We unravel the linear stability properties of an otherwise stagnant ultrathin nonwetting liquid film of thickness $h_o$ coating a spherical substrate of radius $R$. The configuration is known to be unstable due to the competition of the destabilizing van der Waals (vdW) forces and the stabilizing surface tension force. The governing equations of motion written in the Stokes limit of negligible liquid inertia and an accompanying lubrication model are linearized about the zero-velocity base state and decomposed into normal modes to obtain the temporal dispersion relation. Discrete unstable modes are identified and tracked as a function of a capillary number Ca measuring the relative importance of surface tension to vdW forces and the film aspect ratio $\eta =R/h_o$. For small enough values of the capillary number only the first polar mode is unstable, and the corresponding maximum growth rate is shown to be a universal function of $\eta$. Lubrication theory is seen to provide a good quantitative prediction of the film stability properties for $\eta \gg 1$.

Active flow control can achieve substantial performance gains and meet the challenges of next-generation air vehicles and energy-harvesting devices. The use of active flow control techniques with the moving flap or morphing surfaces has been shown to be a viable path to regulating the flow-induced vibration of the foil. However, due to the complex nature of flow over morphing surfaces, all physical phenomena are intertwined, which prevents a clear understanding of the underlying flow physics and, therefore, a successful design of a controlling action to optimally modify them. In this research an active flow control framework with the model predictive control theory is proposed to modulate the flow-induced flutter of a foil using the morphing flap surface. The geometrically weighted dynamic-relevant modes are used to build surrogate models to achieve rapid model-based active control of complex systems. It is shown that the flap is capable of both facilitating and eliminating fluid-induced vibrations by regulating the lift forces exerted on the foil. Furthermore, the control framework provides full knowledge of how the structure modifies the flow and has the potential to identify the ambient environmental change simultaneously.

In this study we investigate stably stratified channel flow (SCF) between two solid walls, focusing on its transition from fully developed turbulence to the onset of global intermittency, characterized by the coexistence of laminar and turbulent patches in the flow. With direct numerical simulations, we examine this transition across various friction Reynolds ($180<{\mathrm{Re}}_{\tau }<960$) and shear Richardson (${\text{Ri}}_{\tau }$) numbers, parameters that are observed to impact intermittency dynamics. To quantify intermittency, we measure the volume fraction of turbulent patches using enstrophy as a criterion and examine the variation of the turbulent fraction along the wall-normal direction. Our findings reveal that intermittency in SCF can originate independently from either near-wall or midchannel regions, depending on the values of ${\mathrm{Re}}_{\tau }$ and ${\mathrm{Ri}}_{\tau }$. With increased stratification, intermittency originating from both regions may merge across the channel's depth. Particular attention is paid to near-wall intermittency (NWI) and identifying its occurrence boundary within the ${\mathrm{Re}}_{\tau }\text{−}{\mathrm{Ri}}_{\tau }$ parameter space. We assess various dimensionless parameters for their ability to predict NWI, discovering that intermittency consistently occurs when the Nusselt number falls below a critical value of approximately 3.0. To establish the intermittency boundary following this Nusselt number criterion, a Reynolds-averaged Navier-Stokes model is formulated based on a first-order closure scheme. This model proves effective in predicting the occurrence of NWI in SCF in terms of ${\mathrm{Re}}_{\tau }$ and ${\mathrm{Ri}}_{\tau }$. Furthermore, we verify the $\mathrm{Nu}$ scaling recently proposed by Zonta et al. [J. Fluid Mech. 945, A3 (2022)], which leads to an intermittency boundary in the form of ${\mathrm{Re}}_{\tau }^2{\mathrm{Ri}}_{\tau }^{-1}=\text{const}$.

The objective of this paper is to investigate the influence of fluid-structure interaction on the cavity dynamics and the vibrations around a flexible hydrofoil by comparing the experimental results of a rigid hydrofoil. Cavitation behavior, vibrations, and lifts are obtained by a synchronized measured system utilizing a high-speed camera, lift measurement, and a portable laser vibrometer. The nose-up twisting deformation results in an increase in the effective angle of attack, which leads to an increase in cavity length and a reduction of cloud cavity shedding frequency. It also accelerates the transition of the cavitation regimes and shedding mechanism of cloud cavities with the decrease in cavitation number, together with the amplification of vibration velocity, and the suppression of higher-frequency oscillations.

