Molecular dynamics simulations are used to investigate the effective slip boundary condition for a simple fluid flowing over surfaces with one-dimensional sinusoidal roughness in the Wenzel state. The effective slip length is calculated as a function of the corrugation amplitude for flows along two principal orientations: transverse and longitudinal to the corrugation. Different atomic configurations, bent and stepped, are examined for strong and weak wall-fluid interactions and high and low wall densities. Molecular dynamics results for sparse bent surfaces quantitatively agree with continuum hydrodynamic predictions with a constant local slip length. Increasing the roughness amplitude reduces the effective slip length and the reduction is larger for transverse flow than longitudinal flow. Atomic effects become important for dense surfaces, because the local slip length varies with the local curvature and atomic spacing along the wall. These effects can be captured by applying a spatially varying boundary condition to the Navier-Stokes equations. Results for stepped surfaces are qualitatively different than continuum predictions, with the effect of corrugation rising linearly with corrugation amplitude rather than quadratically. There is an increased drag for transverse flow that is proportional to the density of step edges and lowers the slip length. Edges tend to increase the slip length for longitudinal flow because of order induced along the edges.

Transient growth of optimal disturbances with a turbulent mean velocity profile in a channel is investigated for Reynolds numbers, based on the wall-shear velocity and channel half height, of ${\mathrm{Re}}_{\tau }=180\sim 10000$. We consider optimal disturbances within near-wall regions ($0<y^{+}\le y_c^{+}$) by suppressing disturbances at $y^{+}>y_c^{+}$. The most amplified disturbances are streamwise velocity streaks induced by streamwise rolls. The wavelength and the growth time of these constrained optimal disturbances normalized in viscous wall units are nearly independent of ${\mathrm{Re}}_{\tau }$ but depend on the cutoff location $y_c^{+}$. The optimal disturbance corresponding to the cutoff location $y_c^{+}=40$, which is roughly the edge of the buffer layer, shows very similar characteristics to those of near-wall turbulence structures observed in turbulent channel flows, thus suggesting that the commonly observed turbulence structures are indeed the optimal disturbance within the buffer layer. The choice of this particular cutoff location, $y_c^{+}=40$, is justified from consideration of the shear rate parameter, $S^{*}=S{q}^2/\epsilon$, which is a measure of whether nonlinearity of turbulence can be neglected.

We study the origins of anomalous dispersion in heterogeneous porous media in terms of the medium and flow properties. To identify and quantify the heterogeneity controls, we focus on porous media which are organized in assemblies of equally sized conductive inclusions embedded in a constant conductivity matrix. We study the behavior of particle arrival times for different conductivity distributions and link the statistical medium characteristics to large-scale transport using a continuous time random walk (CTRW) approach. The CTRW models particle motion as a sequence of transitions in space and time. We derive an explicit map of the conductivity onto the transition time distribution. The derived CTRW model predicts solute transport based on the conductivity distribution and the characteristic heterogeneity length. In this way, heavy tails in solute arrival times and anomalous particle dispersion as measured by the centered mean square displacement are directly related to the medium properties. These findings shed light on the mechanisms of anomalous dispersion in heterogeneous porous media, and provide a basis for the predictive modeling of large-scale transport.

Classic models of fish schools and flying formations of birds are built on the hypothesis that the preferred locations of an individual are determined by the flow left by its upstream neighbor. Lighthill posited that arrangements may in fact emerge passively from hydro- or aerodynamic interactions, drawing an analogy to the formation of crystals by intermolecular forces. Here, we carry out physical experiments aimed at testing the Lighthill conjecture and find that self-propelled flapping wings spontaneously assume one of multiple arrangements due to flow interactions. Wings in a tandem pair select the same forward speed, which tends to be faster than a single wing, while maintaining a separation distance that is an integer multiple of the wavelength traced out by each body. When perturbed, these locomotors robustly return to the same arrangement, and direct hydrodynamic force measurements reveal springlike restoring forces that maintain group cohesion. We also use these data to construct an interaction potential, showing how the observed positions of the follower correspond to stable wells in an energy landscape. Flow visualization and vortex-based theoretical models reveal coherent interactions in which the follower surfs on the periodic wake left by the leader. These results indicate that, for the high-Reynolds-number flows characteristic of schools and flocks, collective locomotion at enhanced speed and in orderly formations can emerge from flow interactions alone. If true for larger groups, then the view of collectives as ordered states of matter may prove to be a useful analogy.

