The short-term transient falling dynamics of a dripping water drop in quiescent air has been investigated through both simulation and experiment. A representative case with a low inflow rate in the dripping regime is considered. The focus is on the short-term behavior and the time range considered covers about eight dominant second-mode oscillations of the drop after it is formed. Due to the small fluid inertia at the inlet, the growth of the drop is quasistatic and is well captured by the static pendant drop theory. Nevertheless, it is demonstrated that the pinching dynamics and the resulting postformation state of the drop trigger a nonlinear oscillation when the drop falls. The initial shape of the drop when it is just formed is decomposed into spherical harmonic modes. The initial mode amplitudes, characterized by the Fourier-Legendre coefficients, are found to be finite for up to the tenth mode. The pinching dynamics such as interface overturning introduces small-scale variation on the drop contour, which in turn contributes to the finite amplitudes of the higher-order modes. Furthermore, the initial kinetic energy when the droplet is just formed is as important as the initial surface energy contained in the drop shape, and is found to amplify the initial oscillation amplitude and to induce a phase shift in the oscillation of all the modes. By incorporating both the initial surface and kinetic energy, the linear model for a free drop oscillation yields very good predictions for the second and third modes. The mode amplitude spectra show both the primary frequencies that are consistent with the Lamb's theory and the secondary frequencies arising from different modes due to nonlinear intermode coupling. Moreover, it is worth to noting that the nonlinear effect is most profound for the fourth mode owing to its resonant coupling with the dominant second mode. The complex transient flow inside and outside the drop is induced by the interaction between the falling motion and the nonlinear oscillation. The streamlines indicate that the internal flow is substantially different from the Hill vortex for a falling drop without oscillation. The temporal evolutions of both the internal flow and the wake morphology follow the dominant second oscillation mode. In the oblate-to-prolate deformation, the internal flow goes against the external flow. As a result, a saddle point arises in the drop, which gives rise to two counterrotating vortices. The vortex dynamics are visualized by the swirling-strength vortex identification criterion and the vorticity. Whereas the potential flow changes direction during a second-mode oscillation cycle, the rotating directions of the vortices remain the same.

Ionization produced by cosmic rays and atmospheric radioactivity creates charged short life-time aerosol droplets in the upper troposphere. Inhomogeneities in the spatial distribution of aerosol droplets lead to time-varying electric fields and space charge, which can often be amplified by more than three orders of magnitude in extreme conditions, such as thunderstorms. The nonlinear coupling between ionized air, charged aerosol droplets, and the background electric field can result in electrohydrodynamic body forces that augment atmospheric turbulence. In this paper, a theoretical and numerical study on the electrohydrodynamic generation of atmospheric turbulence under fair weather and thunderstorm conditions is presented. Linear stability shows that coupling between ionized air and a background electric field acts to increase turbulent kinetic energy (TKE) in the upper troposphere, albeit over long time durations. Direct simulations of charged droplets in homogeneous shear flow demonstrate a nonlinear feedback mechanism capable of accelerating the growth rate. Streamwise velocity gradients induce fluctuations in droplet concentration and electric potential, resulting in a body force that generates vertical velocity fluctuations. Pressure strain then transfers this energy to turbulent fluctuations in the streamwise direction and the process repeats. This feedback mechanism was found to augment TKE at late stages of the shear layer growth.

We studied experimentally the discharge of a vertical silo filled by spherical glass beads and assisted by injection of air from the top at a constant flow rate, a situation which has practical interest for nuclear safety or air-assisted discharge of hoppers. The measured parameters are the mass flow rate and the pressure along the silo, while the controlled parameters are the size of particles and the flow rate of air. Increasing the air flow rate induces an increase in the granular media flow rate. Using a two-phase continuum model with a frictional rheology to describe particle-particle interactions, we reveal the role played by the air-pressure gradient at the orifice. Based on this observation, we propose a simple analytical model which predicts the mass flow rate of a granular media discharged from a silo with injection of gas. This model takes into account the coupling with the gas flow as well as the silo geometry, position, and size of the orifice.

By means of the incremental elastic modulus for small deformations superimposed on creep and subsequent recovery tests, we follow the structural state of various soft-jammed systems (yield stress fluids) in their solid regime. We demonstrate that the solid state of the material is associated with a persistent elastic network of constant elastic modulus up to yielding (solid-liquid transition), while progressively more additional elastoplastic elements are involved. The main features of these elastoplastic elements, i.e., increase of both the plastic and the elastic deformation components with the square of the shear stress, reveal the fundamental characteristics of a simple generic model (independent of material structure) describing the different components of the mechanical behavior of such systems in their solid regime.