We investigate the physical-space locality of interactions in three-dimensional incompressible turbulent flow. To that, we modify the nonlinear terms of the vorticity equation such that the vorticity field is advected and stretched by the locally induced velocity. This space-local velocity field is defined by the truncated Biot–Savart law, where only the neighboring vorticity field in a sphere of radius $R$ is integrated. We conduct direct numerical simulations of the space-local system to investigate its statistics in the inertial range. We observe a standard $E\left(k\right)\propto k^{-5/3}$ scaling of the energy spectrum associated with an energy cascade for scales smaller than the space-local domain size $k\gg R^{-1}$. This result is consistent with the assumption [Kolmogorov, Dokl. Akad. Nauk SSSR 30, 299 (1941)] made for the space locality of the nonlinear interactions. The enstrophy amplification is suppressed for larger scales $k\ll R^{-1}$, and for these scales, the system exhibits a scaling consistent with a conservative enstrophy cascade.

Janus phoretic particles exploit chemical energy stored in their environment to produce mechanical work on the surrounding fluid and self-propel. These active particles modify and respond to their hydrodynamic and chemical environments, thus providing them with a sensibility to external flows and other particles. These chemical and hydrodynamic interparticle interactions are known to lead to nontrivial collective behavior within such biological or synthetic active suspensions (e.g., cluster formation of phoretic particles or bacterial swarming). Recent experiments and analysis have demonstrated that the response of active suspensions to shear flows is nontrivial and can, in fact, lead to significant reductions in viscosity due to the energy conversion at microscopic scales. In this work we numerically analyze using a continuum kinetic model the dynamics and response to shear of dilute and confined suspensions of chemotactic phoretic particles that reorient and drift toward the chemical solutes released by their neighbors. We show that a 1D transient steady distribution driven by the effect of confinement is a common feature for the confinement and shear rate intensities considered. This 1D state is stable for strong confinement and thus observed in the long-term dynamics in sufficiently narrow channels. For wider channels, the transient state becomes unstable to streamwise perturbations due to the chemotactic instability, leading to the formation of particle aggregates along the channel's walls. Their relative arrangements and dynamics are determined by the relative influence of shear intensity and chemotaxis and critically condition the suspension's dynamics and particle-induced flows. In a second step, the feedback effect on the flow and effective viscosity of the self-organized suspension is considered. We show that the induced flow and, consequently, its rheological behavior strongly depend on the self-organization regime, and therefore on the interplay of confinement, shear, and chemotaxis.

We present planar time-resolved particle image velocimetry (PIV) measurements of flow in the streamwise surface-normal plane of a NACA 0012 airfoil at chord-based Reynolds number ${\mathrm{Re}}_c=7\times {10}^4$. The angles of attack $\alpha ={13}^{\circ }$ and ${15}^{\circ }$ correspond to transient stall and deep stall flow regimes, respectively. A Poisson solver is utilized to reconstruct the instantaneous planar pressure fields from the PIV with satisfactory comparison in the mean pressure compared with dynamically matched Reynolds-averaged Navier-Stokes (RANS) simulations. Using the proper orthogonal decomposition (POD), a systematic reduced-order reconstruction of the velocity fields and subsequent pressure fields is used to quantify the required number of velocity modes to achieve a desired accuracy in the instantaneous pressure. Further, a Galerkin projection of the Poisson equation onto the POD subspace is used as a framework to identify the relative contribution of each velocity mode on the resulting pressure field via quadratic stochastic estimation (QSE). In both cases, the zeroth mode (corresponding to the mean) is of leading-order importance. In addition, a tendency of the zeroth mode to interact with vortex-shedding modes is identified.

Fluid-structure interactions between active and passive components are important for many biological systems to function. A particular example is chromatin in the cell nucleus, where ATP-powered processes drive coherent motions of the chromatin fiber over micron lengths. Motivated by this system, we develop a multiscale model of a long flexible polymer immersed in a suspension of active force dipoles as an analog to a chromatin fiber in an active fluid—the nucleoplasm. Linear analysis identifies an orientational instability driven by hydrodynamic and alignment interactions between the fiber and the suspension, and numerical simulations show activity can drive coherent motions and structured conformations. These results demonstrate how active and passive components, connected through fluid-structure interactions, can generate coherent structures and self-organize on large scales.

