamic forces experienced by isolated bubbles moving either in inviscid flows or in slightly viscous laminar flows. A significant part of the paper is devoted to a discussion of drag, added-mass force, and shear-induced lift experienced by spheroidal bubbles moving in inertially dominated, time-dependent, rotational, nonuniform flows. The important influence of surfactants and shape distortion on bubble motion in a quiescent liquid is highlighted. Examples of bubble motion in inhomogeneous flows combining several of the effects mentioned above are discussed.

The three-dimensional flow around a spherical bubble moving steadily in a viscous linear shear flow is studied numerically by solving the full Navier–Stokes equations. The bubble surface is assumed to be clean so that the outer flow obeys a zero-shear-stress condition and does not induce any rotation of the bubble. The main goal of the present study is to provide a complete description of the lift force experienced by the bubble and of the mechanisms responsible for this force over a wide range of Reynolds number (0.1[les ] Re [les ]500, Re being based on the bubble diameter) and shear rate (0[les ] Sr [les ]1, Sr being the ratio between the velocity difference across the bubble and the relative velocity). For that purpose the structure of the flow field, the influence of the Reynolds number on the streamwise vorticity field and the distribution of the tangential velocities at the surface of the bubble are first studied in detail. It is shown that the latter distribution which plays a central role in the production of the lift force is dramatically dependent on viscous effects. The numerical results concerning the lift coefficient reveal very different behaviours at low and high Reynolds numbers. These two asymptotic regimes shed light on the respective roles played by the vorticity produced at the bubble surface and by that contained in the undisturbed flow. At low Reynolds number it is found that the lift coefficient depends strongly on both the Reynolds number and the shear rate. In contrast, for moderate to high Reynolds numbers these dependences are found to be very weak. The numerical values obtained for the lift coefficient agree very well with available asymptotic results in the low- and high-Reynolds-number limits. The range of validity of these asymptotic solutions is specified by varying the characteristic parameters of the problem and examining the corresponding evolution of the lift coefficient. The numerical results are also used for obtaining empirical correlations useful for practical calculations at finite Reynolds number. The transient behaviour of the lift force is then examined. It is found that, starting from the undisturbed flow, the value of the lift force at short time differs from its steady value, even when the Reynolds number is high, because the vorticity field needs a finite time to reach its steady distribution. This finding is confirmed by an analytical derivation of the initial value of the lift coefficient in an inviscid shear flow. Finally, a specific investigation of the evolution of the lift and drag coefficients with the shear rate at high Reynolds number is carried out. It is found that when the shear rate becomes large, i.e. Sr = O (1), a small but consistent decrease of the lift coefficient occurs while a very significant increase of the drag coefficient, essentially produced by the modifications of the pressure distribution, is observed. Some of the foregoing results are used to show that the well-known equality between the added mass coefficient and the lift coefficient holds only in the limit of weak shears and nearly steady flows.

A scenario of transition to turbulence likely to occur during the development of natural disturbances in a flat-plate boundary layer is studied. The perturbations at the leading edge of the flat plate that show the highest potential for transient energy amplification consist of streamwise aligned vortices. Due to the lift-up mechanism these optimal disturbances lead to elongated streamwise streaks downstream, with significant spanwise modulation. Direct numerical simulations are used to follow the nonlinear evolution of these streaks and to verify secondary instability calculations. The theory is based on a linear Floquet expansion and focuses on the temporal, inviscid instability of these flow structures. The procedure requires integration in the complex plane, in the coordinate direction normal to the wall, to properly identify neutral modes belonging to the discrete spectrum. The streak critical amplitude, beyond which streamwise travelling waves are excited, is about 26% of the free-stream velocity. The sinuous instability mode (either the fundamental or the subharmonic, depending on the streak amplitude) represents the most dangerous disturbance. Varicose waves are more stable, and are characterized by a critical amplitude of about 37%. Stability calculations of streamwise streaks employing the shape assumption, carried out in a parallel investigation, are compared to the results obtained here using the nonlinearly modified mean fields; the need to consider a base flow which includes mean flow modification and harmonics of the fundamental streak is clearly demonstrated.

