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)].

Mangrove trees form dense networks of prop roots in coastal intertidal zones. The interaction of mangroves with tidal and river flows is fundamental to the preservation of estuaries and shorelines by providing water filtration, protection against erosion, and habitat for aquatic animals. The impact of mangrove roots on unidirectional flows is mainly characterized by hydrodynamics including drag, flow structures, transport, and fluid-structure interaction. In this work, we focus on the drag coefficient and flow structure downstream of simplified mangrove root models. The mangrove roots were modeled as a cluster of uniformly distributed rigid circular cylinders (patch), with a frontal area per unit volume $\left(a\right)$. Direct force measurements were made in a recirculating water flume. In addition, the unsteady wake was measured using particle image velocimetry (PIV). The models were tested for a Reynolds number range of 600 to 12 000 based on the patch diameter $\left(\mathrm{R}{\mathrm{e}}_D=\frac{\rho UD}{\mu }\right)$, in order to resemble natural conditions. A new length scale, the “effective diameter,” is proposed by comparing the Strouhal number of the patches with the analytical Strouhal number of a canonical cylinder in the flow field that produces the same vortex shedding. We compared different length scales to characterize the hydrodynamics, including the patch diameter $\left(D\right)$, equivalent length proposed by Mazda $\left(L_E\right)$, and an effective diameter $D_{\mathrm{eff}}$. A universal empirical curve describing the drag coefficient based on $\left(L_E\right)$ and $D_{\mathrm{eff}}$ is also presented. It was found that the effective diameter was able to capture competing parameters including patch diameter, porosity, and cylinder diameters into a single parameter to obtain the drag coefficient of the physical models. The results revealed that the time-average drag coefficient decreased with an increased Reynolds number and porosity. It was found that the ratio of $\frac{C_D}{\mathrm{St}}$ to the blockage parameter $(C_{D}aD)$ exhibits a linear relationship, indicating that the parameter $\mathrm{St}aD$ is constant for all patches considered. This finding was also valid using equivalent length and effective diameter as the characteristic lengths. In addition, based on time-resolved PIV results downstream of the physical model, we found that the vorticity magnitude decays and the vortex structure is more streamlined with an increase in porosity. This analysis of the hydrodynamics of mangrove rootlike models can also be extended to predict values of drag coefficient in other canopy flows, including submerged arrays, flexible elements, and bio-inspired coastal infrastructures.

Experiments characterizing the influence of gravity and interfacial tension on Faraday instability in immiscible, confined fluid layers are presented. The variation in interfacial tension was obtained by controlling the temperature of a suitable binary fluid pair while the influence of gravity was analyzed through a series of terrestrial and microgravity (parabolic flight) experiments. These experiments confirm the existence of a crossover frequency, on either side of which gravity plays opposing roles. The current experiments also reveal that the neutral stability curves under Earth's gravity drift toward lower frequencies as the temperature of the liquid pair approaches its upper consolutal value, i.e., the temperature of complete miscibility. Such drifts in the low frequency range are shown to occur primarily due to the reduction in density difference between the layers, whereas at very high frequencies they are controlled by the lowering of interfacial tension. In the absence of gravity, the Faraday waves are characterized by larger wave numbers, and, as in terrestrial conditions, the instability thresholds at high frequencies increase with an increase of temperature, i.e., reduction in interfacial tension value. This surprising stabilization originates from the lowering of the critical wavelength that leads to increased viscous dissipation.

Three-dimensional (3D)-printed microfluidic devices offer new ways to study fluid dynamics. We present a clear visualization of vortex breakdown in a dividing T-junction flow. By individual control of the inflow and two outflows, we decouple the effects of swirl and rate of vorticity decay. We show that even slight outflow imbalances can greatly alter the structure of vortex breakdown, by creating a net pressure difference across the junction. Our results are summarized in a dimensionless phase diagram, which will guide the use of vortex breakdown in T-junctions to achieve specific flow manipulation.