An integral model is developed to describe the merging of multiple forced plumes released from sources arranged evenly around a circle against a linearly stratified background. The velocity potential of an array of line sinks is introduced to identify the distorted boundaries of interacting plumes. The variation of the entrainment coefficient for forced plumes is modeled as a function of the local Richardson number in the model and an improved entrainment assumption based on the boundary-curvature analysis is proposed to regulate the merging. The present model is shown to be feasible to provide a self-consistent prediction for the dynamics of multiple coalescing forced plumes. The amplification of the maximum rise height of two plumes due to superposition is faithfully reproduced and its scaling predicted by the model is reasonably consistent with the observations of available experiments. The model results further suggest that the mean entrainment efficiency per unit length of the plume boundary attains a local minimum at the touching height, implying significant mutual entrainment in that region.

When a solid substrate is withdrawn from a bath of simple, partially wetting, nonvolatile liquid, one typically distinguishes two regimes, namely, after withdrawal the substrate is macroscopically dry or homogeneously coated by a liquid film. In the latter case, the coating is called a Landau–Levich film. Its thickness depends on the angle and velocity of substrate withdrawal. We predict by means of a numerical and analytical investigation of a hydrodynamic thin-film model the existence of a third regime. It consists of the deposition of a regular pattern of liquid ridges oriented parallel to the meniscus. We establish that the mechanism of the underlying meniscus instability originates from competing film dewetting and Landau–Levich film deposition and argue that the mechanism also occurs for other combinations of film instability and lateral driving. Our analysis combines a marginal stability analysis, numerical time simulations and a numerical bifurcation study via path-continuation.

We study numerically the hydrodynamics of a self-propelled particle system consisting of spherical squirmers sedimented on a flat surface. We observe the emergence of dynamic structures, due to the interplay of particle-particle and particle-wall hydrodynamic interactions. At low coverages, our results demonstrate the formation of small chiral spinners: two or three particles are bound together via near-field hydrodynamic interactions and form a rotating dimer or trimer, respectively. The stability of the self-organized spinners can be tuned by the strength of the sedimentation. Increasing the particle concentration leads more interactions between particles and the spinners to become unstable. At higher area fractions we find that pusher particles can align their swimming directions, leading to a stable polar order and enhanced motility. Further, we test the stability of the polar order in the presence of a solid boundary. We observe the emergence of a particle vortex in a cylindrical confinement.

Recent experiments and theories have dismissed the role of increased extensional viscosity during impact of viscoelastic droplets. Here we show that for relatively low Weber numbers, $\mathrm{We}=\rho U_0^2{D}_0/\gamma =O\left({10}^0–{10}^1\right)$, where $\rho$ is the density, $U_0^{}$ the impact velocity, $D_0$ the droplet diameter, and $\gamma$ the surface tension, droplets tend to bounce on an air film with a thickness, $h$, which sets off capillary waves that eventually focus into a single wave. This focusing causes rapid deformation of the droplet thus producing high strain rates, which we verified using a particle-tracking method. Without the addition of polymers, the capillary wave focusing generates droplet contact with the substrate; however, with the addition of polymers, contact is inhibited even for relatively small polymer concentrations (10 ppm). We attribute the inhibition of contact to the large increase in the extensional viscosity near the center of the droplet, which dissipates the kinetic energy of the droplet during impact and deformation.

We study the features of a radial Stokes flow due to a submerged jet directed toward a liquid-air interface. The presence of surface-active impurities confers to the interface an in-plane elasticity that resists the incident flow. Both analytical and numerical calculations show that a minute amount of surfactants is enough to profoundly alter the morphology of the flow. The hydrodynamic response of the interface is affected as well, shifting from slip to no-slip boundary condition as the surface compressibility decreases. We argue that the competition between the divergent outward flow and the elastic response of the interface may actually be used as a practical way to detect and quantify a small amount of impurities.

