It is well known that the reversibility of Stokes flow makes it difficult for small microorganisms to swim. Inertial effects break this reversibility, allowing new mechanisms of propulsion and feeding. Therefore it is important to understand the effects of unsteady and fluid inertia on the dynamics of microorganisms in flow. In this work, we show how to translate known inertial effects for nonmotile organisms to motile ones, from passive to active particles. The method relies on a principle used earlier by Legendre and Magnaudet (1997) to deduce inertial corrections to the lift force on a bubble from the inertial drag on a solid sphere, using the fact that small inertial effects are determined by the far field of the disturbance flow. The method allows us, for example, to compute the inertial effect of unsteady fluid accelerations on motile organisms, and the inertial forces such organisms experience in steady shear flow. We explain why the method fails to describe the effect of convective fluid inertia.

We consider the question of fundamental limitations on the performance of eddy-viscosity closure models for turbulent flows, focusing on the Leith model for two-dimensional large-eddy simulation. Optimal eddy viscosities depending on the magnitude of the vorticity gradient are determined subject to minimum assumptions by solving PDE-constrained optimization problems defined such that the corresponding optimal large-eddy simulation best matches the filtered direct numerical simulation. First, we consider pointwise match in the physical space, and the main finding is that with a fixed cutoff wave number $k_c$, the performance of the large-eddy simulation systematically improves as the regularization in the solution of the optimization problem is reduced, and this is achieved with the optimal eddy viscosities exhibiting increasingly irregular behavior with rapid oscillations. Since the optimal eddy viscosities do not converge to a well-defined limit as the regularization vanishes, we conclude that in this case the problem of finding an optimal eddy viscosity does not in fact have a solution and is thus ill-posed. We argue that this observation is consistent with the physical intuition concerning closure problems. The second problem we consider involves matching time-averaged vorticity spectra over small wave numbers. It is shown to be better behaved and to produce physically reasonable optimal eddy viscosities. We conclude that while better behaved and hence practically more useful eddy viscosities can be obtained with stronger regularization or by matching quantities defined in a statistical sense, the corresponding large-eddy simulations will not achieve their theoretical performance limits.

We simulate and analyze the evolution of a rectilinear vortex tube with initial axial core-size perturbations at circulation-based Reynolds number of 5000. The initial variations in the core size are associated with axial gradients in the azimuthal velocity, which generates azimuthal vorticity. This azimuthal vorticity propagates as twist waves in the axial direction. Varying the initial core-size ratio $A$ shows that the propagation speed of the twist waves varies linearly with $A$ and approaches linear stability results of the long-wave limit of Kelvin waves on rectilinear vortex tubes as $A\to 1$. The simulations show that when two twist waves of opposite handedness meet the core expands radially, forming a pair of local ringlike structures with opposite-signed azimuthal vorticity through a process termed vortex bursting. An analysis of the vorticity dynamics during bursting reveals that initially the flow behaves qualitatively like a head-on collision of two isolated vortex rings, with the azimuthal vorticity dynamics driving radial growth. During bursting, however, the localized radial expansion of the core is also accompanied by an increase in the radial vorticity component, which ultimately arrests the bursting and reverses the sign of the azimuthal vorticity. Through long-time simulations of the periodic tube, we demonstrate that after the primary bursting event the twist waves reverse their direction and interact again, leading to further bursting events. The evolution of the perturbed tubes is then accompanied by sustained elevated enstrophy levels and thus accelerated energy decay as compared to undisturbed Lamb-Oseen vortices of identical initial circulation and energy. Overall, this work provides the first detailed qualitative and quantitative insights into the mechanisms and evolution of vortex bursting on rectilinear vortex tubes. To further assess the relevance and prevalence of bursting in practical settings, subsequent investigations in the stability and sensitivity of our results to varying Reynolds number, nonrectilinear vortex center lines, and external strain fields are needed.

Bendotaxis has recently been theoretically proposed and experimentally observed by Bradley et al. [Phys. Rev. Lett. 122, 074503 (2019)] as a mechanism for self-transport of droplets at small scales. As a result of the coupling between bending elasticity and capillarity in a thin channel, a pressure gradient is induced within a liquid droplet and leads to its spontaneous movement, regardless of whether the droplet is wetting or nonwetting the channel walls. In the present work, using Onsager's variational principle, we present a variational framework for systematically studying the mechanism of bendotaxis. We derive a full model for the thin film dynamics of bendotaxis with thermodynamical consistency. Based on the full model, we specify the conditions under which the simplified model used by Bradley et al. can be validated. Furthermore, we use Onsager's principle as a tool for approximation to derive a reduced model. This model reduction leads to a description for droplet self-transport using a few slow state variables by which a clear physical picture is presented for the mechanism of bendotaxis. The reduced model is validated by comparing its predictions with the numerical results from solving the full model. Finally, we investigate the mechanism of bendotaxis for active droplets capable of self-propelled motion. We find that wettability and activity can jointly operate to enhance or weaken the self-transport effect of bendotaxis, depending on the sign of wettability (hydrophobic or hydrophilic) and the sign of activity (contractile or extensile).