Flapping wings in nature demonstrate a large force envelope, with capabilities far beyond the traditional limits of static airfoil section coefficients. Puffins, murres, and other auks particularly showcase this effect, as they are able to generate both enough thrust to swim and enough lift to fly, using the same wing, purely by changing the wing motion trajectory. The wing trajectory is therefore an additional design criterion to be optimized along with traditional aircraft parameters and could open the door to dual aerial-aquatic robotic vehicles. In this paper we showcase one realization of a three-dimensional flapping-wing actuation system that reproduces the force coefficients necessary for dual aerial-aquatic flight. The wing apparatus oscillates by the root and employs an active upstream and downstream sweep degree of freedom. We analyze two types of motions in detail: aerial motions where the wing tip moves upstream during the power stroke of each flapping cycle and aquatic motions where the wing tip moves downstream during the power stroke. We design these aerial and aquatic flapping-wing trajectories using an experiment-coupled optimization routine, allowing control of the unsteady forces throughout each flapping cycle. Additionally, we elucidate the wakes of these complex wing trajectories using dye visualization, correlating the wake vortex structures with simultaneous experiment force measurements. After optimization, the wing trajectories generate the large force envelope necessary for propulsion in both fluid media and furthermore demonstrate improved control over the unsteady wake.

Diagnostic ultrasound has been shown to cause lung hemorrhage in a variety of mammals, though the underlying damage mechanisms are still unclear. Motivated by this problem, we use numerical simulations to investigate the interaction of an ultrasound wave with the alveolar tissue-air interface. A planar, single-cycle, trapezoidal waveform propagates in tissue (modeled as water) and impinges upon an alveolus of the lung (modeled as air); to represent the alveolar surface roughness, the interface consists of a small-amplitude single-mode perturbation. Because of the sharp density gradient at the interface, we hypothesize that ultrasound waves, despite their relatively low amplitude, deposit sufficient baroclinic vorticity to drive perturbation growth. Our simulations show that the perturbation amplitude grows to sizes many times larger than the original value, well after the wave has passed. We demonstrate that conventional (linear) acoustics cannot account for such deformations; instead, the perturbation growth is driven by nonlinear effects: the baroclinic vorticity deposited along the interface, due to the misalignment of the pressure gradient (across the wave) and the density gradient (across the perturbed gas-liquid interface). Based on dimensional analysis and scaling, we observe that the perturbation amplitude and length of the interface scale with the circulation density and grow according to power laws in time. If the time interval between the pressure increase and decrease is sufficient, both deposit vorticity of the same sign, thus enhancing the perturbation growth; conversely, if the interval is too short, the vorticity deposited by the pressure increase is canceled by the decrease. A further consequence is that one may be able to control the growth of such perturbed interfaces by modulating the incoming waveform.

We report on the scaling between the lift force and the velocity lag experienced by a single particle of different size in a monodisperse dense granular chute flow. The similarity of this scaling to the Saffman lift force in (micro-) fluids, suggests an inertial origin for the lift force responsible for segregation of (isolated, large) intruders in dense granular flows. We also observe an anisotropic pressure field surrounding the particle, which potentially lies at the origin of the velocity lag. These findings are relevant for modeling and theoretical predictions of particle-size segregation. At the same time, the suggested interplay between polydispersity and inertial effects in dense granular flows with stress and strain gradients, implies striking new parallels between fluids, suspensions, and granular flows with wide application perspectives.