Understanding the recovery of gas from reservoirs featuring pervasive nanopores is essential for effective shale gas extraction. Classical theories cannot accurately predict such gas recovery and many experimental observations are not well understood. Here we report molecular simulations of the recovery of gas from single nanopores, explicitly taking into account molecular gas-wall interactions. We show that, in very narrow pores, the strong gas-wall interactions are essential in determining the gas recovery behavior both quantitatively and qualitatively. These interactions cause the total diffusion coefficients of the gas molecules in nanopores to be smaller than those predicted by kinetic theories, hence slowing down the rate of gas recovery. These interactions also lead to significant adsorption of gas molecules on the pore walls. Because of the desorption of these gas molecules during gas recovery, the gas recovery from the nanopore does not exhibit the usual diffusive scaling law (i.e., the accumulative recovery scales as $R\sim t^{1/2}$) but follows a superdiffusive scaling law $R\sim t^n$ ($n>0.5$), which is similar to that observed in some field experiments. For the system studied here, the superdiffusive gas recovery scaling law can be captured well by continuum models in which the gas adsorption and desorption from pore walls are taken into account using the Langmuir model.

A largely unexplored type of hydrodynamic instability is examined: long-time algebraic growth. Such growth is possible when the dispersion relation extracted from classical stability analysis indicates neutral stability. A physically motivated class of partial differential equations that describes the response of a system to disturbances is examined. Specifically, the propagation characteristics of the response are examined in the context of spatiotemporal stability theory. Morphological differences are identified between system responses that exhibit algebraic growth and the more typical case of exponential growth. One key attribute of predicted algebraically growing solutions is the prevalence of transient growth in almost all of the response, with the long-time growth occurring asymptotically at precisely one wave speed.

The settling of heavy spherical particles in a column of quiescent fluid is investigated. The performed experiments cover a range of Galileo numbers $\left(110\le \text{Ga}\le 310\right)$ for a fixed density ratio of $\mathrm{\Gamma }={\rho }_p/{\rho }_f=2.5$. In this regime the particles are known to show a variety of motions [Jenny, Dušek, and Bouchet, Instabilities and transition of a sphere falling or ascending freely in a Newtonian fluid, J. Fluid Mech. 508, 201 (2004)]. It is known that the wake undergoes several transitions for increasing $\text{Ga}$ resulting in particle motions that are successively vertical, oblique, oblique oscillating, and finally chaotic. Not only does this change the trajectory of single, isolated, settling particles, but it also changes the dynamics of a swarm of particles as collective effects become important even for dilute suspensions with volume fraction up to ${\mathrm{\Phi }}_V=O\left({10}^{-3}\right)$, which are investigated in this work. Multicamera recordings of settling particles are recorded and tracked over time in three dimensions. A variety of analyses are performed and show a strong clustering behavior. The distribution of the cell areas of the Voronoï tessellation in the horizontal plane is compared to that of a random distribution of particles and shows clear clustering. Moreover, a negative correlation was found between the Voronoï area and the particle velocity; clustered particles fall faster. In addition, the angle between adjacent particles and the vertical is calculated and compared to a homogeneous distribution of particles, clear evidence of vertical alignment of particles is found. The experimental findings are compared to simulations.

An isolated wind turbine and a very large wind farm are introduced into large-eddy simulations of an atmospheric boundary layer. The atmospheric flow is forced with a constant geostrophic wind and a time-varying surface temperature extracted from a selected period of the CASES-99 field experiment. A control volume approach is used to directly compare the transfer of mean kinetic energy around a characteristic wind turbine throughout a diurnal cycle considering both scenarios. For the very large wind farm case, results illustrate that the recovery of mean kinetic energy around a wind turbine is dominated by the vertical flux, regardless of atmospheric stratification. Contrarily, for an isolated wind turbine, the recovery is dependent on the background atmospheric stratification and it is produced by a combination of advection, vertical flux, and pressure redistribution. The analysis also illustrates that during the unstable stratification periods vertical entrainment of mean kinetic energy dominates, whereas during the stable regime horizontal entrainment is predominant. Finally, it is observed that in both scenarios, the single wind turbine and the large wind farm cases, turbulent mixing is driven by the background convective stratification during the unstable period and by the effect of the wind turbine during the stable regime.

