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.

In wall-bounded parallel flows, sustained turbulence can occur even while laminar flow is still stable. Channel flow is one of such flows and displays spatiotemporal fluctuating patterns of localized turbulence along its way from and to featureless turbulence. By direct numerical simulation, we study the observed inconsistency between turbulence decay according to a two-dimensional directed-percolation $\left(2D\text{−}\mathrm{DP}\right)$ scenario and the presence of sustained oblique localized turbulent bands (LTBs) below the DP critical point. Above Reynolds number ${\mathrm{Re}}_{\mathrm{g}}\approx 700$, sustained LTBs are observed; most LTBs have the same orientation so that the spanwise symmetry of the LTB pattern is broken below ${\mathrm{Re}}_2\approx 1000$. The frequency of transversal splitting, by which an LTB generates another one with opposite obliqueness, so that turbulence spreading becomes intrinsically two dimensional, increases in the range ${\mathrm{Re}}_{\mathrm{g}}<\mathrm{Re}<{\mathrm{Re}}_2$. It reaches a critical rate at ${\mathrm{Re}}_2$, beyond which symmetry is restored. The $2D\text{−}\mathrm{DP}$ behavior is retrieved only above ${\mathrm{Re}}_2$. A mean-field model is proposed which qualitatively accounts for the above symmetry-restoring bifurcation by considering interactions between space-averaged densities of LTBs propagating in either direction.

The net movement of Lagrangian particles under water waves comprises a Stokes drift in the direction of wave propagation and an Eulerian return flow in the opposing direction. Accurate prediction of the Eulerian return flow in the ocean is of importance in modeling the transport of plastic pollution, oil, wreckage, and sediment. Herein, we derive a multiple-scales solution for the Eulerian mean flow under wave packets that is valid for all water depths, relative to both the length of the wave and the length of the wave packet. To validate this solution, we carry out particle tracking velocimetry experiments in a long flume to extract the mean motion from Lagrangian seeding particles under wave packets, finding good agreement. The extraction technique is able to deal with small background motion and subharmonic error waves associated with wave generation by the paddle, the latter being relatively large in finite-depth flume experiments. In finite depth, the return flow is forced by both the divergence of the Stokes transport on the wave-packet scale and the formation of a non-negligible mean set-down underneath the packet, which acts like a bounding streamtube in the form of a convergent-divergent duct. The magnitude of the horizontal return flow is thus enhanced, with particular relevance to transport in the finite-depth coastal environment.

The swimming characteristics achieved by flapping wings, translating motion, and shell pitching are studied from observations of shelled Antarctic pteropods (aquatic snails nicknamed “sea butterflies”). These pteropods (Limacina helicina antarctica) swim with a pair of parapodia (or “wings”) via a unique flapping propulsion mechanism that incorporates similar techniques as observed in small flying insects. The geometric scaling of the wing span ($L$), wing chord ($c$), and minor shell diameter ($d$) with respect to the major shell diameter ($D$) reveal geometric similitude. Thus, the major shell diameter ($D$) is the only length scale required to describe the size of the pteropods. The motion of swimming pteropods is characterized using flapping, translational, and rotational Reynolds numbers (i.e., ${\text{Re}}_f, {\text{Re}}_U$, and ${\text{Re}}_{\mathrm{\Omega }}$). A critical value of the flapping Reynolds number, ${\text{Re}}_f=35$, is found for the onset of translating and pitching locomotion. Finally, the relationship is obtained for the Strouhal number (${\text{St}}_A=fA/U$) for the pteropods using the geometric scalings and the translational and flapping Reynolds numbers. The Strouhal number is found to be between 0.2 and 0.4, which indicates general agreement with other oscillating organisms moving with high propulsion efficiency.

The observability of the flow away from the wall in turbulent channels is studied using noiseless, although potentially incomplete, wall measurements. Reconstructions of the velocities are generated using linear stochastic estimation. All the velocities are well reconstructed in the buffer layer, but only relatively large “wall-attached” eddies are observable farther from the wall. In particular, large-scale structures that account for approximately 50% of the total kinetic energy and of the tangential Reynolds stress are accurately captured up to $y/h\lesssim 0.2$. It is argued that this should allow the use of wall sensors for the detection (and potential control) of the large eddies populating the logarithmic region, and that it suggests a natural quantitative definition for “wall-attached” eddies.