Microorganisms, such as Escherichia coli, are known to display upstream behavior and respond rheotactically to shear flows. In particular, E. coli suspensions have been shown to display strong sensitivity to spatial constrictions, leading to an anomalous densification past the constriction for incoming fluid velocities comparable to the microoganism's self-propulsion speed. We introduce a Brownian dynamics model for ellipsoidal self-propelling particles in a confined channel subject to a constriction. The model allows us to identify the relevant parameters that characterize the relevant dynamical regimes of the accumulation of the active particles at the constriction, and clarify the mechanisms underlying the experimental observations. We find that particles are trapped in butterfly-like attractors in front of the constriction, which is the origin of the symmetry breaking in the emerging density profiles of active particles passing the constriction. In addition, the probability of trapping and thus the strength of asymmetry are affected by size of the particles and geometry of the channel, as well as the ratio of fluid velocity to propulsion speed.

We study transition to chaotic advection in the fluid motion across a plane rectangular domain with periodic boundary conditions. The flow, induced by a combination of time-independent force with constant pumping in both spatial directions, is equivalent to dynamics on the surface of a 2-torus. At considered force amplitudes, the stationary flow pattern includes the global drift and the localized vortices encircled by separatrices of stagnation points. If the Eulerian velocity field is time-independent and rotation number on the torus, controlled by pumping intensities, is irrational, then the power spectrum of the Lagrangian observables is singular continuous (fractal) and the autocorrelation function of velocity displays no ultimate decay. As the increase of the force destabilizes the stationary flow and replaces it by periodically oscillating velocity field, singularities in the numerically evaluated spectrum disappear, whereas temporal correlations vanish after a certain time interval.

The prediction of gust loads during atmospheric flight can aid in the design, assessment and certification of aircraft, and can also enhance the reliability of low-inertia vehicles which are susceptible to large atmospheric disturbances. In this paper, we explore how the vorticity distributions shed from a wing's leading and trailing edges affect its lift history during a large-amplitude transverse gust encounter. Emphasis is placed on comparing experimental lift transients and vorticity distributions with those predicted by Küssner's transverse gust model. Wings with both sharp and blunt leading edges are towed through a vertical jet in a water towing tank to simulate the wing-gust encounter. It is observed that while the quasisteady circulation of Küssner's model increases, its lift prediction provides a good first-order approximation of the experimental lift transient across a large range of gust ratios and Reynolds numbers. The success of the inviscid model is traced to its ability to capture the circulatory characteristics of the viscous separated flow. Its performance deteriorates in the latter phases of the encounter, when the quasisteady circulation decreases. This is shown to be due to a fundamental difference in the lift reduction mechanism between the model and the experiments, resulting in contrasting shed vorticity distributions. Namely, the lift drop-off in the model is governed by the delayed response to a negative change in its quasisteady bound circulation, while in the experiments it is governed by the detachment of the leading-edge vortex and the persistent shedding of negative circulation into the wake.

We perform linear stability calculations for a jet emerging into an ambient medium of a different viscosity but the same density. These calculations are intended to isolate the effects of viscosity variation alone. We conduct a systematic study of the effect of ambient-to-jet viscosity ratio, jet Reynolds number, and velocity profile specified by the shear layer thickness, thickness over which the viscosity change occurs, and radial shifts in velocity profiles on the growth of axisymmetric and helical modes. Additional terms in the disturbance kinetic energy equation that represent the coupling between the velocity fluctuations and the viscosity field are shown to be responsible for the additional destabilization. Radial shifts in velocity profile that represent real effects likely to be encountered in experiments are shown to be strongly destabilizing. In all cases the temporal growth rates of axisymmetric and helical mode are very close, except at low Reynolds numbers. Spatiotemporal analysis suggests that for sufficiently large ambient viscosity, low-viscosity jets become absolutely unstable. Over a wide range of parameters, two modes of absolute instability exist simultaneously, with an axisymmetric mode predicted to dominate a helical mode. Over a certain narrower space, the helical mode dominates. The transition boundary for absolute and convective instability is compared with recent experiments, and the results are found to be in reasonable agreement for the transition of the helical mode, when velocity profiles are used that correspond to the similarity solution for development of the boundary layer under a spatially variable viscosity.

