In this study we consider the effect of a horizontal magnetic field on the Rayleigh-Bénard convection in a finite liquid metal layer contained in a cuboid vessel $(200\times 200\times 40\mathrm{m}{\mathrm{m}}^3)$ of aspect ratio $\mathrm{\Gamma }=5$ . Laboratory experiments are performed for measuring temperature and flow field in the low melting point alloy GaInSn at Prandtl number $Pr\approx 0.03$ and in a Rayleigh number range $2.3\times {10}^4\le Ra\le 2.6\times {10}^5$. The field direction is aligned parallel to one pair of the two side walls. The field strength is varied up to a maximum value of 320 mT ($Ha=2470$, $Q=6.11\times {10}^6$, definitions of all nondimensional numbers are given in the text). The magnetic field forces the flow to form two-dimensional (2D) rolls whose axes are parallel to the direction of the field lines. The experiments confirm the predictions made by Busse and Clever [Busse and Clever, Stability of convection rolls in the presence of a horizontal magnetic field, J. de Méc. Théor. et Appl. 2, 495 (1983)] who showed that the application of the horizontal magnetic field extends the range in which steady 2D roll structures exist (Busse balloon) towards higher Ra numbers. A transition from the steady to a time-dependent oscillatory flow occurs when Ra exceeds a critical value for a given Chandrasekhar number Q, which is also equivalent to a reduction of the ratio $Q/Ra$. Our measurements reveal that the first developing oscillations are clearly of 2D nature, in particular a mutual increase and decrease in the size of adjacent convection rolls is observed without the formation of any detectable gradients in the velocity field along the magnetic field direction. At a ratio of $Q/Ra\approx 1$, the first 3D structures appear, which initially manifest themselves in a slight inclination of the rolls with respect to the magnetic field direction. Immediately in the course of this, there arise also disturbances in the spaces between adjacent convection rolls, which are advected along the rolls due to the secondary flow driven by Ekman pumping. The transition to fully developed 3D structures and then to a turbulent regime takes place with further lowering $Q/Ra$.

Here we investigate the transition from spreading to splashing of drops with radii $R$ varying from millimeters to tens of microns impacting onto a smooth and dry partially wetting substrate at normal atmospheric conditions. Experiments show that the smaller $R$ is, the larger the impact velocity $V$ for the drop to splash needs to be but also that splash is inhibited if ${\mathrm{We}}_{\lambda }=\rho V^2\lambda /\sigma \gtrsim 0.5$, with $\sigma$, $\rho$, and $\lambda$ indicating the interfacial tension coefficient, the liquid density, and the mean free path of gas molecules. This result has been validated for two different values of the Ohnesorge number ${\mathrm{Oh}}_{\lambda }=\mu /\sqrt{\rho \lambda \sigma }$, with $\mu$ indicating the liquid viscosity, defined using only the material properties of the liquid and of the surrounding gaseous atmosphere. The underlying reason for this a priori unexpected finding results from the fact that the thin liquid film ejected after the drop touches the substrate is, under many practical conditions, $H_t\simeq \sigma /\left(\rho V^2\right)$ Riboux and Gordillo [Phys. Rev. Lett. 113, 024507 (2014)]. Then, for sufficiently large values of $V$, the thickness of the lamella becomes similar to the mean free path of gas molecules, i.e., $H_t\approx \lambda$, and, under these conditions, the splash of the drop is inhibited because the lift force causing the liquid to dewet the partially wetting solid is negligible. The spreading to splashing and the splashing to spreading transitions observed experimentally as the impact velocity is increased and the radii of the droplets is above a certain threshold value are very well predicted by the theory in G. Riboux and J. M. Gordillo [Phys. Rev. Lett. 113, 024507 (2014)] and J. M. Gordillo and G. Riboux [J. Fluid Mech. 871, R3 (2019)] once the aerodynamic lift force is set to zero for $H_t/\lambda \lesssim 2$, i.e., when ${\mathrm{We}}_{\lambda }\gtrsim 0.5$.