Experiments were conducted in a wind tunnel to examine the development of coherent structures in a screen cylinder wake over a streamwise range of $10\le x/d\le 60$ (where $d$ is the diameter of the cylinder) at a Reynolds number Re of 7000. The screen cylinder was made of a stainless-steel wire mesh with a porosity (open area ratio) of 67%. Results showed that the flow can be classified into two distinct regimes, characterized by the averaged contributions from the coherent motion to the Reynolds stresses where vortices changed from growing to decaying. The first regime exhibited the growth of small-scale Kelvin-Helmholtz vortices in the shear layer through vortex merging. These small-scale vortices matured quite a distance downstream to form the “large-scale” coherent structures, marked by the change of the root-mean-square transverse velocity fluctuations from a twin-peak to a single peak profile, significantly extending the vortex formation length. The second regime was manifested by the slow decay of the fully formed large-scale vortices, designated by the weak vorticity exchange across the wake centerline. Conceptual models of the vortex formation and decay processes as well as the momentum transport in the screen cylinder wake were proposed and illustrated, and comparisons were made with that of a solid cylinder wake.

Vorticity fluxes are analyzed in fully developed turbulent flow through rectangular ducts with a width-to-height ratio of 3, and both straight and semicylindrical side walls, at a centerplane friction Reynolds number ${\text{Re}}_{\tau ,c}\simeq 180$. The transport of secondary Reynolds stresses by the secondary flow of Prandtl's second kind is analyzed from a vorticity-flux perspective. This analysis reveals that the in-plane transport of viscous stresses locally counteracts the inhomogeneous distribution of the turbulent shear-stress gradient in the spanwise direction. A relationship is established between the mean and fluctuating transport terms that can be useful to improve turbulence models and their ability to accurately predict the secondary flow. Finally, quadrant analysis is used to evaluate the contribution from the different types of bursting events to the fluctuating transport terms.

A train of red blood cells flowing in a round tube will either advect steadily or break down into a complex and irregular flow, depending upon its degree of confinement. We analyze this apparent instability, including full coupling between the viscous fluid flow and the elastic cell membranes. A linear stability analysis is constructed via a complete set of orthogonal perturbations to a boundary integral formulation of the flow equations. Both transiently $\left(t\to 0^{+}\right)$ and asymptotically $\left(t\to \infty \right)$ amplifying disturbances are identified. Those that amplify transiently have short-wavelength shape distortions that carry significant membrane strain energy. In contrast, asymptotic disturbances are primarily rigid-body-like tilts and translations. It is shown that an intermediate cell-cell spacing of about half a tube diameter suppresses long-time train instability, particularly when the vessel diameter is relatively small. Altering the viscosity ratio between the cytosol fluid within the cell and the suspending fluid is found to be asymptotically destabilizing for both higher and lower viscosity ratios. Altering the cytosol volume away from that of a nominally healthy discocyte alters the stability with complex dependence on train density and vessel diameter. Several of the observations are consistent with a switch from predominantly cell-cell interactions for dense trains and predominantly cell-wall interactions for less dense trains. Direct numerical simulations are used to verify the linear stability analysis and track the perturbation growth into a self-sustaining disordered regime.

We study the fronts that appear when a shear-thickening suspension is submitted to a sudden driving force at a boundary. Using a quasi-one-dimensional experimental geometry, we extract the front shape and the propagation speed from the suspension flow field and map out their dependence on applied shear. We find that the relation between stress and velocity is quadratic, as is generally true for inertial effects in liquids, but with a prefactor that can be much larger than the material density. We show that these experimental findings can be explained by an extension of a phenomenological model originally developed to describe steady-state shear thickening. This is achieved by introducing a sole additional parameter: the characteristic strain scale that controls the crossover from startup response to steady-state behavior. The theoretical framework we obtain points out a linkage between transient and steady-state properties of shear-thickening materials.