Generalized network models (GNMs) serve as powerful tools, bridging the intricate gap between pore- and continuum-scale multiphase transport in porous media. An essential step in the development of these models is to extract pore-corner networks from actual porous materials. In this paper, we present a pore-corner-network extraction method involving two steps. In the first step, pore networks, comprising pore bodies interconnected by pore throats, are extracted based on the omnidirectional Euclidean distance concept. Subsequently, corners within each distinct pore unit, consisting of a pore body and half of the connected pore throats, are identified by sweeping the pore unit with a sphere. The radius of the sphere corresponds to the minimal corner radius within the cross-sections at the centers of pore throats within the pore unit. To extract pore-corner networks from three-dimensional images of porous materials efficiently, we introduce a domain decomposition approach. In this approach, the porous material of interest is divided into multiple subdomains, each enveloped by a protective layer. To validate our proposed extraction method, a GNM is developed to simulate evaporation in a porous medium composed of packed spherical beads. This model is systematically compared with microcomputed tomography experimental data. Encouragingly, the modeling results are in good agreement with the experimental data, particularly in terms of the variation of liquid distribution over time. Our proposed extraction method not only contributes to disclosing the structures of pores and corners in real porous media but also benefits the development of GNMs that can be employed to understand in detail the multiphase transport in porous media from the pore-scale perspectives.

In turbulent flows, energy production is associated with highly organized structures, known as coherent structures. Since these structures are three dimensional, their detection remains challenging in the most common situation in experiments, when single-point temporal measurements are considered. While previous research on coherent structure detection from time series employs a thresholding approach, either in spectral or temporal domain, the thresholds are ad hoc and vary significantly from one study to another. To circumvent this issue, we introduce the level-crossing method and show how specific features of a turbulent time series associated with coherent structures can be objectively identified, without assigning a priori any arbitrary threshold. By using two wall-bounded turbulence time-series datasets (at a Reynolds number of ${10}^4$), we successfully extract through level-crossing analysis the impacts of coherent structures on turbulent dynamics and therefore open an alternative avenue in experimental turbulence research. By utilizing this framework further, we discover a metric, characterized by a statistical asymmetry between the peaks and troughs of a turbulent signal, to quantify inner-outer interaction in wall turbulence. Most importantly, through phase-randomized surrogate data modeling, we demonstrate that the level-crossing statistics are quite sensitive to the nonlinear dependencies in a turbulent signal. Physically, this finding implies that the large-scale coherent structures modulate the near-wall turbulent dynamics through a nonlinear interaction associated with low-speed streaks, a mechanism not identifiable from spectral analysis alone. Moreover, a connection is established between extreme value statistics and level-crossing analysis, thereby allowing additional possibilities to study extreme events in other dynamical systems.

In this work, we study a pressure-driven flow of a non-Newtonian electrolyte through a wavy microchannel whose walls are covered with an electrically charged poroelastic layer that models the endothelial glycocalyx layer (EGL). The focus of our work is on the analysis of the electrical and mechanical effects of pressure-driven flow and induced streaming potential. The electrolyte is a viscoelastic fluid that obeys the Phan-Thien-Tanner rheological model. The coupled equations that describe the dynamics of the fluid phase, the elastic EGL, and electric fields are solved asymptotically using the domain perturbation method for the wavy-wall microchannel. The governing equations are nondimensionalized, which depend on dimensionless parameters that characterize the physical phenomenon: the Weissenberg number Wi, the Hartmann number $\chi$, the viscosity ratio ${\mu }_r$ of the fluid in the EGL (assumed as Newtonian) and in the lumen (assumed viscoelastic), and the dimensionless electric charge and thickness of the EGL, $c_s$ and $\mathrm{\Lambda }$, respectively. The viscoelastic fluid's shear stresses and induced streaming potential are lower in magnitude when compared to Newtonian fluids. According to the results, it may be possible to use the streaming potential as a biocompatible and safe energy source for different medical devices and biosensors.