Dissolution of a porous medium creates, under certain conditions, some highly conductive channels called wormholes. The mechanism of propagation is an unstable phenomenon depending on the microscopic properties at the pore scale and is controlled by the injection rate. The aim of this work is to test the ability of a Darcy-scale model to describe the different dissolution regimes and to characterize the influence of the flow parameters on the wormhole development. The numerical approach is validated by model experiments reflecting dissolution processes occurring during acid injection in limestone. Flow and transport macroscopic equations are written under the assumption of local mass non-equilibrium. The coupled system of equations is solved numerically in two dimensions using a finite volume method. Results are discussed in terms of wormhole propagation rate and pore volume injected.

We report an experimental investigation of the motion of bed load particles under steady and spatially uniform turbulent flow above a flat sediment bed of uniform grain size. Using a high‐speed video imaging system, we recorded the trajectories of the moving particles and measured their velocity and the length and duration of their flights, as well as the surface density of the moving particles. Our observations show that entrained particles exhibit intermittent motion composed of the succession of periods of “flight” and periods of rest. During one flight, a particle may go through phases of reptation, during which it moves in nearly persistent contact with the rough bed, and phases of saltation, during which it travels sufficiently high above the bed to reach high velocities. The distributions of longitudinal and transverse particle velocities obey a decreasing exponential and a Gaussian law, respectively. Interestingly, these observations are similar to those previously reported for viscous flows. The experimental results presented here support the erosion‐deposition model of Charru (2006) and allow the calibration of the involved coefficients. In particular, noting τ *, the Shields number, and τ * c , the threshold Shields number, we find that (1) the surface density of moving particles increases linearly with τ * − τ * c ; (2) the average particle velocity increases linearly with τ * 1/2 − τ * c 1/2 , with a finite nonzero value at the threshold; (3) the flight duration scales with a characteristic settling time with no significant dependence on either τ * or the settling Reynolds number; and (4) the flight length increases linearly with τ * 1/2 − τ * c 1/2 . The results presented in this paper should provide a valuable physical framework to describe bed form development in turbulent flows.

One basic effect of turbulence in turbulent premixed combustion is for the fluctuating velocity field to wrinkle the flame and greatly increase its surface area. In the flamelet theory, this effect is described by the flame surface density. An exact evolution equation for the flame surface density, called the Σ-equation, may be written, where basic physical mechanisms like production by hydrodynamic straining and destruction by propagation effects are described explicitly. Direct numerical simulation (DNS) is used in this paper to estimate the different terms appearing in the Σ-equation. The numerical configuration corresponds to three-dimensional premixed flames in isotropic turbulent flow. The simulations are performed for various mixture Lewis numbers in order to modify the strength and nature of the flame-flow coupling. The DNS-based analysis provides much information relevant to flamelet models. In particular, the flame surface density, and the source and sink terms for the flame surface density, are resolved spatially across the turbulent flame brush. The geometry as well as the dynamics of the flame differ quite significantly from one end of the reaction zone to the other. For instance, contrary to the intuitive idea that flame propagation effects merely counteract the wrinkling due to the turbulence, the role of flame propagation is not constant across the turbulent brush and switches from flame surface production at the front to flame surface dissipation at the back. Direct comparisons with flamelet models are also performed. The Bray-Moss-Libby assumption that the flame surface density is proportional to the flamelet crossing frequency, a quantity that can be measured in experiments, is found to be valid. Major uncertainties remain, however, over an appropriate description of the flamelet crossing frequency. In comparison, the coherent flame model of Marble & Broadwell achieves closure at the level of the Σ-equation and provides a more promising physically based description of the flame surface dynamics. Some areas where the model needs improvement are identified.

The mean vertical structure of mesoscale eddies in the Peru‐Chile Current System is investigated by combining the historical records of Argo float profiles and satellite altimetry data. A composite average of 420 (526) profiles acquired by Argo floats that surfaced into cyclonic (anticyclonic) mesoscale eddies allowed constructing the mean three‐dimensional eddy structure of the eastern South Pacific Ocean. Key differences in their thermohaline vertical structure were revealed. The core of cyclonic eddies (CEs) is centered at ∼150 m depth within the 25.2–26.0 kg m −3 potential density layer corresponding to the thermocline. In contrast, the core of the anticyclonic eddies (AEs) is located below the thermocline at ∼400 m depth impacting the 26.0–26.8 kg m −3 density layer. This difference was attributed to the mechanisms involved in the eddy formation. While intrathermocline CEs would be formed by instabilities of the surface equatorward coastal currents, the subthermocline AEs are likely to be shed by the subsurface poleward Peru‐Chile Undercurrent. In the eddy core, maximum temperature and salinity anomalies are of ±1°C and ±0.1, with positive (negative) values for AEs (CEs). This study also provides new insight into the potential impact of mesoscale eddies for the cross‐shore transport of heat and salt in the eastern South Pacific. Considering only the fraction of the water column associated with the fluid trapped within the eddies, each CE and AE has a typical volume anomaly flux of ∼0.1 Sv and yields to a heat and salt transport anomaly of ±1–3 × 10 11 W and ±3–8 × 10 3 kg s −1 , respectively.

