Environmental fluid mechanics underlies a wealth of natural, industrial, and, by extension, societal challenges. As we strive toward a more sustainable planet, there is a wide range of problems to be tackled, 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. The discussions and outcomes of a recent Les Houches School of Physics meeting are summarized here with the intent of providing a resource for the community going forward and a plan of action for the coming decade.

The effective body force associated with the application of a magnetic field to a solution containing rare earth ions produces convection and a time varying flow field that enables separation of the ions from solution.

When particle-laden freshwater is placed above clear saltwater, the ensuing sedimentation process can take one of two forms: For small dimensionless settling velocities, it will be double diffusive in nature, whereas for large settling velocities it will be dominated by Rayleigh-Taylor instability. A high-performance semi-Lagrangian computational approach is introduced that allows for the investigation of these processes in three dimensions.

Internal coastal Kelvin waves were experimentally generated in a two-layer fluid system on a rotating table. Waves are exponentially localized near the tank boundary and propagate in the same direction as the table rotation along boundaries of complex geometries without being scattered. Our experiments suggest a connection between these unusual wave characteristics and topological properties of the underlying governing equations.

Leading edge vortices on flapping wings induce high transient lift during their growth phase and increase maneuverability at low flight speeds. A hypothesis is developed and experimentally validated that the vortex growth phase on a pitching and plunging airfoil can be prolonged with dielectric barrier discharge plasma actuators. This is demonstrated for various airfoils and for different motion dynamics and kinematics.

Boundary layer flame flashback is a phenomenon that may constitute a key challenge for efficient combustion of novel fuels at gas turbine conditions. In the present work, the effect of wall roughness on the laminar boundary layer flashback is studied systematically using numerical simulation. The results indicate that the wall roughness can attenuate flashback speed due to enhanced heat loss in case of low thermal resistance of the wall. The critical velocity gradient of the oncoming flow is shown to decrease with wall roughness level and increase with gas thermal expansion ratio.

It is shown that the basis functions of gradient transport theory are different when there is an additional materially conserved variable. The turbulent fluxes now depend on the mean density gradient indicating the possibility of counter gradient transport from first principles as seen in some laboratory experiments. It is shown that arguments by analogy from constant density transport for the Favre fluxes are not consistent with the Lagrangian results.

Computer simulations are used to study mass transfer from a stationary composite cylinder—made of an inner, initially loaded, core and an outer-coating semipermeable shell—subjected to a crossflow. The transition from steady to unsteady laminar flow regime alters the released solute spatial distribution and the mass transfer efficiency (Sherwood number), which is found to depend explicitly on the shell solute permeability. The cylinder internal structure and the initial condition considered in this study differ and, thus, complement classical studies dealing with homogeneous uncoated cylinders for which surfaces are sustained at either constant concentration or constant mass flux.

The effect of a horizontal magnetic field on the oscillatory instability of convection rolls in a finite liquid-metal layer is investigated. The flow measurements reveal that the first developing oscillations are of a two-dimensional nature. In particular, a mutual increase and decrease in the size of adjacent convection rolls is observed where the periodicity of the “breathing” convection rolls can be related to standing inertial waves. With gradual reduction of the magnetic-field strength, the oscillating convection rolls are increasingly affected by three-dimensional disturbances.

What happens if a box is heated and cooled by a combination of localized and distributed heat sources? This question is investigated using direct numerical simulations for a range of heating regimes to produce different steady states. Two conceptual models are developed, and it is shown that the transition from a stratified to a well-mixed environment occurs when the distributed and localized heating are of equal strength.

Contact-angle hysteresis enables drops to pin to surfaces in the presence of wind or gravity forcing. Under what combined forcing conditions do drops depin and run back along a surface? On noninclined surfaces, drops depin at a constant critical Weber number across a wide range of Bond numbers. On inclined surfaces, two regimes of wind- and gravity-dominated forcing are observed, but a simple correlation may still describe critical depinning conditions.