This paper presents a combined stability analysis and numerical investigation of Rayleigh-Bénard convection in a planar dielectric liquid layer subjected to the simultaneous action of Coulomb and buoyancy forces. For the first time, Rayleigh-Bénard convective instability with electric conduction is considered. Fully coupled set of governing equations for fluid flow, heat transfer, and electrostatics are solved using the finite-volume method (FVM) framework of OpenFOAM. The fluid layer is destabilized under the combined action of buoyancy and Coulomb forces. Rayleigh number $\left(\text{Ra}\right)$ and the Conduction number $\left(C_0\right)$ are the control parameters for fluid flow. Distributions of physical variables in the hydrostatic state are derived. Modal stability analysis is performed to establish the neutral stability curve in the $\text{Ra}\text{−}{C}_0$ plane. Present numerical results are compared with the results of stability analysis. The flow and heat transfer characteristics in the $\text{Ra}\text{−}{C}_0$ parameter space are analyzed. The present study provides deeper insights into the electro-thermo-convective flow mechanism due to the EHD conduction phenomenon occurring at weak and medium electric fields. The results of this study can serve as a benchmark to design flow systems subjected to combined gradients of thermal and electric fields.

We investigate theoretically the stability of thermo-capillary convection within a droplet when subject to localized heating from below. To model the droplet, we use a mathematical model based on lubrication theory. We formulate a base-state droplet profile, and we examine its stability with respect to small-amplitude perturbations in the azimuthal direction. Such linear stability analysis reveals that the base state is stable across a wide parameter space. We carry out transient simulations in three spatial dimensions: the simulations reveal that when the heating is slightly off-centered with respect to the droplet center, vortices develop within the droplet. The vortices persist when the contact line is pinned. These findings are consistent with experimental studies of locally heated sessile droplets.

We present the spectral analysis of three-dimensional dynamics of an elastic filament in a shear flow of a viscous fluid at a low Reynolds number in the absence of Brownian motion. The elastica model is used. The fiber initially is almost straight at an arbitrary orientation, with small perpendicular perturbations in the shear plane and out-of-plane. To analyze the stability of both perturbations, equations for the eigenvalues and eigenfunctions are derived and solved by the Chebyshev spectral collocation method. It is shown that their crucial features are the same as in the case of the two-dimensional elastica dynamics in shear flow [Becker and Shelley, Phys. Rev. Lett. 87, 198301 (2001)] and the three-dimensional elastica dynamics in the compressional flow [Chakrabarti et al., Nat. Phys. 16, 689 (2020)]. We find a similar dependence of the buckled shapes on the ratio of bending to hydrodynamic forces as in the simulations for elastic fibers of a nonzero thickness [Słowicka et al., New J. Phys. 24, 013013 (2022)].

We generalize kinetic theory of inelastic spheres to uniaxial, nonspherical grains by including the orientational tensor as a state variable. The theory has three phenomenological parameters, with one parameter to account for the dependency of the stresses on the orientation, which is exactly one for frictionless cylinders, and the other two parameters to predict the orientational tensor. We model the competition between the alignment induced by shearing and the misalignment due to collisions in the evolution law for the orientational tensor. The theory can predict a significant reduction in the viscosity in response to alignment measured in discrete simulations of homogeneous shear flows of prolate and oblate frictionless cylinders.

Molecular tagging is used to study the dispersion and deformation of patterns written in turbulent air. The writing is done by fusing ${\mathrm{O}}_2$ and ${\mathrm{N}}_2$ molecules into NO in the focus of a strong ultraviolet laser beam. By crossing several of these laser beams, patterns that have both small and large scales can be painted. The patterns are visualized a while later by inducing fluorescence of the NO molecules with a second UV laser and registering the image. The width of the lines that make the pattern is approximately $50\mu \mathrm{m}$, a few times the Kolmogorov length $\eta$, the smallest length scale in turbulence, while the largest size of the patterns ($\approx 4\mathrm{mm}$) is inside the inertial range of the used turbulent jet flow. At small scales molecular clouds disperse under the joint action of molecular diffusion and turbulence. The experiments reveal this highly nontrivial interaction. At inertial-range scales ($\approx 200\eta$) we verify the Batchelor dispersion of objects whose size is inside the inertial range. Patterns are compressible objects and spontaneously develop concentration fluctuations. We show for the first time the nontrivial statistical properties of these fluctuations. Finally, we use the information in written and deformed lines to quantify turbulent intermittency, obtaining results that agree with the established scaling anomaly of velocity structure functions.