We address numerically the deformation and fragmentation dynamics of a single liquid drop subject to impulsive acceleration by a unidirectional gas stream. The density ratio between the liquid and gaseous phases is varied in the $10–2000$ range and comparisons are made with recent drop breakup experiments. We show for low Ohnesorge numbers that the liquid-gas density contrast significantly modifies the critical Weber number for the transition between bursting and stripping fragmentation regimes, on the one hand, and for drop fragmentation, on the other hand. We suggest a simple theoretical argument to predict the transitional Weber number as a function of the density contrast and show that the stabilizing influence of small contrasts can be explained by inertial effects in the nonlinear coupling between drop stretching and centroid acceleration.

This paper is associated with a poster winner of a 2018 APS/DFD Milton van Dyke Award for work presented at the DFD Gallery of Fluid Motion. The original poster is available online at the Gallery of Fluid Motion, https://doi.org/10.1103/APS.DFD.2018.GFM.P0002

A time-evolution of a slightly rarefied gas from a uniform equilibrium state at rest is investigated on the basis of the linearized Boltzmann equation under the acoustic time scaling. By a systematic asymptotic analysis, linearized Euler sets of equations and acoustic-boundary-layer equations are derived, together with their slip and jump boundary conditions, as well as the correction formula in the Knudsen layer. Analysis is done up to the first order of the Knudsen number ($\mathrm{Kn}$), with ${\mathrm{Kn}}^{1/2}$ being the small parameter. Several rarefaction effects, which are known as the effects of the second order in $\mathrm{Kn}$ in the diffusion scaling, are enhanced to be of the first order in $\mathrm{Kn}$. This is because the variation of the macroscopic quantities along the normal direction is steep in the boundary layer and the compressibility of the gas is comparatively strong. The occurrence of secular terms associated with the Hilbert expansion is pointed out and a remedy for it is also given. Finally, as an application example, a sound propagation in a half space caused by a sinusoidal oscillation of flat boundary is examined on the basis of the Bhatnagar–Gross–Krook equation. The asymptotic solution agrees well with the direct numerical solution.

The dynamics of an adhesive two-dimensional vesicle doublet under various flow conditions is investigated numerically using a high-order, adaptive-in-time boundary integral method. In a quiescent flow, two nearby vesicles move slowly toward each other under the adhesive potential, pushing out fluid between them to form a vesicle doublet at equilibrium. A lubrication analysis on such draining of a thin film gives the dependencies of draining time on adhesion strength and separation distance, which are in good agreement with numerical results. In a planar extensional flow, we find that a stable vesicle doublet forms only when two vesicles collide head-on around the stagnation point. In a microfluid trap where the stagnation of an extensional flow is dynamically placed in the middle of a vesicle doublet through an active control loop, novel dynamics of a vesicle doublet are observed. Numerical simulations show that there exists a critical extensional flow rate above which adhesive interaction is overcome by the diverging stream, thus providing a simple method to measure the adhesion strength between two vesicle membranes. In a planar shear flow, numerical simulations reveal that a vesicle doublet may form provided that the adhesion strength is sufficiently large at a given vesicle reduced area. Once a doublet is formed, its oscillatory dynamics is found to depend on the adhesion strength and their reduced area. Furthermore the effective shear viscosity of a dilute suspension of vesicle doublets is found to be a function of the reduced area. Results from these numerical studies and analysis shed light on the hydrodynamic and rheological consequences of adhesive interactions between vesicles in a viscous fluid.

Understanding the force on a finite-sized particle immersed in a turbulent boundary layer close to a rough wall is of fundamental importance in predicting particle motion in a variety of industrial and environmental applications. Here we perform fully resolved direct numerical simulations with an immersed boundary method to investigate the forces on a stationary finite-sized particle in wall turbulence over a rough bed. Results show that for the particle sitting on the rough bed, lift is the main contributor to wall-normal force and can be well predicted with proper application of existing force models. The higher lift force is mainly due to the sweep events which temporarily increase the relative velocity as well as local shear magnitude. In contrast, for a particle located slightly away from the rough bed, the wall-normal force is mainly due to the wall-normal component of drag, so ejections and outward interactions are responsible for the increase in the wall-normal force. The standard drag law with near-wall correction can reasonably predict this wall-normal force on the particle, except for the large fluctuations due to self-induced vortex shedding.