Leaves falling in air and bubbles rising in water provide daily examples of nonstraight paths associated with the buoyancy-driven motion of a body in a fluid. Such paths are relevant to a large variety of applicative fields such as mechanical engineering, aerodynamics, meteorology, and the biomechanics of plants and insect flight. Although the problem has attracted attention for ages, it is only recently that the tremendous progress in the development of experimental and computational techniques and the emergence of new theoretical concepts have led to a better understanding of the underlying physical mechanisms. This review attempts to bring together the main recent experimental, computational, and theoretical advances obtained on this fascinating subject. To this end it describes the first steps of the transition in the wake of a fixed body and its connection with the onset and development of the path instability of moving bodies. Then it analyzes the kinematics and dynamics of various types of bodies along typical nonstraight paths and how the corresponding information can be used to build low-dimensional predictive models.

This work reports the first part of a series of numerical simulations carried out in order to improve knowledge of the forces acting on a sphere embedded in accelerated flows at finite Reynolds number, Re. Among these forces added mass and history effects are particularly important in order to determine accurately particle and bubble trajectories in real flows. To compute these hydrodynamic forces and more generally to study spatially or temporally accelerated flows around a sphere, the full Navier–Stokes equations expressed in velocity–pressure variables are solved by using a finite-volume approach. Computations are carried out over the range 0.1 ≤ Re ≤ 300 for flows around both a rigid sphere and an inviscid spherical bubble, and a systematic comparison of the flows around these two kinds of bodies is presented. Steady uniform flow is first considered in order to test the accuracy of the simulations and to serve as a reference case for comparing with accelerated situations. Axisymmetric straining flow which constitutes the simplest spatially accelerated flow in which a sphere can be embedded is then studied. It is shown that owing to the viscous boundary condition on the body as well as to vorticity transport properties, the presence of the strain modifies deeply the distribution of vorticity around the sphere. This modification has spectacular consequences in the case of a rigid sphere because it influences strongly the conditions under which separation occurs as well as the characteristics of the separated region. Another very original feature of the axisymmetric straining flow lies in the vortex-stretching mechanism existing in this situation. In a converging flow this mechanism acts to reduce vorticity in the wake of the sphere. In contrast when the flow is divergent, vorticity produced at the surface of the sphere tends to grow indefinitely as it is transported downstream. It is shown that in the case where such a diverging flow extends to infinity a Kelvin–Helmholtz instability may occur in the wake. Computations of the hydrodynamic force show that the effects of the strain increase rapidly with the Reynolds number. At high Reynolds numbers the total drag is dramatically modified and the evaluation of the pressure contribution shows that the sphere undergoes an added mass force whose coefficient remains the same as in inviscid flow or in creeping flow, i.e. C M = ½, whatever the Reynolds number. Changes found in vorticity distribution around the rigid sphere also affect the viscous drag, which is markedly increased (resp. decreased) in converging (resp. diverging) flows at high Reynolds numbers.

International audience

ABSTRACT Worldwide, obstructions on watercourses have interfered with migratory pathways of fish species, reducing life‐cycle success and often eliminating diadromous fish species altogether from river basins. Over the last century, efforts to mitigate these effects were initially directed at developing fishways for upstream, high‐value migrant adult salmon. In more recent years, efforts have turned to developing fishways for other species. Results of past research suggest that the development of effective fishways requires biological knowledge of fish behaviour when encountering variable flows, velocity and turbulence, combined with hydraulic and civil engineering knowledge and expertise to develop facilities that provide appropriate hydraulic conditions that fish will exploit. Further, it often requires substantial financial resources for biological and hydraulic testing as well as engineering design, particularly where prior knowledge of the behaviour of target fish species does not exist. Where biological or engineering knowledge (or both) is absent, development of effective passage facilities must take on a trial and error approach that will almost certainly require years to attain success. Evaluations of existing adult and juvenile fish passage facilities, where they have been carried out, suggest that migrant fish reject areas with hydraulic conditions they determine unsuitable. Even well designed fish ladders or nature‐like bypass channels for upstream migrants, even those with good attraction flows, will fail if incorrectly sited. Although progress has been made, developing successful installations for downstream migrants remains much more difficult, probably because downstream fish move with the flow and have less time to assess cues at entrances to any bypasses that they encounter. Copyright © 2011 John Wiley & Sons, Ltd.