In this work we investigate symmetry breaking in the presence of a turbulent environment. The transition from a symmetric state to a symmetry-breaking state is demonstrated using two examples: (1) the transition of a two-dimensional flow to a three-dimensional flow as the fluid layer thickness is varied and (2) the dynamo instability in a thin layer flow as the magnetic Reynolds number is varied. We show that these examples have similar critical exponents that differ from the mean-field predictions. The critical behavior can be related to the multiplicative nature of the fluctuations and can be predicted in certain limits using results from the statistical properties of random interfaces. Our results indicate the possibility of existence of a new class of out-of-equilibrium phase transition controlled by the multiplicative noise.

Iceberg meltwater is a critical freshwater flux from the cryosphere to the oceans. Global climate simulations therefore require simple and accurate parametrizations of iceberg melting. Iceberg shape is an important but often neglected aspect of iceberg melting. Icebergs have an enormous range of shapes and sizes, and distinct processes dominate basal and side melting. We show how different iceberg aspect ratios and relative ambient water velocities affect melting using a combined experimental and numerical study. The experimental results show significant variations in melting between different iceberg faces, as well as within each iceberg face. These findings are reproduced and explained with multiphysics numerical simulations. At high relative ambient velocities melting is largest on the side facing the flow, and mixing during vortex generation causes local increases in basal melt rates of over 50%. Double-diffusive buoyancy effects become significant when the relative ambient velocity is low. Existing melting parametrizations do not reproduce our findings. We propose several corrections to capture the influence of aspect ratio on iceberg melting.

This paper focuses on the statistical analysis of a droplet population produced by a pressure-atomized jet spray, laying in the second-wind-induced regime, far behind the nozzle. The droplet size and axial velocity derived from droplet tracking velocimetry measurements are shown to follow bimodal distributions and their modeling is tackled in the framework of turbulence and of combustion applications, respectively. In addition, the existence of subsets of droplets showing specific behaviors is brought to light from the analysis of the experimental droplet-size–velocity joint probability distribution function (PDF). Such subsets can be precisely defined using the properties of the size and axial-velocity distributions. Finally, the trend of the joint PDF is depicted due to a quadratic relationship which is derived in the context of combustion and shown to work here as well, far behind the nozzle.

The three-dimensionality of turbulent motions in a massively separated Mach 2.49 longitudinal cylinder wake is investigated using tomographic particle image velocimetry (TPIV). Measurements were acquired within six volumetric subregions of the flow, including the separated shear layer, the recirculation region, the shear layer reattachment region, and the trailing wake, with a large ensemble of measurement volumes (between 2100 and 3300) acquired and processed per region to allow for adequate statistical convergence in the various analyses used. Large streamwise-elongated turbulent structures with a quasiaxial orientation were commonly observed to exist in regions of the flow encountering the adverse pressure gradient associated with shear layer reattachment. The statistical geometry and orientation of these structures within this region of the flow are demonstrated using linear stochastic estimation. The snapshot proper orthogonal decomposition method was also used to decompose the TPIV data into mode shapes. Both an energy-based and an enstrophy-based decomposition were performed, as the three-dimensional TPIV data allow for calculation of all components of the vorticity vector. It is demonstrated that the highest energy-containing modes for many of the TPIV subregions are associated with coherent turbulent structures, such as hairpin vortices or the aforementioned quasiaxial structures. The highest energy-containing mode from the recirculation region data represented 30% of the turbulent kinetic energy within a single mode, and appears to indicate a large-scale global flow interaction between the recirculation region and the separated shear layer with a helical orientation. This large-scale behavior appears consistent with past computational simulations of this flow that also predicted that low-order azimuthal and helical instability modes within the recirculation region play a significant role in the generation of large-scale structures and the production of pressure drag.