The near wake of wind turbines is characterized by the presence of the hub vortex, which is a coherent vorticity structure generated from the interaction between the root vortices and the boundary layer evolving over the turbine nacelle. By moving downstream, the hub vortex undergoes an instability with growth rate, azimuthal and axial wavenumbers determined by the characteristics of the incoming wind and turbine aerodynamics. Thus, a large variability of the hub vortex instability is expected for wind energy applications with consequent effects on wake downstream evolution, wake interactions within a wind farm, power production, and fatigue loads on turbines invested by wakes generated upstream. In order to predict characteristics of the hub vortex instability for different operating conditions, linear stability analysis is carried out by considering different statistics of the incoming wind turbulence, thrust coefficient, tip speed ratio, and blade lift distribution of a wind turbine. Axial and azimuthal wake velocity fields are modeled through Carton-McWilliams velocity profiles by mimicking the presence of the hub vortex, helicoidal tip vortices, and matching the wind turbine thrust coefficient predicted through the actuator disk model. The linear stability analysis shows that hub vortex instability is strongly affected by the wind turbine loading conditions, and specifically it is promoted by a larger thrust coefficient. A higher load of the wind turbines produces an enhanced axial velocity deficit and, in turn, higher shear in the radial direction of the streamwise velocity. The axial velocity shear within the turbine wake is also the main physical mechanism promoting the hub vortex instability when varying the lift distribution over the blade span for a specific loading condition. Cases with a larger velocity deficit in proximity of the wake center and less aerodynamic load towards the blade tip result to be more unstable. Moreover, wake swirl promotes hub vortex instability, and it can also affect the azimuthal wave number of the most unstable mode. Finally, higher Reynolds stresses and turbulent eddy viscosity decrease both growth rate and azimuthal wave number of the most unstable mode.

We analyze the effect of the Basset history force on the sedimentation of nearly neutrally buoyant particles, exemplified by marine snow, in a three-dimensional turbulent flow. Particles are characterized by Stokes numbers much smaller than unity, and still water settling velocities, measured in units of the Kolmogorov velocity, of order one. The presence of the history force in the Maxey-Riley equation leads to individual trajectories which differ strongly from the dynamics of both inertial particles without this force and ideal settling tracers. The main effect of the history force is an extraordinary slow, power-law type convergence to an asymptotic settling velocity of the center of mass, which is found numerically to be the settling velocity in still fluid. The spatial extension of the ensemble grows diffusively after an initial ballistic growth lasting up to circa one large eddy turnover time. We demonstrate that the settling of the center of mass for such light aggregates is best approximated by the settling dynamics in still fluid found with the history force, on top of which fluctuations appear which follow very closely those of the turbulent velocity field.

Observations are presented to show that in an adverse pressure gradient boundary layer, beneath free-stream turbulence, the interaction between Klebanoff streaks and naturally arising instability waves leads to helical disturbances which break down to form turbulent spots. This occurs under low to moderate levels, 1%–2%, of free-stream turbulence. At high levels of free-stream turbulence, conventional bypass mechanisms are seen. The helical structures are clearly identifiable in visualizations of isosurfaces of streamwise perturbation velocity. A direct numerical simulation also was performed in zero pressure gradient, with a time-periodic Tollmien-Schlichting wave eigenfunction at the inlet. Again, under a moderate level of free-stream turbulence, helices were observed, and found to trigger transition. Their wave speed is on the order of $\frac{1}{2}{U}_{\infty }$, so helical breakdown can be viewed as a type of inner mode, secondary instability.

We present a direct numerical simulation (DNS) data set for a statistically axisymmetric turbulent jet, plume, and forced plume in a domain of size $40r_0\times 40r_0\times 60r_0$, where $r_0$ is the source diameter. The data set supports the validity of the Priestley-Ball entrainment model in unstratified environments (excluding the region near the source) [Priestley and Ball, Q. J. R. Meteor. Soc. 81, 144 (1955)], which is corroborated further by the Wang-Law and Ezzamel et al. experimental data sets [Wang and Law, J. Fluid Mech. 459, 397 (2002); Ezzamel et al., J. Fluid Mech. 765, 576 (2015)], the latter being corrected for a small but influential coflow that affected the statistics. We show that the second-order turbulence statistics in the core region of the jet and the plume are practically indistinguishable from each other, although there are significant differences near the plume edge. The DNS data indicate that the turbulent Prandtl number is about 0.7 for both jets and plumes. For plumes, this value is a result of the difference in the ratio of the radial turbulent transport of radial momentum and buoyancy. For jets, however, the value originates from a different spread of the buoyancy and velocity profiles, in spite of the fact that the ratio of radial turbulent transport terms is approximately unity. The DNS data do not show any evidence of similarity drift associated with gradual variations in the ratio of buoyancy profile to velocity profile widths.