The rheological properties and microstructure of neutrally buoyant elliptical particle suspensions are studied using the immersed boundary-lattice Boltzmann method. For dilute suspensions containing only one particle, with the increase of aspect ratio Ar, the particle ceases to rotate due to the inertia at a critical aspect ratio ${\text{Ar}}_c$, and the value of ${\text{Ar}}_c$ decreases with increasing Re. The inertia-induced rotation arrest causes a nonmonotonic variation of particle alignment with the flow direction, and thence the relative viscosity, with increasing Ar, for a fixed Re. The relative viscosity first decreases, with increasing Ar due to the increasing alignment (on average) of tumbling particles; however, rotation arrest leads to a subsequent increase in the relative viscosity for $\text{Ar}>{\text{Ar}}_c$. This nonmonotonic variation persists over the entire range of Re and Ar examined here. For dense suspensions containing multiple particles, with increasing Ar, particles align more with the flow, but the orientation becomes almost constant when Ar is greater than a threshold ${\text{Ar}}_t$. Smaller values of ${\text{Ar}}_t$ are observed for higher Re. Meanwhile, ${\eta }_r$ decreases due to particle alignment for $\text{Ar}<{\text{Ar}}_t$ and then increases due to high particle-particle interaction for $\text{Ar}>{\text{Ar}}_t$. Further, the contributions of stresslet ($S$), particle acceleration stress ($P$), and Reynolds stress ($R$) on ${\eta }_r$ and the first normal stress difference $N_1$ are analyzed. In addition to the major contribution of stresslet, Reynolds stress contributes more as Ar increases at high Re. In addition, the microstructure and the probability density functions of lateral velocity $\left(U_y\right)$ and angular velocity (${\omega }_p$) are also analyzed. Our results may be helpful to understand the rheological properties of nonspherical particle suspensions.

In this study based on direct numerical simulations (DNS) of homogeneous bubbly flows, an analysis of velocity fluctuations is performed and a methodology for the development of a bubble-induced agitation (or pseudoturbulence) model is described. This process is based on the separation of two phenomena causing velocity fluctuations in the liquid: the agitation resulting from wakes and their collective interactions [wake-induced agitation (WIA)], which is our main focus, and the nonturbulent fluctuations resulting from averaged wakes and potential flows around bubbles [potential flow and averaged wake fluctuations (PWFs)]. We run DNS of fixed bubbles, with random spatial distribution, and compare the results to free-bubble simulations in order to build a model for those phenomena. The simulation of motionless bubbles allow the decomposition of the Reynolds stress transport equation to study WIA and PWFs separately. Then the main characteristics of bubbly flows are analyzed. The signature of an energy conversion from wake kinetic energy (PWFs) to turbulent kinetic energy (WIA) is observed, revealing the importance of nonlinear interactions and transfers between PWFs and WIA. A first proposal of model is made, which gives satisfactory results on our database for a wide range of bubble Reynolds numbers and is consistent with experimental observations. It is operational and can be implemented and assessed in an averaged code.

Under the assumptions that the random sweeping decorrelation hypothesis applies and that the velocity statistics are near Gaussian, the logarithmic variation of high-order moments of longitudinal velocity with distance from a boundary in the inertial region (where the logarithmic law holds for the mean longitudinal velocity) is explained by the existence of a $-1$ power law in the longitudinal velocity spectrum. During the idealized horizontal planar array study for quantifying surface heterogeneity, measurements and profiles of longitudinal velocity were collected within the first meter from the surface under mild atmospheric thermal stratification. These measurements show good agreement with the proposed theory. Further investigation into the validity of the random sweeping decorrelation hypothesis reveals that it is not strictly valid across all scales but can be viewed as operationally viable due to inherent cancellation in its interaction terms. More importantly, deviations from the random sweeping decorrelation hypothesis predictions appear consistent across the logarithmic region and captured by a quasiconstant, suggesting possible avenues for correction in the modeling of high-order moments.

