As part of the response efforts that followed the Deepwater Horizon oil spill event, chemical dispersants were applied at the ocean surface and at the wellhead to increase biodegradation rates and reduce the environmental impact of the spill. Among other factors, the effectiveness of the application hinges on how it modifies complex fluid mechanical transport processes. The breakup of surface slicks and the vertical dilution of oil in the water column depends on the transport of oil droplets by turbulence in the ocean mixed layer. The trapping of oil deep in the water column results from the complex dynamics of multiphase plumes rising in the stratified ocean. We use a framework based on multiscale coupled computational domains to simulate deep-water blowouts that accurately represents these complex processes, tracking the oil from the wellhead to its transport in the ocean mixed layer. Simulation results show that dispersant application at the wellhead can be effective in trapping the oil in deep-water intrusions. For the conditions simulated here, surface application of the dispersant has important effects on the oil transport: after about 40 h, the mean advection velocity of the oil plume is reduced by a factor of four and the horizontal diffusivity is increased by a factor of 10.

We performed a numerical study to train smart inertial particles to target specific flow regions with high vorticity through the use of reinforcement learning algorithms. The particles are able to actively change their size to modify their inertia and density. In short, using local measurements of the flow vorticity, the smart particle explores the interplay between its choices of size and its dynamical behavior in the flow environment. This allows it to accumulate experience and learn approximately optimal strategies of how to modulate its size in order to reach the target high-vorticity regions. We consider flows with different complexities: a two-dimensional stationary Taylor-Green-like configuration, a two-dimensional time-dependent flow, and finally a three-dimensional flow given by the stationary Arnold-Beltrami-Childress (ABC) helical flow. We show that smart particles are able to learn how to reach extremely intense vortical structures in all the tackled cases.

The classical energy cascade in turbulence as described by Richardson and Kolmogorov is predominantly a conjecture relying on the locality of interactions between scales of turbulence. This picture is generally accepted and assumes that energy and enstrophy transfers occur between neighboring scales of turbulence and that vortex stretching plays a major role in the dynamics of this energy cascade. Direct numerical simulation data for ${\text{Re}}_{\lambda }$ ranging from 37 to 1131 is used to gather evidence for the cascade by investigating the energy and enstrophy fluxes between scales and the interplay between vorticity at one scale and strain at an adjacent scale. This is achieved by using a bandpass filter to educe the turbulent structures at various length scales, allowing one to determine the fluxes between these scales and to interrogate the role of nonlocal (in physical space) vortex stretching. It is shown that the structures of a length scale $L$ mostly transfer their energy to structures of size $0.3L$ and that most of the enstrophy flux goes from structures of scale $L$ to $0.3L$. Furthermore, vortical structures of a length scale $L_{\omega }$ are stretched mostly by straining structures of size $3L_{\omega }$ to $5L_{\omega }$, and the stretching by eddies of sizes larger than $10L_{\omega }$ is negligible. The stretching is dominated by the most extensive principal strain rate of the straining structures. These observations are found to be independent of ${\text{Re}}_{\lambda }$ for the range investigated in this study. These results provide strong evidence for the classical view of an energy cascade transferring energy from large to small scales through a hierarchy of steps, each step consisting of the stretching of vortices by somewhat larger structures.

The diffusion of active microscopic organisms in complex environments plays an important role in a wide range of biological phenomena from cell colony growth to single organism transport. Here, we investigate theoretically and computationally the diffusion of a self-propelled particle (the organism) embedded in a complex medium composed of a collection of nonmotile solid particles that mimic soil or other cells. Under such conditions we find that the rotational relaxation time of the swimming direction depends on the swimming velocity and is drastically reduced compared to a pure Newtonian fluid. This leads to a dramatic increase (of several orders of magnitude) in the effective rotational diffusion coefficient of the self-propelled particles, which can lead to “self-trapping” of the active particles in such complex media. An analytical model is put forward that quantitatively captures the computational results. Our work sheds light on the role that the environment plays in the behavior of active systems and can be generalized in a straightforward fashion to understand other synthetic and biological active systems in heterogenous environments.