Superhydrophobic surfaces offer many industrial advantages such as drag reduction and self-cleaning behavior as long as the liquid remains suspended above the composite solid/gas interface (Cassie state). These advantages are hindered when liquid penetrates the gas cavities (Wenzel state), and this is commonly referred to as impalement. Current efforts to drive impaled liquid out of, or dewet, the cavities—such as boiling or mechanical vibrations—are locally disruptive to the flow. In this work, we reveal that passive dewetting is possible during droplet impingement on micropillar substrates under the right thermodynamical conditions. Exploration included substrates with pillar-to-pillar spacing of 8 and $16\mu \mathrm{m}$, pillar diameters of 3 and $6\mu \mathrm{m}$, and pillar heights of 4 to $8\mu \mathrm{m}$ and 8 to $18\mu \mathrm{m}$, respectively. The substrate temperature range considered was $23<T_s<96{}^{\circ }\mathrm{C}$. Results revealed that dewetting increases with increasing pillar height and increasing substrate temperature. Two hypotheses for the driving mechanism are formulated based on evaporation and surface energy. First-order models are consequently constructed, revealing that dewetting does not occur due to evaporation, but is caused by surface energy gradients at the interface. Dissipation in the flow is taken into account due to hydrodynamic and nonhydrodynamic mechanisms; the latter is found to dominate resistance.

Immiscible fluid displacement with average front velocities in the capillary-dominated regime is studied in a transparent Hele-Shaw cell with cylindrical posts. Employing various combinations of fluids and wall materials allows us to cover a range of advancing contact angles ${46}^{\circ }\le {\theta }_a\le {180}^{\circ }$ of the invading fluid in our experiments. In parallel, we study the displacement process in particle-based simulations that account for wall wettability. Considering the same arrangement of posts in experiments and simulation, we find a consistent crossover between stable interfacial displacement at ${\theta }_a\lesssim {80}^{\circ }$ and capillary fingering at high contact angles ${\theta }_a\gtrsim {120}^{\circ }$. The position of the crossover is quantified through the evolution of the interface length and the final saturation of the displaced fluid. A statistical analysis of the local displacement processes demonstrates that the shape evolution of the fluid front is governed by local instabilities as proposed by Cieplak and Robbins for a quasistatic interfacial displacement [Cieplak and Robbins, Phys. Rev. Lett. 60, 2042 (1988)]. The regime of stable front advances coincides with a corresponding region of contact angles where cooperative interfacial instabilities prevail. Capillary fingering, however, is observed only for large ${\theta }_a$, where noncooperative instabilities dominate the invasion process.

We investigate electroconvection and its impact on ion transport in a model system comprised of an ion-selective membrane, an aqueous electrolyte, and an external electric field applied normal to the membrane. We develop a direct numerical simulation code to solve the governing Poisson-Nernst-Planck and Navier-Stokes equations in three dimensions using a specialized parallel numerical algorithm and sufficient resolution to capture the high frequency and high wavenumber physics. We show a comprehensive statistical analysis of the transport phenomena in the highly chaotic regime. Qualitative and quantitative comparisons of two-dimensional (2D) and 3D simulations include prediction of the mean concentration fields as well as the spectra of concentration, charge density, and velocity signals. Our analyses reveal a significant quantitative difference between 2D and 3D electroconvection. Furthermore, we show that high-intensity yet short-lived current density hot spots appear randomly on the membrane surface, contributing significantly to the mean current density. By examining cross correlations between current density on the membrane and other field quantities we explore the physical mechanisms leading to current hot spots. We also present analysis of transport fluxes in the context of ensemble-averaged equations. Our analysis reveals that in the highly chaotic regime the mixing layer (ML), which spans the majority of the domain extent, is governed by advective fluctuations. Furthermore, we show that in the ML the mean electromigration fluxes cancel out for positive and negative ions, indicating that the mean transport of total salt content within the ML can be represented via the electroneutral approximation. Finally, we present an assessment of the importance of different length scales in enhancing transport by computing the cross covariance of concentration and velocity fluctuations in the wavenumber space. Our analysis indicates that in the majority of the domain the large scales contribute most significantly to transport, while the effects of small scales become more appreciable in regions very near the membrane.