We analyze the resolvent operator in three flows around a nominal NACA-0012 airfoil at ${\text{Re}}_C=50,000$ and $5^{\circ }$ angle of attack. In particular, we study two naturally developing flows (around the airfoil with straight and blunt trailing edges) and one tripped flow. The naturally developing flows exhibit laminar separation, transition and turbulent reattachment, while the tripped flow remains attached in the suction side. For all cases, the time-averaged flow fields are computed from separate DNS simulations. The resolvent analysis can identify the areas of maximum receptivity of the flow field as well as the most amplified modes (optimal response). The former was located close to the leading edge, and in the case of naturally developing flows, also in the free-stream. The spatial distribution of optimal forcing was dominated by structures tilted against the mean flow, in agreement with other studies of boundary layer flows. The optimal response of the two naturally developing flows were different. For the NACA-0012 airfoil with straight trailing edge, the response was maximized at the natural frequency of the separating shear layer, and the shape matched closely with the corresponding DMD mode obtained from processing the DNS results. For the blunt airfoil, the receptivity of the separating shear layer was suppressed in the region of natural frequency, while it was maximized at the frequency of vortex shedding from the trailing edge. This is attributed to the lock-in mechanism between the shedding and the separating shear layer observed in the DNS simulations; the lock-in makes the separating shear layer less sensitive to forcing. In the tripped flow, the amplification of the perturbations is significantly diminished, and only by restricting the resolvent analysis to a region close to the suction side can we get a dominant frequency that matches with DNS at that region. The dominant resolvent modes were used to get estimations of the velocity spectra based only on the mean flow and the signal of one velocity component at discrete calibration points. Very good approximation is observed with only one or two points (depending on the flow examined), provided that they are located in energetic regions of the flow that contain sufficient spectral content at the relevant frequencies.

Jet drops ejected from bursting bubbles are ubiquitous, transporting aromatics from sparkling beverages, pathogens from contaminated water sources, and sea salts and organic species from the ocean surface to the atmosphere. In all of these processes, the smallest drops are noteworthy because their slow settling velocities allow them to persist longer and travel further than large drops, provided they escape the viscous sublayer. Yet it is unclear what sets the limit to how small these jet drops can become. Here we directly observe microscale jet drop formation and demonstrate that the smallest jet drops are not produced by the smallest jet drop-producing bubbles, as predicted numerically by Duchemin et al. [Duchemin et al., Phys. Fluids 14, 3000 (2002)]. Through a combination of high-speed imaging and numerical simulation, we show that the minimum jet drop size is set by an interplay of viscous and inertial-capillary forces both prior and subsequent to the jet formation. Based on the observation of self-similar jet growth, the jet drop size is decomposed into a shape factor and a jet growth time to rationalize the nonmonotonic relationship of drop size to bubble size. These findings provide constraints on submicron aerosol production from jet drops in the ocean.

Introducing a model to study deposition and erosion of single particles at microscopic scale, we investigate the clogging and erosive processes in a pore. The particle diameter, concentration, and adhesive forces rule the way particles are deposited and, therefore, characterize the clogging process. We study the hydraulic pressure that induces erosive bursts and conclude that this pressure depends linearly on the deposited volume and inversely on the pores' diameter. While cohesion does not play an important role for erosive bursts, the adhesion is the main force initiating clogging, and when overcome by the hydraulic pressure, erosive bursts are triggered. Finally, we show how the magnitude of erosive bursts depends on the pore length, particle diameter, and pore size.

We extend the vortex-surface field (VSF), a Lagrangian-based structure-identification method, to study the structural evolution in Klebanoff-type boundary-layer transition. The VSF is constructed from the instantaneous vorticity fields in a series of sliding windows at different times and streamwise locations using the boundary-constraint method. The visualization of VSF isosurfaces displays the Lagrangian-like evolution of vortex surfaces consisting of vortex lines. The near-wall VSF isosurfaces evolve from wall-parallel planar vortex surfaces through a train of hairpin-like structures into turbulent spots. In the inception of turbulent spots, the train of hairpin-like bulges of vortex surfaces induces sinuous spanwise perturbations on the adjacent flank of lower wavy vortex surfaces, and then triggers the Kelvin-Helmholtz instability in the spanwise direction. The resultant sinuous distortion of vortex surfaces propagates in the spanwise direction, which can lead to the mass production of small-scale, skewed hairpin-like structures and the rapid lateral growth of turbulent spots. The streaky and hairpin-like structures have strong interactions in the present Klebanoff-type transition. On the other hand, these signature structures can be interpreted as different evolutionary geometries of the same set of VSF isosurfaces at different times and spatial regions, rather than considering them as two different elementary structures visualized by different structure-identification methods. Furthermore, the quantified distortion of near-wall vortex surfaces in the lateral growth of young turbulent spots is highly correlated to the surge of the skin-friction coefficient in the transition.