Nonlinear internal waves propagating in a quasi-two-layer stratification with a shear background current are investigated by means of high-resolution direct numerical simulations. The simulations are performed in a two-dimensional rectangular domain, representing a laboratory-scale tank of finite length. The internal waves are generated using the lock-release mechanism, while the background shear currents are induced by basin-scale internal seiches created using a tilted tank suddenly returned to the untilted configuration. Both mechanisms are readily realizable in a laboratory environment. Depending on the configuration of the initial density profile, both internal solitary-like waves (ISWs) and finite-amplitude dispersive wave trains (DWTs) may be observed in the simulations. The ISWs are observed when the pycnocline is located relatively far away from the middepth and/or the background shear is oriented against the wave-induced velocity shear. Comparison of the waveforms observed in the simulations to those described by the fully nonlinear Dubreil-Jacotin–Long (DJL) theory suggests that these waves are indeed solitary-like, implying that laboratory experiments of ISWs propagating in a shear background current can be realized in a relatively straightforward manner. As the pycnocline approaches the middepth and/or the background shear reverses its polarity and increases its magnitude, the waves tend to have a smaller amplitude and a larger half-width. When a wave's amplitude is less than approximately 3% of its half-width, the dispersive effect becomes dominant and the wave loses its solitary-like form. In this case, a finite-amplitude DWT is formed instead, in which the leading wave has a reduced propagation speed from the ISW propagation speed. Analysis based on the DJL theory suggests that exact solitary waves of similar amplitude in such a background environment have an extremely large half-width that is on the same order of magnitude as the finite length of the simulation domain, implying that their formation cannot be supported in a laboratory environment.

Recent discoveries have allowed a mathematical and computational foundation for understanding the rheology of particles suspended in viscoelastic fluids. We employ these new tools to understand the extensional rheology of such suspensions. We accomplish this by first calculating the renormalized particle contribution to the extensional viscosity in such a suspension in the dilute particle limit over a wide range of extensional Weissenberg number and Hencky strain. The models we use for the suspending fluids are the simplest dumbbell models—the Oldroyd-B, FENE-P, and Giesekus models—such that our results are general for polymer solutions which exhibit strong strain hardening at values of the Weissenberg number above those which engender the coil-stretch transition, $\mathrm{Wi}\ge 0.5$. We demonstrate that the effect of particles on the “extra elongational viscosity” relative to the fluid is nonmonotonic in strain (increasing for small strain and then decreasing for large strain). Thus at a fixed strain, the particle “extra viscosity” relative to the fluid may increase or decrease with Wi. We demonstrate that this interesting behavior is due to the interplay between the two contributions of the “particle-induced fluid stress” (PIFS) and the “stresslet” to the extra viscosity. The contribution of the particle-induced fluid stress to the suspension viscosity increases at small strain but plateaus and then decreases at higher values of the strain. Thus, at small strain the local velocity gradients near a particle increase the polymer stretch, while for greater strain, polymers which have undergone the coil-stretch transition collapse in the neighborhood of a given particle. On the other hand, the stresslet contribution to the viscosity relative to the fluid decreases monotonically as the polymer stretch surrounding a given particle “shields” the particle and thus reduces the local surface tractions. Beyond Hencky strain of approximately 2 the decreasing value of the stresslet coupled with the plateauing of the PIFS, causes the overall reduction in the particle-induced extra viscosity relative to that of the fluid.