Ring vortices are efficient at transporting fluid across long distances. They can be found in nature in various ways: they propel squids, inject blood in the heart, and entertain dolphins. These vortices are generally produced by ejecting a volume of fluid through a circular orifice. The impulse given to the vortex rings moving away results in a propulsive force on the vortex generator. Propulsive vortex rings have been widely studied and characterized. After four convective times, the vortex moves faster than the shear layer it originates from and separates from it. When the vortex separates, the circulation of the vortex reaches a maximum value, and the nondimensional energy attains a minimum. The simultaneity of these three events obfuscates the causality between them. To analyze the temporal evolution of the nondimensional energy of ring vortices independent of their separation, we analyze the spatiotemporal development of vortices generated in the wake of cones. Cones with different apertures and diameters were accelerated from rest to produce a wide variety of vortex rings. The energy, circulation, and velocity of these vortices were extracted based on time-resolved velocity field measurements. The vortex rings that form behind the cones have a self-induced velocity that causes them to follow the cone, and they continue to grow as the cone travels well beyond the limiting vortex formation timescales observed for propulsive vortices. The nondimensional circulation, based on the vortex diameter, and the nondimensional energy of the drag vortex rings converge after three convective times to values comparable to their propulsive counterparts. This result proves that vortex pinch-off does not cause the nondimensional energy to reach a minimum value. The limiting values of the nondimensional circulation and energy are mostly independent of the cone geometry and translational velocity and fall within an interval of $10\%$ around the mean value. The velocity of the vortex shows only $6\%$ of variation and is the most unifying quantity that governs the formation of vortex rings behind cones.

Despite the relevance of the Kelvin force in many physical and electrochemical systems involving magnetic species, the underlying convective flows are scarcely understood. For that purpose, we simulate a simplified rare-earth system in the presence of competing Kelvin and gravity forces. The results are experimentally validated using interferometry and microscopic particle image velocimetry. Based on the excellent agreement of numerical and experimental results, the underlying mechanism of ions' magnetic separation can be explained, which paves the way for a prospective application in rare-earth beneficiation.

Mass transfer from a composite cylinder—made of an inner core and an outer enveloping semipermeable shell—under channel crossflow is studied numerically using two-dimensional lattice-Boltzmann simulations. The core is initially loaded with a solute that diffuses passively through the shell toward the fluid. The cylinder internal structure and the initial condition considered in this study differ and thus complement the classical studies dealing with homogeneous uncoated cylinders whose surfaces are sustained at either constant concentration or constant mass flux. Here, the cylinder acts as a reservoir endowed with a shell that controls the leakage rate of the encapsulated solute. The transition from steady to unsteady laminar flow regime, around the cylinder, alters the released solute spatial distribution and the mass transfer efficiency, which is characterized by the Sherwood number (the dimensionless mass transfer coefficient). Moreover, the reservoir involves unsteady and continuous boundary conditions, which lead to unsteady and nonuniform distribution of both the concentration and the mass flux at the cylinder surface. The effect of adding a coating shell is highlighted, for a given ratio of the cylinder diameter to the channel width, by extracting a correlation from the computed data set. This new correlation shows explicit dependency of the Sherwood number upon the shell solute permeability (the shell mass transfer coefficient).

Pulsatile pressure gradients are widely present in microfluidic multiphase systems where the movement of fluids is affected by the presence of fluid-fluid interfaces. We present a simple theoretical model that incorporates dynamic interfacial curvatures produced as a response to pulsatile external forcing. Our equations make evident a singular character of the dynamics at low frequencies, due to surface tension. Analytical solution of the model shows the emergence of a resonant behavior for the dynamic permeability. We have designed and implemented microfluidic experiments to observe both the low-frequency dynamics and the resonance. We have studied a fluid slug whose length was chosen in order to look for resonances as predicted by our theoretical model, in the range of operational frequencies of our piezoelectric actuator. We have obtained the experimental dynamic permeability for water and a 70.0% glycerol solution in water and observed agreement with theoretical findings. Our model, validated by experiments, allows us to understand differences of several orders of magnitude in the amplitude of flow velocity at low frequencies, between systems with and without interfaces.

The mean stress is one of the most important quantities of interest in turbulent boundary layers. The governing equations for the mean flow are used to derive a relation between the mean total stress and the mean velocity in a zero pressure gradient turbulent boundary layer, allowing the mean shear stress to be written as a function of wall-normal distance. The relation contains an unknown term, which is modeled using a linear function of the wall-normal distance, inspired by existing data sets. The model for the mean total stress requires the wall-normal mean velocity profile, which requires modeling if not available. The existing data sets and scaling arguments are used to obtain a simple and compact fit for the mean wall-normal velocity, which is subsequently used to obtain a simple model for the mean total stress. The model shows good agreement with the available simulation and experimental data for a large range of Reynolds number.