The stability of the interface between a low-viscosity fluid and a granular medium in a horizontal rotating cylinder is experimentally studied. We consider a moderate rotation when heavy granules are able to form an annular layer near a cylindrical wall under the action of centrifugal force. The gravitational force acting on the particles of the granular material fluidizes the granular bed and induces the rotation of the particles at the interface with a velocity different from that of the rotating fluid. The effect of gravity can be characterized by the ratio of the gravitational force to the inertial centrifugal force $\mathrm{\Gamma }\equiv \frac{g}{{\left(2\pi f\right)}^{2}a}$, and it increases with the decrease of the cylinder rotation rate. The observations revealed previously unobserved regular ripples at the interface in a narrow range of rotation rates. At a sufficiently low rotation rate, a large number of granules become suspended, and regular ripples disappear under the action of gravitational force. In the present study, the geometric characteristics and spatiotemporal dynamics of regular ripples are studied in a wide range of granular bed thickness, and a possible mechanism of the ripple formation is discussed.

An experimental study was conducted to investigate the influence of sphere diameter and Reynolds number on synthetic jet vortex rings impinging on a spherical wall. Laser-induced fluorescence and two-dimensional particle image velocimetry techniques were applied to visualize flow and measure flow velocity, respectively. In this experiment, the stroke length was kept constant $(L=3.6)$, and different diameters ($d/D=1$, 6, and 16) and Reynolds numbers (${\mathrm{Re}}_{sj}=227$ and 682) were analyzed. In addition to flow visualization images and phase-averaged ${\lambda }_{ci}$ fields, the vortex ring trajectories and circulation are presented to reveal the evolution features of the vortex rings. The results demonstrated that the Reynolds number mainly determined the strength and induced ability of the primary vortex ring (PVR) and the sphere-diameter effect was reflected by the expansion distance of the PVR and its separation from the wall boundary layer. It was found that only a secondary vortex ring (SVR) was induced in the case of a small diameter or a low Reynolds number. As the diameter and Reynolds number increased, the PVR expanded continuously along the wall and induced a SVR and tertiary vortex ring. In particular, driven by the curve, the strength of the induced vortex ring decreased with the increase in the sphere diameter.

Smooth muscle-lined organs like the gut, the ureter, and the fallopian tubes transport matter by generating traveling contractile waves. Intestinal peristalsis is characterized by rhythmic trains of shallow, low-amplitude myogenic waves and high-amplitude, lumen-obliterating neurogenic waves. In this paper, we develop a simple analytical Poiseuille-flow model to predict the flow rates induced by these different contractions as a function of all relevant wave parameters, and compare them to a numerical fluid-solid finite element model. We rationalize experimentally observed bolus to-and-fro motion induced by shallow myogenic waves. We show that occluding waves induce considerable bolus mixing due to an upstream vortex. We then investigate the hydrodynamics induced by two waves propagating either in the same direction (colinear) or in opposite directions, as happens in the digestive tract. For colinear waves, we find that the bolus reflux is maximal at a distance between successive myogenic waves close to the one observed physiologically. Colliding waves create a high pressure region that gives rise to rapid fluid flow, high shear stress, and radial mixing upon annihilation. Our paper provides fundamental insight on the fluid dynamics (reflux, propulsion, and mixing) generated by different contraction patterns of the intestine.

Whipping is a peculiar nonaxisymmetric instability experienced by electrified liquid jets and utilized in electrospinning to produce fine polymer fibers; however, it manifests itself in a chaotic and uncontrollable fashion. We impose two perturbations in the form of small mechanical oscillations, orthogonal with each other, to alter and curb instabilities of electrified liquid jets. The oscillations cause transverse positioning disturbance to the nozzle and therefore the initial positioning of the jet. The effects of parameters including the excitation frequency, amplitude, and phase difference of the imposed perturbations and the axial electric field are investigated. The steady helicoidal whipping structure with a linearly growing lateral amplitude in air has been demonstrated, offering a feasible solution for electrospinning to fabricate fibers of uniform thickness. Furthermore, the superposition of two sinusoidal orthogonal perturbations enables deposition of complex patterns, such as Lissajous curves.