Direct numerical simulation of pore-scale turbulence is performed in a unit cell of a face-centered cubic lattice at three different pore Reynolds numbers (300, 500, and 1000). The pore-geometry gives rise to very low porosity resulting in rapid acceleration and deceleration of the flow in different regions. Eulerian statistics of mean velocity and turbulent kinetic energy are first described to provide a good understanding of the overall flow topology. In addition, the spatial variances and probability density functions for the instantaneous and temporal fluctuation velocities are computed to assess the higher-order statistics. The flow field is then analyzed using angular Lagrangian multiscale statistics of fluid particles to study their directional change at different timescales. Two power laws are observed for the evolution of the mean absolute angle as a function of time lag, demarking the early time and an intermediate, inertial range. The effect of the geometric confinement on the asymptotic behavior of the angular statistics is examined in detail. An asymptotic limit different than $\pi /2$ (corresponding to equidistribution of the mean angle, observed for three-dimensional isotropic turbulence with periodic boundaries) or $\frac{2}{3}\pi$ (observed for two-dimensional wall-bounded turbulence) is obtained, representing the strong effect of geometric confinement on turbulence. Besides, the probability density functions (PDFs) for the instantaneous curvature angles are computed and the normalized PDFs are fit to a Fisher distribution. Furthermore, a Monte Carlo-based stochastic model is developed to predict the asymptotic curvature angle.

The present contribution investigates the mixing of a passive scalar by a homogeneous bidimensional bubble swarm rising at high Reynolds number in a liquid initially at rest. Mixing experiments are performed in a Hele-Shaw cell for gas volume fractions $\alpha$ ranging from 3.0% to $14.0\%$. A weakly diffusive passive dye is injected within the swarm, and the temporal evolution of the spatial distribution of concentration is measured. The vertical distribution of concentration shows an upward propagation and a spreading due to the mixing induced by the unsteady open wakes of the bubbles. A one-dimensional large-scale model involving an intermittent and convective mechanism has been developed to describe the global evolution of the concentration distribution in the vertical direction. Based on experimental observations, it assumes that each bubble catches a given volume of fluid $V_t$ in its wake and transports it over a certain length $L$ before releasing it. A good agreement is found between the experimental concentration profiles measured in the vertical direction and the model prediction. The comparison between the model and the experiments allows the determination of the transported volume $V_t$ and the transport length $L$ as a function of the gas volume fraction. It appears that the transported volume is related to the characteristic length of the velocity deficit at the rear of the bubble. The transport length, which is related to the correlation length of the dye patches, shows two regimes. At low gas volume fraction, it is controlled by the viscous length related to the flow damping at the walls, whereas, at higher gas volume fraction, it is limited by the distance between two successive bubbles. The mixing properties are finally characterized from the first three-order moments of the dye distribution, which are determined by means of the model. The upward propagation of the dye is shown to scale as $\alpha V$, where $V$ is the bubble rise velocity. The spreading of the concentration distribution is characterized by an effective diffusivity, which presents strong similarities with the diffusion coefficient measured in a three-dimensional bubble column [Alméras et al. J. Fluid Mech. 776, 458 (2015)]. At low gas volume fraction, it increases as $\sqrt{\alpha }$, whereas it saturates at high gas volume fraction. The dye distribution also is asymmetric with a significant skewness coefficient which slowly decreases in time. Therefore, the dye transport cannot be described as a purely diffusive process over the time required for the dye to spread over the cell.

Three-dimensional, time-dependent direct simulations of step emulsification microdevices highlight two essential mechanisms for droplet formation: first, the onset of an adverse pressure gradient driving a backflow of the continuous phase from the external reservoir to the microchannel, and second, the striction of the flowing jet which leads to its subsequent rupture. It is also shown that such a rupture is delayed and eventually suppressed by increasing the flow speed of the dispersed phase within the channel, due to the stabilizing effect of dynamic pressure. This suggests a new criterion for dripping-jetting transition, based on local values of the capillary and Weber numbers.