Controlled gliding is one of the most energetically efficient modes of transportation for natural and human powered fliers. Here we demonstrate that gliding and landing strategies with different optimality criteria can be identified through deep-reinforcement-learning without explicit knowledge of the underlying physics. We combine a two-dimensional model of a controlled elliptical body with deep-reinforcement-learning (D-RL) to achieve gliding with either minimum energy expenditure, or fastest time of arrival, at a predetermined location. In both cases the gliding trajectories are smooth, although energy/time optimal strategies are distinguished by small/high frequency actuations. We examine the effects of the ellipse's shape and weight on the optimal policies for controlled gliding. We find that the model-free reinforcement learning leads to more robust gliding than model-based optimal control strategies with a modest additional computational cost. We also demonstrate that the gliders with D-RL can generalize their strategies to reach the target location from previously unseen starting positions. The model-free character and robustness of D-RL suggests a promising framework for developing robotic devices capable of exploiting complex flow environments.

When wind blows at the surface of a liquid of sufficiently high viscosity, a wave packet of small amplitude is first generated, which sporadically forms large-amplitude fluid bumps that rapidly propagate downstream. These nonlinear structures, first observed by Francis [J. R. D. Francis, Philos. Mag. 42, 695 (1954)], have an almost vertical rear facing the wind and a weak slope at the front. We call them viscous solitons. We investigate their dynamics in a wind-tunnel experiment using silicon oil of kinematic viscosity $1000{\mathrm{mm}}^2{\mathrm{s}}^{-1}$ by means of laser sheet profilometry and particle image velocimetry. We give evidence of their subcritical nature: They are emitted in a region of large shear stress but, once formed, they are sustained by the wind and propagate in a region of lower stress. Their propagation velocity is given by the balance between aerodynamic drag in the air and viscous drag in the liquid. The stable soliton branch of the subcritical bifurcation diagram is reconstructed from the measured soliton amplitude at various wind velocities and distances along the channel. At large wind velocity, the emission frequency of solitons increases, resulting in a long-range sheltering of downstream mature solitons by newly formed upstream solitons, which limits their course.

Capillary fingering is a displacement process that can occur when a nonwetting fluid displaces a wetting fluid from a homogeneous disordered porous medium. Here, we investigate how this process is influenced by a pore size gradient. Using microfluidic experiments and computational pore-network models, we show that the nonwetting fluid displacement behavior depends sensitively on the direction and the magnitude of the gradient. The fluid displacement depends on the competition between a pore size gradient and pore-scale disorder; indeed, a sufficiently large gradient can completely suppress capillary fingering. By analyzing capillary forces at the pore scale, we identify a nondimensional parameter that describes the physics underlying these diverse flow behaviors. Our results thus expand the understanding of flow in complex porous media and suggest a new way to control flow behavior via the introduction of pore size gradients.

The motion of helicoidal swimmers moving in a pool filled with a granular medium is studied experimentally. The horizontal displacement through granular beads is measured considering geometrical modifications of the swimmer, the size, and frictional properties of the media. We found three main parameters which affect the swimming performance: the diameter, the wavelength, and the angle of the helix. The swimming speed scales with the rotation speed, $\omega R$. The size of particles does not affect the swimming speed significantly; the swimming speed is reduced when the particle's angle of repose increases. It was found that a maximum swimming speed is achieved when the helix angle is close to ${55}^{\circ }$. The experimental data are compared with predictions of the granular resistive force theory, which was extended to be applicable for a swimmer with a rigid helical tail, leading to good agreement.

We consider the steady flow of a viscoelastic liquid film over an inclined wall with sinusoidal corrugations of arbitrary wavelength and depth. We develop a computational model and carry out detailed numerical simulations based on the finite-element method to investigate this flow. To this end, we solve the two-dimensional momentum and mass conservation equations while employing the Phan-Thien-Tanner (PTT) constitutive model to account for the rheology of the viscoelastic material. An elliptic grid generation scheme is used to follow the large deformations of the liquid film. We perform a thorough parametric analysis to investigate the combined effects of elasticity, inertia, and capillary and viscous forces on the characteristics of the steady flow. The results of our simulations indicate that fluid elasticity suppresses interfacial deformation at low flow rates, whereas at moderate values of $\mathrm{Re}$ it enhances the deformation considerably. In the latter case, elastic forces may even give rise to the formation of a static hump and a cusp at the free surface, the size of which increases with the relaxation time of the liquid. The resonance of the liquid film with the substrate undulations is also enhanced by shear thinning. Interestingly, it is predicted that under certain conditions the transition to the inertia regime is not smooth and a hysteresis loop arises, which is the signature of an abrupt change of the film shape, since its high deformations cannot be sustained. Additionally, we have performed calculations for a wide range of different geometrical characteristics of the substrate. We find that viscoelastic effects become more pronounced in the case of long-wavelength wall undulations, while for substrates with short wavelengths the effect of shear thinning is less significant due to the presence of vortices inside the corrugations.