The draw resonance effect appears in fiber drawing processes when the draw ratio, defined as the ratio between the take-up and the inlet velocities, exceeds a critical value. In many cases, inertia, gravity, and surface tension cannot be neglected, and a model combining all these effects is necessary in order to correctly describe the physics of the phenomenon. Additionally, it is also known that cooling can have a highly stabilizing effect on the draw resonance instability. However, a detailed analysis encompassing the effect of inertia, gravity, surface tension, and temperature is still lacking. Due to a destabilizing effect induced by geometry in the heat equation, we first show that the maximum critical draw ratio for fiber drawing can be two orders of magnitude lower than the one for the film casting problem when the heat transfer coefficient is assumed constant. By introducing a scaling making the fiber aspect ratio an independent parameter, we next show that the high value of the critical draw ratio encountered in industrial applications could be rationalized only if we consider that the heat transfer coefficient is not constant but depends on both the velocity and the cross-section area of the fiber. Within this framework, we show how the practical stability window is affected by the five control parameters: the draw ratio, the fiber aspect ratio, the inlet temperature, the convective heat transfer coefficient, and the stiffness of the non-homogeneous ambient temperature. We finally discuss the influence of radiative heat transfer on the stability.

While landing, birds often perform a perching maneuver, which involves pitching their wings upward while decelerating to a complete stop. This study is motivated by the observation that some birds fold their wings to create a wing sweep during such perching. The objective of this study is to find out whether such a wing sweep helps during a perching maneuver. We use two flat plates, one with a sweep and another without any sweep, and consider a deceleration maneuver where both of them decelerate to stop from Reynolds number $\text{Re}=13000$. We consider two cases: one, where the wings undergo only heaving, and two, where the wings perform both heaving and pitching. The latter maneuver was designed to mimic perching. By performing experiments and simulations, we compare the temporal evolution of the instantaneous forces and the vortex dynamics of both these plates. We show that during a major part of the deceleration, the instantaneous lift forces are higher in the case of the plate with sweep compared to the plate with no sweep during both kinematics. Our results indicate that the higher lift in the swept plate case was contributed by a stable leading-edge-vortex (LEV) which remains attached to the plate. This increase in stability was contributed by the spanwise vorticity convection caused by a distinct spanwise flow on the swept plate, as revealed by the numerical simulation. We also show that combined pitching and heaving resulted in higher force peaks, and the forces also decayed at a faster rate in this case compared to the heave-only case. Finally, by using an analytical model for unsteady flows, we prove that the higher lift characteristics of the swept plate were entirely due to higher circulatory forces.

We investigate the global frequency selection of two-dimensional vortex shedding in the flat plate wake. The analysis is based on the mean-flow velocity profiles obtained from experimental measurements carried out for two values of Reynolds number, 1850 and 3350, which are based on the plate thickness and the free-stream velocity. Two different trailing edge geometries of the flat plate are considered in this study: blunt and circular. By performing local spatiotemporal analyses on the measured mean-flow velocity profiles, we estimate the global shedding frequency of the flow. This is in excellent agreement with the shedding frequency measured experimentally. To complement the study, we carry out a low-dimensional modeling based on the proper orthogonal decomposition (POD) of the flow fields which is novel for flat plate wakes. We observe that a model based on only two POD modes produces an accurate estimate of the global shedding frequency. Our results also highlight the role of the interaction strength between the mean flow and the higher harmonics thereby experimentally supporting the theoretical criterion outlined in Sipp and Lebedev [J. Fluid Mech. 593, 333 (2007)].

Flow-induced fluttering has a significant role in aircraft stability, renewable energy extraction, animal locomotion, and many other applications. While being a ubiquitous phenomenon, the control of the flutter response has been primarily limited to simplified systems and, often, with the help of linear inviscid flow theories. In this paper, we numerically investigate how the plunging response of a foil can be regulated using an active flap to improve structural safety or enhance the energy extraction efficiency of the foil with a tightly coupled fluid-structure interaction algorithm. A broad range of foil and flap settings was tested, and their flow dynamics have been investigated. A multiscale modal analysis technique suitable for fluid-structure interaction systems is employed to systematically isolate the active flap-induced and flow-induced modes. It is observed that the competition between these two modes dictates the plunging response of the foil. The active flap can modulate the leading edge vortex shedding with larger flapping amplitude and regulate the foil heaving motion. The ratio of the competing modal energy is proposed to evaluate the control efficacy of the morphing surface, and the onset of the lock-in is associated with the ratio approaching unity. It is shown that the morphing flap is a good candidate for active flow control.