Aggregates of red blood cells (RBCs) are normally dissociated reversibly by moderate flow stresses. Numerical simulations show that the RBCs doublet may be robust even for very high shear stress compromising oxygen delivery to organs and tissues. A link with pathological conditions (several common blood diseases) is demonstrated.

The work demonstrates the dynamics of a compound droplet under the combined influence of an applied electric field and shear flow. 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 electric field. The investigations for leaky dielectric fluids reveal that the ratio of electrical permittivity and conductivity between the two phases play a critical role in deciding the magnitude of deformation and orientation of the compound droplet. The electric field can be suitably applied to engender breakup of the compound

Jets in the second wind induced atomization regime are challenging to investigate experimentally and theoretically. Using droplet tracking velocimetry measurements performed far from the nozzle, this study shows the bimodal nature of the size and velocity distributions of droplets generated by such jets, at a distance of between 400 and 800 nozzle diameters. Developments from turbulence and combustion applications are used to obtain satisfying models not only for the distribution of the size and the velocity but also for their joint distribution.

An investigation shows that, counterintuitively, the splash of drops impacting with velocities of a few tens of meters per second is suppressed because the aerodynamic lift force that would cause the liquid film to separate from the substrate and to break into much finer droplets is inhibited. This occurs as a consequence of the fact that the thickness of the lamella becomes similar to the mean-free path of gas molecules.

Computer simulations show the self-transition between ordered and disordered emulsions in divergent microfluidic channels. The transition is driven by the nonlinear competition between viscous dissipation and surface tension forces as controlled by the device geometry. An unexpected route back to order is observed in the regime of large opening angles where a trend towards increasing disorder would be intuitively expected.

Precise manipulation of micro and nanosized particles has enabled investigations into various applications ranging from mechanobiology of biomolecules and cells to self-assembly of two-dimensional colloids. This work is focussed on studying the nature of a noninvasive electrothermal vortex based micro-manipulation tool called rapid electrokinetic patterning (REP). Using the equipartition method, we show that a REP trap is Hookean in nature and has an ultralow trap stiffness on the order of femtonewtons/μm. The dynamic tunability of an optically induced REP trap makes it a versatile tool for various biophysical applications.

In nature, unsaturated porous media, like soils or plant tissues, are often submitted to temperature gradients which can trigger water transport. A nanofluidic tool is employed here to measure the changes in water potential in response to temperature variations in a model geometry. Variations of -7.9 MPa/K are observed in agreement with previous measurements but which differ from a simple modeling, pointing at subtle couplings between natural convection and the Soret effect at play in the setup.

How iceberg shape affects melting is investigated in a combined experimental and numerical study of ice melting in warm salt water. Experiments show that, in contrast to previous models, melting is highly nonuniform—side melt rates can be up to 3 times larger than bottom melt rates, and melt rates vary significantly within each face. Numerical simulations reveal that vortices accelerate melting at high flow speeds, and double diffusive effects matter at low flow speeds. Improved parameterizations to incorporate nonuniform iceberg melting are proposed.

An energy model is developed to describe the linear viscous fingering (VF) phenomena from the perspective of evolution paths of energy dissipation rate. By means of the variational method, rate-altering control schemes with different scaling laws are constructed in the energy model to control whether the VF instability develops or is suppressed. Furthermore, a stable and continuous forward movement of the fluid-fluid interface is achieved through a periodic suppression scheme. The effectiveness of the energy model and all control schemes are well verified by our experiments.

The precise role of the Orr mechanism in transition of parallel shear flow is investigated. We found two transition scenarios, oblique and streak transition, in which the Orr mechanism plays a central role in triggering transition. In the oblique transition, the spanwise velocity perturbation amplified with the Orr mechanism initiates both streak amplification and breakdown, whereas in the streak transition, the role of the Orr mechanism is limited only to the streak breakdown at the late stage of transition.