We present a numerical investigation on the dynamics of a compound droplet under the combined influence of an applied electric field and shear flow. The paper is carried out by solving the electro-hydrodynamic equations in a two-dimensional framework, and the interface is captured using a volume-of-fluid approach. Both perfect dielectric as well as leaky dielectric fluids are considered. For the case of dielectric fluids, the deformation of both the inner and outer interfaces can be modulated by either variation of the permittivity contrast between the fluids or the applied field strength. The nature of the polarization forces acting at both the interfaces can be either compressive or tensile depending on the magnitude of the permittivity ratio. The investigations for leaky dielectric fluids reveal that the ratio of electrical permittivity and conductivity between the two phases plays a critical role in deciding the magnitude of deformation and orientation of the compound droplet. The variation of charge accumulated at the interfaces modifies the behavior of the Coulombic forces thereby fundamentally altering the droplet deformation and orientation characteristics. Furthermore, it is demonstrated that the electric field can be suitably applied to engender breakup of the compound droplets.

Environmental fluid mechanics underlies a wealth of natural, industrial, and, by extension, societal challenges. In the coming decades, as we strive towards a more sustainable planet, there are a wide range of Grand Challenge problems that need to be tackled, ranging from fundamental advances in understanding and modeling of stratified turbulence and consequent mixing, to applied studies of pollution transport in the ocean, atmosphere, and urban environments. A workshop was organized in the Les Houches School of Physics in France in January 2019 with the objective of gathering leading figures in the field to produce a road map for the scientific community. Five subject areas were addressed: multiphase flow, stratified flow, ocean transport, atmospheric and urban transport, and weather and climate prediction. This article summarizes the discussions and outcomes of the meeting, with the intent of providing a resource for the community going forward.

Red blood cells (RBCs)—erythrocytes—suspended in plasma tend to aggregate and form rouleaux. During aggregation the first stage consists in the formation of RBC doublets [S. M. Bertoluzzo, A. Bollini, M. Rasia, and A. Raynal, Blood Cells Mol. Dis. 25, 339 (1999)]. While aggregates are normally dissociated by moderate flow stresses, under some pathological conditions the aggregation becomes irreversible, which leads to high blood viscosity and vessel occlusion. We perform here two-dimensional (2D) simulations to study the doublet dynamics under shear flow in different conditions and its impact on rheology. A few illustrative results obtained here in 3D agree with 2D results. We sum up our results on the dynamics of doublet in a rich phase diagram in the parameter space (flow strength, adhesion energy) showing four different types of doublet configurations and dynamics. We find that membrane tank-treading plays an important role in doublet disaggregation, in agreement with experiments on RBCs. A remarkable feature found here is that when a single cell performs tumbling (by increasing vesicle internal viscosity) the doublet formed due to adhesion (even very weak) remains stable even under a very strong shear rate. It is seen in this regime that an increase of shear rate induces an adaptation of the doublet conformation allowing the aggregate to resist cell-cell detachment. We show that the normalized effective viscosity of doublet suspension increases significantly with the adhesion energy, a fact which should affect blood perfusion in microcirculation.

In this paper, we investigate quantitatively the coupling between gradients of temperature and of chemical or water potential under steady-state conditions in the vapor phase. This coupling is important for the measurement and modeling of the dynamics of water in unsaturated environments such as soils and plants. We focus on a simple nonequilibrium scenario in which a gradient of temperature exists across an air-filled gap that separates two aqueous phases with no net transfer of water. This scenario is relevant for measurements of the water potential in environmental and industrial contexts. We use a tool, a microtensiometer, to perform these measurements. We observed variations of the water potential with a difference of temperature across the air gap of $-7.9\pm 0.3\mathrm{MPa}{\mathrm{K}}^{-1}$, in agreement with previous measurements. Our result is close to a first-order theoretical prediction, highlighting that most of the effect comes from the variation of saturation pressure with temperature. We then show that thermodiffusion (Soret effect) coupled to natural convection could occur in our experiment and discuss how these effects could explain the small discrepancy observed between measurements and first-order theoretical predictions.