Direct numerical simulations and linear stability analysis are performed to study the three-dimensional electro-thermo-convective (ETC) flow between two parallel plates under a simultaneously applied temperature difference and voltage. Entropy generation analysis and hexagonal pattern analysis are used to illustrate the transient evolution and stationary dissipative structures of an ETC flow. Numerical simulations with a large computational domain are first performed to reproduce the experimentally observed motion pattern under strong unipolar charge injection. The results show that an infinitesimal random perturbation first grows into a rolls pattern, then partially breaks up into polygons, and finally evolves into hexagons after a long period of transition. Linear stability analysis is conducted to obtain the stability criteria (electric Rayleigh number $T_c$ and Rayleigh number ${\mathrm{Ra}}_c$) and the critical wave number $\left(k_c\right)$ of the ETC flow, and these critical values are found to be consistent with the numerically obtained ones. In addition, it is found that the basic features of the numerically obtained ETC hexagonal flow pattern agree with those of the analytically derived cell pattern. By entropy generation analysis of ETC in a periodic region, it is found that the formation of the rolls pattern has a larger total entropy generation and a larger mean-square temperature gradient than the hexagon pattern, which means that the rolls pattern is more stable than the hexagon under this specific simulation condition.

Nonlinear Richtmyer-Meshkov instability and the mixing transition induced by a Mach 1.45 shock and subsequent reshock at an interface between two ideal gases (sulfur hexafluoride and air) with high Atwood number are studied with second-moment analysis using data from high-resolution compressible Navier-Stokes simulations. The analysis first addresses the importance of two second-order moments: turbulent mass flux and density-specific-volume covariance, together with their transport equations. These quantities play an essential role in the development of Favre-averaged Reynolds stress and turbulent kinetic energy in this variable-density flow. Then, grid sensitivities and the time evolution of the turbulent quantities, which include the second moments, are investigated, followed by a detailed study of the transport equations for the second moments, including the Reynolds stress and the turbulent kinetic energy with well-resolved data before reshock. After reshock, budgets of the same but large-scale turbulent quantities are studied with the effects of the subfilter-scale stress taken into account. The budgets of these large-scale quantities are shown to have an insignificant influence from the numerical regularization. Finally, the effects of the subfilter-scale stress on the budgets of the large-scale turbulent quantities with different degrees of filtering are also examined.

We propose a scaling law for the onset of turbulence in pipe flow of neutrally buoyant suspensions. This scaling law, based on a large set of experimental data, relates the amplitude of the particle-induced perturbations $\epsilon$ to the critical suspension Reynolds number ${\text{Re}}_{s,c}$. Here $\epsilon$ is a function of the particle-to-pipe diameter ratio and the volume fraction of the suspended particles, $\epsilon ={(d/D)}^{1/2}{\varphi }^{1/6}$. ${\text{Re}}_{s,c}$ is found to scale as ${\epsilon }^{-1}$. Furthermore, the perturbation amplitude allows a distinction between classical, intermediate, and particle-induced transitions.

Multiphase flows are challenging systems to study, not only from a fundamental point of view, but also from a practical one due to the difficulties in visualizing phases with similar refraction indices. An additional challenge arises when the multiphase flow to be observed occurs in the submillimetric range. A common solution in experimental fluid dynamics is the addition of a color dye for contrast enhancement. However, added dyes can act as surface-active agents and significantly influence the observed phenomena. In the recently reported Marangoni bursting phenomenon, where a binary droplet on top of an oil bath is atomized into thousands of smaller droplets by Marangoni stresses, visualization is particularly challenging and the use of color dyes is naturally tempting. In this work, we quantify experimentally the significant influence of added methyl blue dye, as well as the obtained contrast enhancement. We find that the reaction of the system to such an additive is far from trivial and brings an opportunity to learn about such a complex phenomenon. Additionally, we propose a simple method to analyze the contrast enhancement as a function of dye concentration, with the aim of finding the minimum concentration of dye for successful imaging in similar systems.

Subaqueous granular collapse on an inclined plane was investigated by considering the effects of particle size and initial concentration in densely packed conditions. This study adopted the multiphase model developed by Lee [J. Fluid Mech. 907, A31 (2021)], which can capture pore pressure feedback (an important mechanism in subaqueous granular flows). A new set of laboratory experiments were performed to validate the multiphase model with four different particle sizes (from fine sand to very coarse sand). Generally, the multiphase model can reproduce all the experimental collapse processes well. Four particle sizes and four initial concentrations were examined numerically. The simulated results reveal that both the volume of the sliding mass in the early stages (initial sliding volume) and the front speed increase with increasing particle size. In addition, increasing the initial concentration reduces the initial sliding volume and front speed. The simulated results suggest that the front speed can be expressed as a function of the initial sliding volume. A simplified force balance analysis was performed to examine why the particle size and the initial concentration affect the initial sliding volume.