Turbulent flows are special examples of extended dynamical systems distinguished by their intermittent, chaotic, and irreversible behavior. However, the exact nature of the effect of intermittency on the chaotic nature of turbulence, and vice versa, is still not known. By using a recent discovery [U. Frisch, A. Pomyalov, I. Procaccia, and S. S. Ray, Phys. Rev. Lett. 108, 074501 (2012)] of Fourier decimation, we manipulate the nonlinearity to try and isolate the origins of intermittency, chaos, and irreversibility in homogeneous, isotropic turbulence. In particular, we show that within the Lagrangian framework it is possible to have nonintermittent, yet chaotic, turbulent flows, with an emergent time reversibility as the effective degrees of freedom are reduced through decimation. These results suggest a new microscopic way, starting from the equations of motion, of understanding turbulence beyond what is possible through phenomenological models.

The influence of external intermittency on the scaling of the dissipation scale distribution is examined in turbulent boundary layer flow at ${\text{Re}}_{\tau }\approx 1000$. Probability density functions (PDFs) of the dissipative scales are compared with, and without, accounting for the external intermittency using an intermittency detection function. Results showed that accounting for the external intermittency produces better consistency in the shapes of the PDFs at the same wall-normal location at different instances in time. In addition, properly scaling the dissipation scale distribution collapses the probability density functions calculated at different wall-normal locations. This improvement in the scaling of the dissipation scale distribution supports prior observations of universality of the small-scale description of the turbulence for wall-bounded flow.

Reynolds-averaged Navier-Stokes (RANS) equations are widely used in engineering turbulent flow simulations. However, RANS predictions may have large discrepancies due to the uncertainties in modeled Reynolds stresses. Recently, Wang et al. demonstrated that machine learning can be used to improve the RANS modeled Reynolds stresses by leveraging data from high-fidelity simulations [J.-X. Wang et al., Phys. Rev. Fluids 2, 034603 (2017)]. However, solving for mean flows from the improved Reynolds stresses still poses significant challenges due to potential ill-conditioning of RANS equations with Reynolds stress closures. Enabling improved predictions of mean velocities is of profound practical importance, because often the velocity and its derived quantities (quantities of interest, e.g., drag, lift, and surface friction), and not the Reynolds stress itself, are of ultimate interest in RANS simulations. To this end, we present a comprehensive framework for augmenting turbulence models with physics-informed machine learning, illustrating a complete workflow from identification of input features to final prediction of mean velocities. This work has two innovations. First, we demonstrate a systematic procedure to generate mean flow features based on the integrity basis for mean flow tensors. Second, we propose using machine learning to predict linear and nonlinear parts of the Reynolds stress tensor separately. Inspired by the finite polynomial representation of tensors in classical turbulence modeling, such a decomposition is instrumental in overcoming the ill-conditioning of RANS equations. Numerical tests demonstrate the merits of the proposed framework.