In this paper, we show that Stokes drift may be significantly affected when an incident intermediate or shallow water surface wave travels over a corrugated sea floor. The underlying mechanism is Bragg resonance: reflected waves generated via nonlinear resonant interactions between an incident wave and a rippled bottom. We theoretically explain the fundamental effect of two counterpropagating Stokes waves on Stokes drift and then perform numerical simulations of Bragg resonance using the high-order spectral method. A monochromatic incident wave on interaction with a patch of bottom ripple yields a complex interference between the incident and reflected waves. When the velocity induced by the reflected waves exceeds that of the incident, particle trajectories reverse, leading to a backward drift. Lagrangian and Lagrangian-mean trajectories reveal that surface particles near the up-wave side of the patch are either trapped or reflected, implying that the rippled patch acts as a non-surface-invasive particle trap or reflector. On increasing the length and amplitude of the rippled patch, reflection, and thus the effectiveness of the patch, increases. The inclusion of realistic constant current shows noticeable differences between Lagrangian-mean trajectories with and without the rippled patch. Theoretical analysis reveals additional terms in the Stokes drift arising from the particular solution due to mean-current–bottom-ripple interactions, irrespective of whether Bragg resonance condition is met. Our analyses may be useful for designing artificial, corrugated sea-floor patches for mitigating microplastics and other forms of ocean pollution. We also expect that sea-floor corrugations, especially in the near-shore region, may significantly affect oceanic tracer transport.

When particle-laden freshwater is placed above clear saltwater, double-diffusive sedimentation can arise. Navier-Stokes direct numerical simulations by Burns and Meiburg showed that this process can be dominated by either Rayleigh-Taylor or double-diffusive fingering instabilities. Based on two-dimensional simulations, those authors identify a single dimensionless parameter that can be employed to distinguish between these regimes. Here we develop a high-performance semi-Lagrangian computational approach that enables us to extend these high Schmidt number simulations to three dimensions, and to confirm the validity of their proposed scaling law for three-dimensional flows.

Liquid drops adhere to solid surfaces due to surface tension but can depin and run back along the surface due to wind or gravity forcing. This work develops a simple mechanistic model for depinning by combined gravity and high-Reynolds-number wind forcing and tests that model using water drops on a roughened aluminum surface. On noninclined surfaces, drops depin at a constant critical Weber number ${\text{We}}_{\mathrm{crit}}=7.9$ for the present wettability conditions. On inclined surfaces, ${\text{We}}_{\mathrm{crit}}$ decreases linearly with the product of the Bond number and the width-to-height aspect ratio of the unforced drop. The linear slope is different in distinct wind- and gravity-dominated forcing regimes above and below ${\text{We}}_{\mathrm{crit}}=4$. Contact-line shapes and drop profile shapes are measured at depinning conditions but do not adequately explain the differences between the two forcing regimes.

The Orr mechanism is revisited to understand its precise role in the transition of plane Couette flow. By considering homogeneous shear flow and plane Couette flow, it is identified that the Orr mechanism induces a lift-up effect which significantly amplifies spanwise velocity. An optimal perturbation analysis for an individual velocity component reveals that the amplification of spanwise velocity is most active at the streamwise length comparable to the given spanwise length of the perturbation. The relevance of this mechanism to transition is subsequently examined in plane Couette flow. To this end, a set of initial conditions, which combines the optimal perturbation for spanwise velocity with the one for all the velocity components, is considered by varying their amplitudes. Two representative transition scenarios are found: oblique and streak transitions. In the former, the spanwise velocity perturbation amplified with the Orr mechanism initiates both streak amplification and breakdown, whereas in the latter, its role is limited only to the streak breakdown at the late stage of transition. As such, the oblique transition offers a route to turbulence energetically more efficient than the streak transition, at least for the cases examined in the present paper. Finally, the oblique transition is found to share many physical similarities with the transition by the minimal seed.