We model the problem of path instability of a rising bubble by considering the bubble as a spheroidal body of fixed shape, and we solve numerically the coupled fluid-body problem. Numerical results show that this model exhibits path instability for large enough values of the control parameters. The corresponding characteristics of the zigzag and spiral paths are in good agreement with experimental observations. Analysis of the vorticity field behind the bubble reveals that a wake instability leading to a double threaded wake is the primary cause of the path instability.

Abstract The SuperCam instrument suite provides the Mars 2020 rover, Perseverance, with a number of versatile remote-sensing techniques that can be used at long distance as well as within the robotic-arm workspace. These include laser-induced breakdown spectroscopy (LIBS), remote time-resolved Raman and luminescence spectroscopies, and visible and infrared (VISIR; separately referred to as VIS and IR) reflectance spectroscopy. A remote micro-imager (RMI) provides high-resolution color context imaging, and a microphone can be used as a stand-alone tool for environmental studies or to determine physical properties of rocks and soils from shock waves of laser-produced plasmas. SuperCam is built in three parts: The mast unit (MU), consisting of the laser, telescope, RMI, IR spectrometer, and associated electronics, is described in a companion paper. The on-board calibration targets are described in another companion paper. Here we describe SuperCam’s body unit (BU) and testing of the integrated instrument. The BU, mounted inside the rover body, receives light from the MU via a 5.8 m optical fiber. The light is split into three wavelength bands by a demultiplexer, and is routed via fiber bundles to three optical spectrometers, two of which (UV and violet; 245–340 and 385–465 nm) are crossed Czerny-Turner reflection spectrometers, nearly identical to their counterparts on ChemCam. The third is a high-efficiency transmission spectrometer containing an optical intensifier capable of gating exposures to 100 ns or longer, with variable delay times relative to the laser pulse. This spectrometer covers 535–853 nm ( $105\text{--}7070~\text{cm}^{-1}$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mn>105</mml:mn> <mml:mtext>–</mml:mtext> <mml:mn>7070</mml:mn> <mml:mspace/> <mml:msup> <mml:mtext>cm</mml:mtext> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> </mml:math> Raman shift relative to the 532 nm green laser beam) with $12~\text{cm}^{-1}$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mn>12</mml:mn> <mml:mspace/> <mml:msup> <mml:mtext>cm</mml:mtext> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> </mml:math> full-width at half-maximum peak resolution in the Raman fingerprint region. The BU electronics boards interface with the rover and control the instrument, returning data to the rover. Thermal systems maintain a warm temperature during cruise to Mars to avoid contamination on the optics, and cool the detectors during operations on Mars. Results obtained with the integrated instrument demonstrate its capabilities for LIBS, for which a library of 332 standards was developed. Examples of Raman and VISIR spectroscopy are shown, demonstrating clear mineral identification with both techniques. Luminescence spectra demonstrate the utility of having both spectral and temporal dimensions. Finally, RMI and microphone tests on the rover demonstrate the capabilities of these subsystems as well.

We show that stable localized waves can be generated in the vicinity of an inverted Hopf bifurcation. We compute the size of the localized wave envelope perturbatively in the case of slightly dissipative systems. The size selection traces back to the broken scale invariance by the dissipative terms. This mechanism is a possible explanation for the localized structures, widely observed in various hydrodynamic flows in dissipative systems driven far from equilibrium.

Abstract This chapter describes the basic phenomena controlling reacting flows and the corresponding computational methodologies. Combustion regimes (premixed or diffusion flames, laminar or turbulent cases, stable or unstable behavior) are first defined before introducing the basic terminology required to understand numerical techniques for reacting flows. The governing equations for combustion are more complex than those used in classical aerodynamics, and their specificities are discussed before describing numerical methods for laminar flames. Finally, the various methods used for turbulent flames are discussed, focusing on recent techniques such as Direct Numerical Simulations and Large Eddy Simulations.