The electrohydrodynamic interaction of liquid drop pairs suspended in another immiscible liquid and subjected to uniform electric field is examined using the leaky dielectric model and the explicit forcing lattice Boltzmann method, by taking into account the nonlinear inertia effects. This facilitates explorations of wider parametric contrast, precise electrohydrodynamic interaction, and postcoalescence breakup phenomena that remained unknown. The influence of dielectrophoretic and electrohydrodynamic forces in prolate- and oblate-shaped deformations, coalescences, and repulsive motion of leaky drop pairs appearing at widely varied incidence angle $\left(\alpha \ge 0^{\circ }\right)$ to the applied electric field is studied. The electrically driven flow at $\alpha =0^{\circ }$ evolves in the form of decisively important outflow- and inflow-natured counterrotating vortex pairs in and around the drops. With suitably tuned conductivity $\left({\sigma }_{\mathrm{in}}/{\sigma }_{\mathrm{out}}\right)$ and permittivity $\left({\varepsilon }_{\mathrm{in}}/{\varepsilon }_{\mathrm{out}}\right)$ ratios of drop fluid to surrounding outer medium, the relative impacts of attractive electric force versus outflow- or inflow-natured vortex pair-induced hydrodynamic force was optimized to distinctly facilitate the prolate- and the oblate-type deformations of a drop pair, their coalescence, departure, and the postcoalescence breakup. For varied ${\varepsilon }_{\mathrm{in}}/{\varepsilon }_{\mathrm{out}}$ over a range $0.25\le {\varepsilon }_{\mathrm{in}}/{\varepsilon }_{\mathrm{out}}\le 20.0$, and using fixed conductivity ratio ${\sigma }_{\mathrm{in}}/{\sigma }_{\mathrm{out}}=5.0$ and electric capillary number $\mathrm{C}{\mathrm{a}}_E=0.46$ (the ratio of electric force and surface tension), the dipolar electric force is appropriately set with respect to the surrounding four outflow-type outer vortex pair-induced hydrodynamic force to enforce two prolately deformed drops move apart for ${\varepsilon }_{\mathrm{in}}/{\varepsilon }_{\mathrm{out}}<{\left({\varepsilon }_{\mathrm{in}}/{\varepsilon }_{\mathrm{out}}\right)}_{\mathrm{crit}1}\approx 2.4$ and coalesce for $2.4<{\varepsilon }_{\mathrm{in}}/{\varepsilon }_{\mathrm{out}}<9.57$. The low pressure that grew at the neck of near-contact or coalescing drops facilitated the transport of inner fluid into neck region and helped the drop pair's coalescence. For ${\varepsilon }_{\mathrm{in}}/{\varepsilon }_{\mathrm{out}}>{\left({\varepsilon }_{\mathrm{in}}/{\varepsilon }_{\mathrm{out}}\right)}_{\mathrm{crit}3}\approx 9.57$, exceeding a critical value, the deformed oblate drop pair moved closer and coalesced; and depending on ${\varepsilon }_{\mathrm{in}}/{\varepsilon }_{\mathrm{out}}$ the coalesced drop subsequently broke into a number of satellite or daughter drops spread in a direction perpendicular to the electric field; and such a phenomenon is newly identified. For the nonaligned drop pairs with $\alpha <54.7^{\circ }$ or $\alpha >125.3^{\circ }$, the attractive radial $\left({\mathit{F}}_{\mathit{r}}\right)$ component of dielectrophoretic force drove two drops closer, while the torque produced by tangential $\left({\mathit{F}}_{\mathit{t}}\right)$ components of the electric force made them rotate and align to the electric field upon coalescence. For $54.7^{\circ }<\alpha <125.3^{\circ }$ the dipolar radial force $\left({\mathit{F}}_{\mathit{r}}\right)$ appeared repulsive and drop pair moved apart. Importantly for nonaligned drop pairs both oblate and prolate deformations are noticed, for suitably selected dielectric properties.

A hydrophilic liquid, such as water, forms hydrogen bonds with a hydrophilic substrate. The strength and locality of the hydrogen bonding interactions prohibit slip of the liquid over the substrate. The question then arises how the contact line can advance during wetting. Using large-scale molecular dynamics simulations we show that the contact line advances by single molecules moving ahead of the contact line through two distinct processes: either moving over or displacing other liquid molecules. In both processes friction occurs at the molecular scale. We measure the energy dissipation at the contact line and show that it is of the same magnitude as the dissipation in the bulk of a droplet. The friction increases significantly as the contact angle decreases, which suggests suggests thermal activation plays a role. We provide a simple model that is consistent with the observations.