When two sessile drops of the same liquid touch, they merge into one drop, driven by capillarity. However, the coalescence can be delayed, or even completely stalled for a substantial period of time, when the two drops have different surface tensions, despite being perfectly miscible. A temporary state of noncoalescence arises, during which the drops move on their substrate, only connected by a thin neck between them. Existing literature covers pure liquids and mixtures with low surface activities. In this paper, we focus on the case of large surface activities, using aqueous surfactant solutions with varying concentrations. It is shown that the coalescence behavior can be classified into three regimes that occur for different surface tensions and contact angles of the droplets at initial contact. However, not all phenomenology can be predicted from surface tension contrast or contact angles alone, but strongly depends on the surfactant concentrations as well. This reveals that the merging process is not solely governed by hydrodynamics and geometry, but also depends on the molecular physics of surface adsorption.

We study experimentally the effects of a pipe axial rotation on a stratified displacement flow, using two miscible fluids of different density, in a long inclined pipe. Increasing the pipe rotation speed induces transverse mixing and results in a complete removal of the displaced fluid above a critical transition, described by $\text{Rb}\approx 5/2\pi \text{Fr}{\left(1-\text{Fr}\right)}^{-1}$, relating the Rossby number (Rb) to a modified Froude number (Fr). In addition, we quantify the variation of the leading and trailing displacement front velocities $({\widehat{V}}_f,{\widehat{V}}_t)$, as a function of the mean displacement velocity (${\widehat{V}}_0$), showing that for $\text{Rb}/\text{Fr}\gtrsim 5/2\pi$ we find ${\widehat{V}}_f\approx 1.3{\widehat{V}}_0$ and ${\widehat{V}}_t\approx 0.8{\widehat{V}}_0$. These findings offer insights to greatly improve displacement efficiency using rotational motion.

We show that a freshly sedimented granular bed settles and creeps forward over extended periods of time under an applied hydrodynamic shear stress which is below the critical value for bedload transport. The rearrangements are found to last over a timescale which is millions of times the sedimentation timescale of a grain in the fluid. Compaction occurs uniformly throughout the bed, but creep is observed to decay exponentially with depth and decreases over time. The granular volume fraction in the bed is found to increase logarithmically, saturating at the random close packing value ${\varphi }_{\text{rcp}}\approx 0.64$, while the surface roughness is observed to remain essentially unchanged. We demonstrate that an increasingly higher shear stress is required to erode the bed, after a subcritical shear is applied, which results in an increase in its volume fraction. Thus, we find that bed armoring occurs due to a deep shear-induced relaxation of the bed toward the volume fraction associated with the glass transition.

We present a computational study of the hydrodynamic coarsening in three dimensions of a critical mixture using the Cahn-Hilliard/Navier-Stokes model. The topology of the resulting intricate bicontinuous microstructure is analyzed through the principal curvatures to prove self-similar morphological evolution. We find that the self-similarity exists for both systems: isoviscous and with variable viscosity. However, the two systems have a distinct topological character. Moreover, an effective viscosity that accurately predicts the coarsening rate is proposed.

Empirical data reveal a broad variety of hull shapes among the different ship categories. We present a minimal theoretical approach to address the problem of ship hull optimization. We show that optimal hull aspect ratios result—at given load and propulsive power—from a subtle balance among wave drag, pressure drag, and skin friction. Slender hulls are more favorable in terms of wave drag and pressure drag, while bulky hulls have a smaller wetted surface for a given immersed volume, thus reducing skin friction. We compare our theoretical results to real data and discuss discrepancies in the light of hull designer constraints, such as stability and maneuvrability.