The response of a side branch aperture to harmonic forcing is a key element of the feedback loop describing flow-induced aeroacoustic instability in deep cavities. We derive and validate two physics-based models which, after calibration at a given condition, predict the influence of frequency, mean flow speed, and acoustic pressure amplitude on the response. Notably, these low-order models enable robust analytical amplitude predictions of self-sustained oscillations in deep cavities under turbulent grazing flow

To aid in the recycling of ionic liquids, a method that takes advantage of capillary phenomena at small scales is presented. The phase separation is performed in a temperature gradient by the joint effects of sedimentation and thermocapillary actuation. This gives rise to a complex three-dimensional flow structure, which is quantitatively captured by our model.

The influence of the slippage phenomenon over the interfacial dynamics of a millimeter-order fluid drop exposed to surface acoustic wave atomization is numerically studied under hydrophilic conditions. Implementation of the Navier-slip model into the governing hydrodynamic equations yields an interfacial evolution equation. The solution suggests that slippage at the wall constitutes a valuable phenomenon to manipulate the parent drop geometric aspect ratio and consequently the characteristic aerosol size during the atomization process.

A theoretical and experimental study shows that the coupled effect of interfaces and pulsatile forcing of fluid slugs, at microscales, allows for controlling the magnitude of flow velocity by simply changing the frequency of the driving. This behavior, which at low frequencies, is radically different from that of a single fluid, could potentially be exploited in organ-on-a-chip devices to tune the physiological mechanical conditions of cells, or to study how cells would respond to various nonphysiological stresses.

The marginal regeneration process responsible for foam film drainage is revisited. It is shown that a horizontal, micron thick, foam film in contact with a meniscus destabilizes and that patches of thinner film grow along the meniscus, forming a very regular pattern.

The laminar flow in a weakly bent pipe exhibits very rich dynamical properties. The flow is stationary, periodic or chaotic depending on one control parameter. A very practical simplification inspired by Dean is capable of reproducing this behavior with remarkable accuracy.

The mechanical oscillations of a miniaturized resonator generate viscous oscillatory nanoflows in the surrounding fluid. As a result, the fluid presents an effective added mass and damping to the resonator, which is commonly predicted by a two-dimensional flow model. Here, the limitations to the two-dimensional model are examined when a substrate and axial flow are present. Results from experiments and three-dimensional finite element models are presented to illustrate where and why the two-dimensional flow models break down.

Experiments, i.e. micro-PIV and flow visualization, and direct numerical simulations, are used jointly to investigate how stratification affects mixing and chemical reaction in a T-shaped microreactor fed with two miscible liquids exhibiting a small density difference. The work analyzes the dependence of the degree of mixing on the Reynolds number and correlates the reaction yield with the Damköhler number to help to devise strategies for the practical operation of microreactors with fluids of practical interest.

Simultaneous applications of particle image velocimetry and planar laser-induced fluorescence in a refractive index matched facility are used to visualize the phase distribution and measure velocity in an immiscible low Reynolds number buoyant oil jet injected into water. Initially, mixing involves entrainment of water ligaments inward and oil ligaments outward, followed by phase fragmentation into blobs and then droplets. Phase-based conditioning reveals spatially varying discrepancies between the velocity and all Reynolds stress components in the oil and water phases. Trends are attributed to intermittency and differences in turbulence production rate.

How anisotropic particles rotate and orient in a flow depends on the hydrodynamic torque they experience. The torque acting on a small spheroid in a uniform flow is computed by numerically solving the Navier-Stokes equations. Overall, the numerical results provide a justification of recent theories for the orientation statistics of ice crystals settling in cold clouds.

Three-phase turbulent flows are crucial in a number of practical problems involving particulate abatement, from scavenging of air pollutants by precipitation to scrubbing processes. These flows are extremely rich in physics and challenging to simulate. Through direct numerical simulations of turbulence, coupled with a phase field interface description and Lagrangian particle tracking, the capture dynamics of small solid particles by large deformable drops is examined in detail. The role of the topologically changing drop interface in connection with the local turbulence structure is highlighted, and a simple transport model for predicting capture efficiency is derived.