We investigate immiscible fluid displacement at small scales where slip lengths are on the order of characteristic system sizes, whereby Cox's law is not expected to be valid. Molecular dynamics simulations show that in this limit hydrodynamic bending becomes small and interfaces remain approximately spherical. In this case the only relevant angle for describing the interface shape is the dynamic microscopic angle at the fluid-solid interface. In our simulations, this angle is found to be described well by the molecular-kinetic theory originally proposed by Blake and Haynes. In general, this implies a different functional dependence between the contact angle (and related quantities) and the flow speed (or capillary number); this is demonstrated for the case of the force on the boundary for immiscible fluid displacement in a two-dimensional channel.

We consider the two-dimensional problem of mass transport from a cylindrical body of circular cross section which is immersed in a fluid whose ambient velocity varies linearly with position. Such a flow is quantified by a single parameter $\mathrm{\Omega }$ representing the ratio of its associated vorticity to its characteristic rate-of-strain magnitude, $\mathrm{\Omega }=\pm 1$ corresponding to simple shear. Using matched asymptotic expansions to analyze the limit of small Péclet numbers, $\mathrm{Pe}\ll 1$, we find that the leading-order Nusselt number is $2/\left[log(1/\mathrm{Pe})+\lambda \left(\mathrm{\Omega }\right)\right],$ wherein the function $\lambda \left(\mathrm{\Omega }\right)$ is provided in terms of simple quadratures. No steady solutions exist for $\left|\mathrm{\Omega }\right|>1$, where the streamlines of the ambient flow are closed. The case of simple shear, analyzed by Frankel and Acrivos [Phys. Fluids 11, 1913 (1968)], is accordingly a borderline one. Using conformal mappings, the more general problem of arbitrary cross-sectional shape is recast as the above transport problem about a circle, with the Péclet number appropriately modified. While the more general problem is unsteady in the case of a freely suspended cylinder, the associated Nusselt number is independent of time.

We analyze the dewetting of printing plates for gravure printing with well-defined gravure cells. The printing plates were mounted on a rotating horizontal cylinder that is half immersed in an aqueous solution of the anionic surfactant sodium 1-decanesulfonate. The gravure plates and the presence of surfactants serve as one example of a real-world dewetting situation. When rotating the cylinder, a liquid meniscus was partially drawn out of the liquid forming a dynamic contact angle at the contact line. The dynamic contact angle is decreased on a structured surface as compared to a smooth one. This is due to contact line pinning at the borders of the gravure cells. Additionally, surfactants tend to decrease the dynamic receding contact angle. We consider the interplay between these two effects. We compare the height differences of the meniscus on the structured and unstructured area as a function of dewetting speeds. The height difference increases with increasing dewetting speed. With increasing size of the gravure cells, this height difference and the induced changes in the dynamic contact angle increased. By adding surfactant, the height difference and the changes in the contact angle for the same surface decreased. We further note that although the liquid dewets the printing plates, some liquid is always left in the gravure cell. At high enough surfactant concentrations or high enough dewetting speed, the dynamic contact angles in the structured surface approach those in flat surfaces. We conclude that surfactant reduces the influence of surface structure on dynamic dewetting.

In this work, we use direct-numerical-simulation-based Eulerian-Lagrangian simulations to investigate the dynamics of small gyrotactic swimmers in free-surface turbulence. We consider open-channel flow turbulence in which bottom-heavy swimmers are dispersed. Swimmers are characterized by different vertical stability, so that some realign to swim upward with a characteristic time smaller than the Kolmogorov timescale, while others possess a reorientation time longer than the Kolmogorov timescale. We cover one order of magnitude in the flow Reynolds number and two orders of magnitude in the stability number, which is a measure of bottom heaviness. We observe that large-scale advection dominates vertical motion when the stability number, scaled on the local Kolmogorov timescale of the flow, is larger than unity: This condition is associated to enhanced migration toward the surface, particularly at low Reynolds number, when swimmers can rise through surface renewal motions that originate directly from the bottom-boundary turbulent bursts. Conversely, small-scale effects become more important when the Kolmogorov-based stability number is below unity: Under this condition, migration toward the surface is hindered, particularly at high Reynolds, when bottom-boundary bursts are less effective in bringing bulk fluid to the surface. In an effort to provide scaling arguments to improve predictions of models for motile microorganisms in turbulent water bodies, we demonstrate that a Kolmogorov-based stability number around unity represents a threshold beyond which swimmer capability to reach the free surface and form clusters saturates.