The linear hydrodynamic stability of a film of viscoelastic fluid flowing down an inclined wavy surface is studied. We investigate the stability of the flow with respect to infinitesimal two- and three-dimensional (2D and 3D) disturbances and employ the Floquet-Bloch theory to examine the effect of periodic disturbances of any wavelength. The study is based on the numerical solution of the momentum equations along with the Phan-Thien–Tanner (PTT) model to account for material viscoelasticity. The generalized eigenvalue problem is solved using Arnoldi's algorithm, in a Newton-like implementation in order to calculate faster the critical conditions for the onset of the instability. Our results are in excellent agreement with the previous experimental and theoretical results in the case of Newtonian liquids flowing over flat and undulating substrates and viscoelastic liquids over flat substrates. We present detailed stability maps for finite amplitude of the wall corrugations and a wide range of material parameters. Our calculations indicate that fluid elasticity is primarily stabilizing, while shear thinning of the fluid tends to destabilize the fluid flow. In order to investigate the mechanisms involved, we perform an energy analysis of the flow under long-wave disturbances indicating that the convection of stress-gradient disturbances provides an additional viscoelastic mechanism for the destabilization of the flow, in contrast to the base state stress gradients which contribute to stabilization of the flow. Besides the usual long-wave instability, conditions are identified which lead to unstable disturbances of wavelength equal or smaller than the wavelength of the substrate. Experimental observations for Newtonian liquids have indicated that these short-wave instabilities will dominate and a similar behavior is predicted for viscoelastic liquids. Sometimes, before the short-wave instabilities, a hysteresis loop in the steady flow can be identified, which leads to a sharp change in the critical frequency. Finally, we examine the stability of the flow when subjected to disturbances in the spanwise direction and show that for highly elastic liquids 3D instabilities may arise.

The passage of microfluidic droplets in miscible thread-forming flows is shown to improve the mixing efficiency of low- and high-viscosity fluids at the small scale. Hydrodynamic interactions between recirculating flow patterns and viscous core-annular flows are experimentally investigated in square microchannels. The deformation of thick segmented flows injected in thin fluids is examined through the evolution of droplet size, spacing, and velocity along a square microchannel. Droplets also help in probing the various states of lubrication of the viscous central stream in the bulging, tubing, and threading regimes at various capillary and Péclet numbers. A range of intriguing flow phenomena is revealed using a dual approach based on thread and droplet mutual behaviors, including droplet breakup, formation of low-viscosity currents, thread splitting, viscous fingering, and viscous buckling instabilities. The thread-forming ability of miscible fluids having large viscosity contrasts is discussed in conjunction with mixing applications where a thinner or a viscosifier is continuously added to a viscosity-differing fluid in confined microsystems.

Practically all flows are turbulent in nature and contain some kind of irregularly shaped particles, e.g., dirt, pollen, or life forms such as bacteria or insects. The effects of the particles on such flows and vice versa are highly nontrivial and are not completely understood, particularly when the particles are finite sized. Here, we report an experimental study of millimetric fibers in a strongly sheared turbulent flow. We find that the fibers show a preferred orientation of $-0.38\pi \pm 0.05\pi$ ($-68\pm 9^{\circ }$) with respect to the mean flow direction in high-Reynolds-number Taylor-Couette turbulence, for all studied Reynolds numbers, fiber concentrations, and locations. Despite the finite size of the anisotropic particles, we can explain the preferential alignment by using Jefferey's equation, which provides evidence of the benefit of a simplified point-particle approach. Furthermore, the fiber angular velocity is strongly intermittent, again indicative of point-particle-like behavior in turbulence. Thus large anisotropic particles still can retain signatures of the local flow despite classical spatial and temporal filtering effects.