Droplets spontaneously move when they are placed at the tip of a cone surface. Using three-dimensionally-printed structures, an experimental exploration of a large panel of configurations regarding the aperture angle of the cone finds evidence for a change of the droplet geometry while moving along the conical fiber—from barrel to clamshell shape. The position of this geometrical transition is estimated and two models are proposed to describe the motion of the barrel and the clamshell droplets.

An active inline mixer, called Rotating Arc-Wall mixer (RAW), suitable for flows at low Reynolds number and high Péclet number, is studied. The forcing protocol, imposed by three rotating circular arc-walls, is time periodic. We use simple phenomenological arguments to estimate heuristically the mixing efficiency with two nondimensional control parameters: the frequency of the forcing protocol, and the strength of the cross flow relative to the primary flow. The validity and limitations of the proposed mixing conditions are explained by the transport mechanisms in the mixer, and the beneficial role of chaotic advection for mixing is highlighted.

We study the fragmentation of deformable and brittle fibers in the inertial range of turbulence using laboratory experiments and numerical simulations. The fragmentation process is shown to be limited at small scales by a physical cut-off length due to fluid-structure interactions of the object with turbulence, and thus independent of the fiber brittleness. This scenario, comprehensively modeled by an evolution equation, leads to the accumulation of fragments slightly longer than the cut-off scale, as smaller fragments are too short to be deformed and broken by the turbulence. This result may improve our understanding of microplastic formation in the ocean.

This work focuses the simulation of incompressible flat-plate boundary layers in streamwise periodic domains under our proposed homogenized Navier-Stokes equations. These simulations are conducted without needing multiple stations while also achieving statistical stationarity. The global quantities and profiles obtained via this method are comparable to those obtained via spatially developing simulations. These results were obtained at a computational cost approximately an order of magnitude lower than that of the spatially developing simulations.

The governing equations for mean flow and available turbulent databases are used to derive a model for the mean shear stress in turbulent boundary layers. The model requires mean wall-normal velocity, for which a simple and compact fit is derived using existing data and scaling arguments. The model shows good agreement with available data over a range of Reynolds number.

The turbulence structure in massively separated supersonic flows is highly complex and dominated by three-dimensional turbulence mechanisms. Analysis of large ensembles of tomographic particle image velocimetry measurements acquired in the near-wake of a Mach 2.49 blunt-based cylinder wake reveals multiple coherent high-energy turbulence mechanisms. These mechanisms have strong contributions to the turbulent kinetic energy, and several of them appear consistent with past computational simulations of this flow.

Symmetry breaking in laminar flows is well known in the transition to turbulence scenario. Here we consider the breaking of a remaining symmetry in an already turbulent flow, as in the transition from a two-dimensional turbulent flow shown in the figure to a three-dimensional turbulent flow. We show that such cases have critical exponents that differ from the mean-field predictions and our results indicate the possible existence of a new class of out-of-equilibrium phase transition controlled by the multiplicative turbulent noise.

We establish subgrid-scale (SGS) characteristics of a finite volume vorticity-transport-based approach for large-eddy simulations. Modified equation analysis indicates that dissipation can be controlled locally via nonlinear limiting of the gradient employed for the vorticity reconstruction. The enstrophy budget highlights the remarkable ability of the truncation terms to mimic the true SGS dissipation and diffusion. Numerical dissipation in under-resolved simulations can be characterized by diffusion terms discovered in the modified equation analysis.

A physics informed approach is applied to neural networks for subgrid-scale scalar flux modeling. We show that several invariances of the scalar transport equation are not enforced by existing parametric models, which reduce their interpretability and question their application. A new architecture embedding these invariances as hard and soft constraints is proposed. Through different flow configurations, we show that the proposed constraints increase both the performances and the generalization capabilities of the model.