In a previous work [Bogey, J. Fluid Mech. 859, 1022 (2019)], the potential-core closing of temporally developing isothermal round jets at a Mach number $M=0.9$ was shown to generate a strong axisymmetric noise component in the downstream direction. The persistence of this component is investigated in the present work for jets at $M=0.3$, 0.6, 1.3, and 2 computed by direct numerical simulation, from a low subsonic to a high supersonic Mach number. The flow and sound fields are presented, and the Mach number scaling of their magnitudes and spectral content is examined. The centerline velocity and hydrodynamic pressure spectra are close to each other using $k_z{r}_0$ in abscissa, where $k_z$ and $r_0$ are the axial wave number and the initial jet radius, respectively. The sound spectra for $M\le 1.3$ collapse well when they are plotted as a function of $k_z{r}_0{M}^{-1}$ and adjusted in amplitude using a $M^{7.5}$ power law, whereas a $k_z{r}_0$ scaling and a lower power-law exponent seem to apply to the spectra for $M\ge 1.3$. The flow and sound fields are then correlated with each other, and conditionally averaged based on a synchronization of the fields with the minimum values of centerline velocity at potential-core closing. The noise component radiated in the downstream direction for $M=0.9$ is clearly identified for $M=0.6$, 1.3, 2, and is also detected, albeit with more difficulty, for $M=0.3$, indicating the presence of the associated sound source over a wide range of Mach numbers. In all cases, its generation process extracted by the conditional averaging consists in the growth of a spot of low velocity and a high vorticity level in the inner side of the mixing layer, reaching a peak intensity at its arrival on the axis and weakening subsequently. The use of different trigger conditions for the averaging suggests that, for a given Mach number, the amplitude of the acoustic waves radiated during that stage depends linearly on the velocity deficit and the strength of the vortical structures on the jet centerline at the time of potential-core closing.

Direct numerical simulations are performed to investigate turbulent flows behind two different types of cylinder arrays (i.e., one is a widely used regular array and the other is a less studied multiscale array) with the same blockage ratio. Some important characteristics (e.g., mean velocity, turbulence intensity, and pressure drop) of the two flows are evaluated. It is demonstrated that the overall pressure drops in the two cases are almost the same. In the downstream region, the characteristics of the regular flow resemble those of the homogeneous flow, whereas the flow behind the multiscale array exhibits wakelike behavior. For the regular case, the vortex shedding frequencies due to different cylinders are the same since the cylinders involved are virtually identical and the vortex wakes formed by two neighboring cylinders are always in antiphase synchrony. In contrast, the multiscale array can generate wakes with multiple scales of both space and time. To quantitatively evaluate the difference between the features of the coherent structures in the two flows, we adopt the so-called snapshot proper orthogonal decomposition. It is found that immediately behind the regular array, most of the energy is contained in a few of the first modes. In the multiscale case, however, due to cylinders of various sizes, the increase in the energy cumulation is considerably slower than the regular case. This observation is in accord with the suggestion that by using multiscale structures, turbulence with a wider range of scales can be generated. One perhaps interesting and less reported discovery is that in the downstream region for the two cases the profiles of the energy cumulation are somewhat close to each other, although slight deviation can still be identified when normalized by the dominant vortex shedding frequency. This observation seems to tell us that the multiscale flow may not have a long-lasting memory and can eventually forget its multiscale initial conditions. These findings contribute to the understanding of the recently proposed space-scale unfolding mechanism [Phys. Rev. E 86, 046302 (2012) and J. Fluid Mech. 764, 52 (2015)], which outlines a conceptual model for explaining the high mixing efficiency of the multiscale and fractal structures and objects.

Bileaflet mechanical heart valves (BMHVs) have been related to the production of unphysiological turbulent flow in the ascending aorta. These valves comprise a pair of rigid blunt plates (leaflets), which are immersed in a confined flow with Reynolds numbers up to 10 000. They are prone to develop impinging leading-edge vortex (ILEV) instabilities [K. Hourigan et al., J. Fluids Struct. 15, 387 (2001); S. Deniz and T. Staubli, J. Fluids Struct. 11, 3 (1997)] on the leaflets because of their relatively large chord-to-thickness ratio and their low angle of incidence. These instabilities can produce strong disturbances between the leaflets which may contribute to the onset and intensity of turbulent flow in the wake of the valve. The complex nature of the flow around BMHVs prevents a detailed theoretical analysis of the underlying instability mechanisms. Therefore, we defined a two-dimensional submodel of the flow with fixed leaflets, which renders the problem accessible to the rich toolbox of hydrodynamic stability theory. High-order numerical simulations of this flow configuration indicated the systolic development of unstable ILEVs on the inner side of the leaflets during systolic acceleration of the flow. We found that the ILEV instabilities can only be observed with sufficiently high spatial resolution, which may explain why these phenomena have not been observed so far in most computational studies of BMHV flow. Orr-Sommerfeld eigenmodes with high growth rates confirmed the unstable character of this flow. We further identified a pocket of absolute instability which acts as a wave maker between the leaflets. Finally, we confirmed that this wave-maker region has a direct effect on the nonlinear breakdown in the wake of the valve. To this end, the leaflet geometry was modified such that the ILEV (and the associated wave maker) was eliminated and it was shown numerically that the wake remains laminar for the modified geometry. The results of this study are a first step toward a detailed understanding of the hydrodynamic instability mechanisms which lead to turbulent flow past BMHVs.