We provide a demonstration that gas-kinetic methods incorporating molecular chaos can simulate the sustained turbulence that occurs in wall-bounded turbulent shear flows. The direct simulation Monte Carlo method, a gas-kinetic molecular method that enforces molecular chaos for gas-molecule collisions, is used to simulate the minimal Couette flow at $\mathrm{Re}=500$. The resulting law of the wall, the average wall shear stress, the average kinetic energy, and the continually regenerating coherent structures all agree closely with corresponding results from direct numerical simulation of the Navier-Stokes equations. These results indicate that molecular chaos for collisions in gas-kinetic methods does not prevent development of molecular-scale long-range correlations required to form hydrodynamic-scale turbulent coherent structures.

The transient spreading of a viscous fluid beneath an elastic sheet adhered to the substrate is controlled by the dynamics at the tip where the divergence of viscous stresses necessitates the formation of a vapor tip separating the fluid front and fracture front. The model for elastic-plated currents is extended for an axisymmetric geometry with analysis showing that adhesion gives rise to the possibility of static, elastic droplets and to two dynamical regimes of spreading; viscosity dominant spreading controlled by flow of viscous fluid into the vapor tip, and adhesion dominant spreading. Constant flux experiments using clear, PDMS elastic sheets enable new, direct measurements of the vapor tip and confirm the existence of spreading regimes controlled by viscosity and adhesion. The theory and experiments thereby provide an important test coupling the dynamics of flow with elastic deformation and have implications in fluid-driven fracturing of elastic media more generally.

To elucidate the pure physics of evaporation which is free from surface effects, the pendant mode of evaporation is employed in the present study. The present study brings out the evaporation kinetics of a combined surfactant and nanoparticle colloidal system. We also segregate the contributing effects of surfactants alone, particle alone, and the combined effect of surfactant and particles in modulating the evaporation kinetics. It is observed that the rate of evaporation is a strong function of the particle concentration for nanocolloidal suspensions of particle alone and concentration of surfactant molecules up to the micellar concentration and thereafter insensitive to concentration for an aqueous surfactant solution. The combined colloidal system of nanoparticles and surfactant exhibited the maximum evaporation rate, and the rate is a strong function of the concentration of both the particle and surfactant. The theoretical classical diffusion-driven evaporation falls short of the experimentally observed evaporation rate in aqueous surfactant and colloidal solutions. Evidence of convective currents was observed in flow visualization studies in aqueous surfactant solutions, nanocolloidal solution of particle alone, and an oscillatory convective circulation in a combined surfactant-impregnated nanocolloidal solution. Thermal Marangoni and Rayleigh numbers are calculated from the theoretical examination and are found not potent enough to induce strong circulation currents in such systems from a stability map. Scaling analysis of solutal Marangoni is observed to be capable of inducing circulation from a stability map in all the systems and the enhanced thermophoretic drift and Brownian dynamics, and enhancement in the diffusion coefficient of the nanoparticles is also contributing to the enhanced evaporation rate for only nanocolloidal solutions. The oscillatory convective current arising out of two opposing driving potential enhances the evaporation rate of surfactant-impregnated nanocolloids. The present findings could reveal the effect of surfactants in tuning the evaporation rate of colloidal solutions.

Preferential concentration of inertial particles by turbulence is a well-recognized phenomenon. This study investigates how this phenomenon impacts the mean heat transfer between the fluid phase and the particle phase. Using direct numerical simulations of homogeneous and isotropic turbulent flows coupled with Lagrangian point particle tracking, we explore this phenomenon over a wide range of input parameters. Among the nine independent dimensionless numbers defining this problem, we show that the particle Stokes number, defined based on a large-eddy time, and an identified number called the heat-mixing parameter have the most significant effect on particle-to-gas heat transfer, while variation in other nondimensional numbers can be ignored. An investigation of regimes with significant particle mass loading suggests that the mean heat transfer from particles to gas is hardly affected by momentum two-way coupling. Using our numerical results, we propose an algebraic reduced-order model for heat transfer in particle-laden turbulence.