In this work, a new method for computing the boundary layer thickness is proposed by reconstructing an approximate inviscid solution based on the Bernoulli equation. The viscous streamwise velocity profile $U[y]$ agrees with this inviscid reconstruction $U_I[y]$ outside the boundary layer, and the solutions diverge from each other at the boundary layer edge. The boundary layer thickness is readily determined by examining the discrepancy between these profiles. Extensive validation suggests that the present method is more robust and more widely applicable than existing methods.

We analyze the vector nulls of velocity, Lagrangian acceleration, and vorticity, coming from direct numerical simulations of forced homogeneous isotropic turbulence. We study the scaling of clusters of these null points and compare them with datasets of point inertial particles with different Stokes numbers. We find that inertial particles display preferential concentration with a degree of clustering that resembles some properties of the clustering of the Lagrangian acceleration nulls.

The complexity of a shock-wave/turbulent boundary layer interaction (SWTBLI) in the presence of sidewalls is investigated both qualitatively and quantitively in this work. Additional spanwise no-slip conditions led to the occurrence of secondary flows, which were not observed in the quasi-two-dimensional cases. Statistical analysis revealed asymmetric back-and-forth motion of the interaction across the midspan, possibly caused by the variation in the instantaneous size of the sidewall separated zones. Coupling between corner and centerline interactions was also observed as a result of higher confinement ratio.

The study of vortex rings formed behind accelerating bluff bodies is necessary to reduce their harmful effects or harvest their potential. The scaling of the vortex growth is usually performed by comparing the vortex circulation with the body size and velocity. This study investigates various kinematics and conical body geometries to propose a more robust scaling based on the vortex circulation, energy, and self-induced velocity.

We investigate discrepancies between the two-dimensional cylinder flow and a quasilinear model (i.e.~resolvent analysis) from an energy transfer perspective at Re=100. The energy balances achieved by the true flow are characterized and compared to predictions from resolvent analysis. The impact of the neglected nonlinear energy transfer on the resolvent mode shapes is clarified by analyzing the spatial distribution of the energy transfer mechanisms. This provides insights into the extent to which resolvent analysis correctly models energy transfer mechanisms, which is essential for understanding the limitations of quasilinear approximations and improving the modeling of nonlinear flows.

The effect of dynamic spanwise bending on the vortex dynamics of an accelerating flat plate is studied with experiments and numerical simulations. A flat plate, held at an angle of attack of 30 degrees, is accelerated from rest to Reynolds number 2400. It was bent dynamically along the span in a controlled manner with a bending ratio of 0.65. We find that a dynamic spanwise bending induces a change in the effective shear layer velocity along the span’s bent part and creates spanwise vorticity convection. As a result, the growth of circulation in the leading-edge-vortex gets delayed along the bent part, and the final circulation is smaller than the no bending case.

A unidirectional surface gravity wave over a flat bottom topography causes a unidirectional Stokes drift of floating particles. However, rippled bottom topography can resonantly interact with incident surface waves and generate reflected waves. This introduces a backward drift component that counters the unidirectional forward motion of the floating particles. Hence rippled bottom topography can act as a non-surface-invasive particle trap or reflector and thus help in mitigating ocean pollution.

Coupled triads (two sets of resonant triads with one member in common) can arise in linearly stratified fluids. Such coupling may induce modulation instabilities which are otherwise absent for component triads in isolation themselves. Long wavelength instabilities will imply the occurrence of internal rogue waves which may attain amplitudes much larger than their surface wave counterparts.

Holmboe waves are long-lived traveling waves commonly found in environmental stratified shear flows. Here we study their finite-amplitude properties in the nonlinear but nonturbulent regime, with a weakly nonlinear temporal stability analysis. Using a versatile amplitude expansion method, we analyze supercritical bifurcation diagrams both in Reynolds number and Richardson number, transient phase portraits, and the vertical structures of all components modes up to third order. We believe these results provide a basis for a future fully nonlinear analysis of the Holmboe dynamical system.