Relative flow between granular material and gas can create phenomena in which particles behave like a liquid with bubbles rising through them. In this paper, magnetic resonance imaging is used to measure the velocities of the gas and solid phases in a bubbling fluidized bed. Comparison with theory shows that the average velocity of gas through the interstices between particles is predicted correctly by classic analytical theory. Experiments were also used to validate predictions from computer simulations of gas and solid motion. The experiments show a wide distribution of gas velocities in both bubbling and emulsion regions, providing a different direction for computational and analytical theory.

Particle image velocimetry is conducted in the near field of two distinct wall-mounted trips for the artificial generation of a high Reynolds number turbulent boundary layer. The first of these trips consists of high aspect ratio obstacles, which are supposed to minimize the influence of their wakes on the near-wall region, contrasting with low aspect ratio trips, which would enhance this influence. A comprehensive study involving flow description, turbulent-nonturbulent interface detection, a low-order model description of the flow and an exploration of the influence of the wake in the near-wall region is conducted and two different mechanisms are clearly identified and described. First, high aspect ratio trips generate a wall-driven mechanism whose characteristics are a thinner, sharper, and less tortuous turbulent-nonturbulent interface and a reduced influence of the trips' wake in the near-wall region. Second, low aspect ratio trips generate a wake-driven mechanisms in which their turbulent-nonturbulent interface is thicker, less sharply defined, and with a higher tortuosity and the detached wake of the obstacles presents a significant influence on the near-wall region. Study of the low-order modeling of the flow field suggests that these two mechanisms may not be exclusive to the particular geometries tested in the present study but, on the contrary, can be explained based on the predominant flow features. In particular, the distinction of these two mechanisms can explain some of the trends that have appeared in the literature in the past decades.

It is now well established that nearby beating pairs of eukaryotic flagella or cilia typically synchronize in phase. A substantial body of evidence supports the hypothesis that hydrodynamic coupling between the active filaments, combined with waveform compliance, provides a robust mechanism for synchrony. This elastohydrodynamic mechanism has been incorporated into bead-spring models in which the beating flagella are represented by microspheres tethered by radial springs as they are driven about orbits by internal forces. While these low-dimensional models reproduce the phenomenon of synchrony, their parameters are not readily relatable to those of the filaments they represent. More realistic models, which reflect the underlying elasticity of the axonemes and the active force generation, take the form of fourth-order nonlinear partial differential equations (PDEs). While computational studies have shown the occurrence of synchrony, the effects of hydrodynamic coupling between nearby filaments governed by such continuum models have been examined theoretically only in the regime of interflagellar distances $d$ large compared to flagellar length $L$. Yet in many biological situations $d/L\ll 1$. Here we present an asymptotic analysis of the hydrodynamic coupling between two extended filaments in the regime $d/L\ll 1$ and find that the form of the coupling is independent of the microscopic details of the internal forces that govern the motion of the individual filaments. The analysis is analogous to that yielding the localized induction approximation for vortex filament motion, extended to the case of mutual induction. In order to understand how the elastohydrodynamic coupling mechanism leads to synchrony of extended objects, we introduce a heuristic model of flagellar beating. The model takes the form of a single fourth-order nonlinear PDE whose form is derived from symmetry considerations, the physics of elasticity, and the overdamped nature of the dynamics. Analytical and numerical studies of this model illustrate how synchrony between a pair of filaments is achieved through the asymptotic coupling.

We study fully three-dimensional droplets that slide down an incline by employing a thin-film equation that accounts for capillarity, wettability, and a lateral driving force in small-gradient (or long-wave) approximation. In particular, we focus on qualitative changes in the morphology and behavior of stationary sliding drops. We employ the inclination angle of the substrate as control parameter and use continuation techniques to analyze for several fixed droplet sizes the bifurcation diagram of stationary droplets, their linear stability, and relevant eigenmodes. The obtained predictions on existence ranges and instabilities are tested via direct numerical simulations that are also used to investigate a branch of time-periodic behavior (corresponding to repeated breakup-coalescence cycles, where the breakup is also denoted as pearling) which emerges at a global instability, the related hysteresis in behavior, and a period-doubling cascade. The nontrivial oscillatory behavior close to a Hopf bifurcation of drops with a finite-length tail is also studied. Finally, it is shown that the main features of the bifurcation diagram follow scaling laws over several decades of the droplet size.