The emergence of dynamic mode decomposition (DMD) as a practical way to attempt a Koopman mode decomposition of a nonlinear partial differential equation (PDE) presents exciting prospects for identifying invariant sets and slowly decaying transient structures buried in the PDE dynamics. However, there are many subtleties in connecting DMD to Koopman analysis, and it remains unclear how realistic Koopman analysis is for complex systems such as the Navier-Stokes equations. With this as motivation, we present here a full Koopman decomposition for the velocity field in the Burgers equation by deriving explicit expressions for the Koopman modes and eigenfunctions. As far as we are aware the first time this has been done for a nonlinear PDE. The decomposition highlights the fact that different observables can require different subsets of Koopman eigenfunctions to express them, and it presents a nice example in which (i) the Koopman modes are linearly dependent and so they cannot be fit a posteriori to snapshots of the flow without knowledge of the Koopman eigenfunctions, and (ii) the Koopman eigenvalues are highly degenerate, which means that computed Koopman modes become initial-condition-dependent. As a way of illustration, we discuss the form of the Koopman expansion with various initial conditions, and we assess the capability of DMD to extract the decaying nonlinear coherent structures in run-down simulations.

We develop a nonlinear, Fourier-based analysis of the evolution of a perturbed, converging cylindrical strong shock using the approximate method of geometrical shock dynamics (GSD). This predicts that a singularity in the shock-shape geometry, corresponding to a change in Fourier-coefficient decay from exponential to algebraic, is guaranteed to form prior to the time of shock impact at the origin, for arbitrarily small, finite initial perturbation amplitude. Specifically for an azimuthally periodic Mach-number perturbation on an initially circular shock with integer mode number $q$ and amplitude proportional to $\epsilon \ll 1$, a singularity in the shock geometry forms at a mean shock radius $R_{u,c}\sim {\left(q^2\epsilon \right)}^{-1/b_1}$, where $b_1\left(\gamma \right)<0$ is a derived constant and $\gamma$ the ratio of specific heats. This requires $q^2\epsilon \ll 1, q\gg 1$. The constant of proportionality is obtained as a function of $\gamma$ and is independent of the initial shock Mach number $M_0$. Singularity formation corresponds to the transition from a smooth perturbation to a faceted polygonal form. Results are qualitatively verified by a numerical GSD comparison.

The notion of sympathetic interactions between solids immersed in fluids is ubiquitous in applied physics, and the complexity of these interactions often results in unexpected outcomes. In this paper, we study the water entry of a rigid wedge in the presence of a neutrally buoyant solid cylinder below the water surface. We combine particle image velocimetry and direct measurements to elucidate the fluid-structure interaction. While the fluid confinement from the cylinder elicits a predictable increase in the pressure close to the keel, it is also responsible for a surprising reduction in the pressure toward the pileup. Through a detailed solution based on potential flow theory, we offer an explanation for this phenomenon. Our results may find application in the study of marine vessels that maneuver in occluded waters and seabirds that plunge and dive close to rocks or ice.

A fluid droplet suspended in an extensional flow of moderate intensity may break into pieces, depending on the amplitude of the initial droplet deformation. In subcritical uniaxial extensional flow the nonbreaking base state is linearly stable, implying that only a finite-amplitude perturbation can trigger breakup. Consequently, the stable base solution is surrounded by its finite basin of attraction. The basin boundary, which separates initial droplet shapes returning to the nonbreaking base state from those becoming unstable and breaking up, is characterized using edge tracking techniques. We numerically construct the edge state, a dynamically unstable equilibrium whose stable manifold forms the basin boundary. The edge state equilibrium controls if the droplet breaks and selects a unique path towards breakup. This path physically corresponds to the well-known end-pinching mechanism. Our results thereby rationalize the dynamics observed experimentally [H. A. Stone and L. G. Leal, J. Fluid Mech. 206, 223 (1989)].