The focus of this paper is on investigating the noise produced by an airfoil at high angles of attack over a range of Reynolds number $\text{Re}\approx 2\times {10}^5–4\times {10}^5$. The objective is not modeling this source of noise but rather understanding the mechanisms of generation for surface pressure fluctuations, due to a separated boundary layer, that are then scattered by the trailing edge. To this aim, we use simultaneous noise and surface pressure measurement in addition to velocimetric measurements by means of hot wire anemometry and time-resolved particle image velocimetry. Three possible mechanisms for the so-called “separation-stall noise” have been identified in addition to a clear link between far-field noise, surface pressure, and velocity fields in the noise generation.

It is known that the dynamics of particles dispersed in turbulent flows can be significantly altered by electric charges and external electric fields. The next step therefore involves the investigation of whether these electric interactions can be exploited in engineering applications to control processes involving the transport of particles in turbulence. In this study, direct numerical simulations of incompressible turbulent channel flows laden with a positively isocharged suspension of monodisperse small inertial particles are employed to investigate the effect of electric charges carried by the particles on their dispersion, and to illustrate the intentional abatement of turbophoretic effects using incident electric fields. An Eulerian-Lagrangian formulation is employed along with a fast multipole method for the electric potential conveniently corrected with wall boundary conditions. Operating conditions are identified in terms of characteristic dimensionless parameters where an AC electric field applied across the channel walls decreases the time-averaged concentration of particles near the walls by up to two orders of magnitude.

We examine the dispersion of a passive scalar released in an incompressible fluid flow in an unbounded domain. The flow is assumed to be spatially periodic, with zero spatial average, and random in time, in the manner of the random-phase alternating sine flow which we use as an exemplar. In the long-time limit, the scalar concentration takes the same, predictable form for almost all realizations of the flow, with a Gaussian core characterized by an effective diffusivity, and large-deviation tails characterized by a rate function (which can be evaluated by computing the largest Lyapunov exponent of a family of random-in-time partial differential equations). We contrast this single-realization description with that which applies to the average of the concentration over an ensemble of flow realizations. We show that the single-realization and ensemble-average effective diffusivities are identical but that the corresponding rate functions are not, and that the ensemble-averaged description overestimates the concentration in the tails compared with that obtained for single-flow realizations. This difference has a marked impact for scalars reacting according to the Fisher-Kolmogorov-Petrovskii-Piskunov (FKPP) model. Such scalars form an expanding front whose shape is approximately independent of the flow realization and can be deduced from the single-realization large-deviation rate function. We test our predictions against numerical simulations of the alternating sine flow.

Compressible wall-bounded turbulence is generally assumed to be devoid of genuine compressibility effects, meaning that the effect of finite fluid dilatation is regarded as “small,” at least in the absence of disturbing pressure gradients. In the present paper we attempt to answer the basic question of how small these effects are, by interrogating a DNS database of compressible channel flow and by using Helmholtz decomposition to infer the relative magnitude and correlations between the solenoidal and the dilatational parts of turbulence velocity fields. Not surprisingly, we find dilatational velocity fluctuations to be much smaller than solenoidal ones, but perhaps unexpectedly, we find that finite correlation between the two components accounts for a nonnegligible fraction (about 10%) of the turbulent shear stress near walls, and for up to 4% of the wall skin friction. Quadrant analysis of the dilatational velocity fluctuations shows that the largest contribution to the turbulent shear stress results from significant correlation between positive streamwise solenoidal velocity fluctuations (i.e., high-speed streaks), and positive vertical dilatational velocity fluctuations, which tend to mitigate the intensity of wall-ward sweep events.