The evolution of jets and vortices induced by a pair of symmetrically placed plasma actuators is investigated under various modulation frequencies using two-dimensional, time-resolved particle image velocimetry. Despite similar time-averaged jet shapes, the peak jet velocity increases with the modulation frequency and eventually reaches a plateau. Due to the combined effects of the vortex induction and the modulation frequency, the high-velocity region concentrates near the actuator tip at higher frequencies and shifts downstream at lower frequencies. Compared to the continuous plasma jet, modulated jets demonstrate superior electro-hydrodynamic conversion efficiency and significantly enhanced lateral spreading, leading to increased momentum flux and entrainment coefficient. Despite frequency-induced variations, all jet velocity profiles collapse in the far field when properly non-dimensionalized. The modulation frequency governs the formation of three distinct plasma-induced vortical patterns, including vortex-free, leapfrogging, and multi-vortex, which in turn yield different turbulent kinetic energy distributions. The streamwise trajectories of vortices collapse when scaled by the convection time for three flow patterns. Estimated vortex-induced velocities account for approximately half of the total jet velocity at high modulation frequencies, confirming the crucial role of vortex dynamics in the plasma jet development. These findings highlight the importance of the modulation frequency in optimizing jet performance and actuator placement for effective flow control.

Precessional flows arise in a precessing cylinder or in a rotating cylinder with a precessing tilted top. Alternatively, a similar flow can be observed in a partially filled rotating cylinder tilted with respect to the vertical, since the free surface undergoes precession in the cylinder's reference frame. Here, we unify the various models developed for these three configurations. The base flow consists of a superposition of inertial modes (Kelvin modes) with an azimuthal wave number $m=1$. Each Kelvin mode reaches resonance when the cylinder height is a multiple of half its wavelength, leading to complex dynamics even under weak precessional forcing. In the inviscid linear model, the amplitude of the Kelvin mode diverges at resonance. However, its saturation can be accurately predicted by incorporating both viscous and nonlinear effects, in good agreement with experimental and numerical results. For strong precessional forcing, the resonant Kelvin mode becomes unstable due to a triadic instability involving two additional Kelvin modes whose azimuthal wave numbers differ by 1. This nonlinear interaction enables an analytical prediction of the growth rate and critical onset amplitude, with results that closely match experiments and simulations. Finally, we discuss the mixing efficiency of precessional flows based on numerical simulations using nondiffusive tracers and experiments using a diffusive dye.

For a sufficient concentration of long-chain polymers in a Newtonian solvent, turbulent wall-bounded flows reach a universal state known as maximum drag reduction (MDR). Through direct numerical simulations of MDR pipe flows at ${\mathrm{Re}}_{\tau }=310$ and $\mathrm{Wi}={10}^4$, we show that the wall-normal kinetic energy flux characterizing Newtonian wall-bounded turbulence is suppressed, and that polymers primarily sustain velocity fluctuations. We derive an expression for the mean velocity profile that aligns with experimental data and is no longer dependent on characteristic quantities of wall-bounded turbulence. For a sufficiently high concentration, MDR flows achieve an asymptotic universal profile, $U_{\alpha }=ln{y}_{\alpha }$, consistent with Virk's law at large Reynolds number.

The low-frequency linear dynamics of a family of incompressible, pressure-gradient (PG)-induced turbulent separation bubbles (TSBs) are studied by means of modal and nonmodal linear analysis. The investigated data consist of Reynolds-averaged Navier-Stokes simulations and experimental measurements that are used for validation purposes. The TSBs are generated on a flat plate by means of adverse (APG) and favorable (FPG) PGs, such that the family of TSBs consists of three distinct cases—small, medium, and large—where the size of the separation bubble is controlled by the strength and location of the maximum APG and FPG. The investigation of the linear dynamics of the family of TSBs reveals two significant results: First, the low-frequency receptivity of the TSB flow, characterized by the low-pass filter behavior of the optimal gain, remains unaffected by the absence of a closed TSB in the time average for the small-sized TSB (small-bubble case). Second, although the large TSB flow is predicted to be globally unstable for a set of spanwise wavenumbers, the amplifier dynamics of the flow appear to dominate over the oscillator dynamics, as evidenced by the persistence of low-frequency unsteadiness in the experimental large-bubble flow. These results suggest that a common physical mechanism, characterized by the stationary, weakly damped global mode, governs the low-frequency unsteadiness across the entire family of TSBs, irrespective of their separation extent or stability characteristics.

Material assemblies at liquid-fluid interfaces on the microscale control the macroscopic behavior of multiphase processes by reducing interfacial tension, generating Marangoni stresses and introducing surface viscoelasticity. These interfacial effects directly impact processes such as energy extraction, drug formulation, and advanced material synthesis. Here we experimentally investigate the dynamics of falling silica dispersion droplets in a stationary oil phase containing surfactants. While oblate-prolate oscillations of Newtonian droplets are well documented for clean interfaces, we report that the in situ formation of a highly condensed interfacial material rapidly transforms the droplet into an oblate shape and attenuates its oscillations. The observed suppression of oscillations is consistent with theoretical predictions for droplets submerged in immiscible fluids with inextensible interfaces. These results highlight the impact of interfacial viscoelasticity on falling droplet dynamics, driven by the in situ formation of a viscoelastic emulsion layer at the nanoparticle dispersion-micellar solution interface.

In this paper, thermal-slip coefficients in slip boundary conditions of the Stokes equation are derived using the generalized slip-flow theory, with special interest in the role of near-wall potential in micro- and nanoscale flows. As the model of fluids and fluid-solid interaction, we employ the model Boltzmann equation for dilute gases and the diffuse-reflection boundaries with near-wall potential, respectively. It is found that, when the mean free path of gas molecules and the effective range of potential are of the same order of magnitude, the thermal-slip boundary condition can be derived in the near-continuum limit. In the derived slip-flow theory, the thermal-slip coefficient and the boundary-layer corrections (i.e., Knudsen-layer corrections) are determined by solving the kinetic boundary-layer problems (i.e., Knudsen-layer problems) that include external- force terms and inhomogeneous terms both driven by the potential. As an application of the slip-flow theory, thermo-osmosis between two parallel plates with uniform temperature gradients is analyzed. The results of the slip-flow theory are validated by comparing them with those of the direct numerical analysis of the same problem. Furthermore, it is found that thermo-osmosis and thermal slip on the plates are significantly affected by the features of the near-wall potential; even the gas-flow direction can be reversed when the near-wall potential is repulsive. Such a flow reversal is qualitatively similar to thermo-osmosis in liquids reported in existing molecular dynamics simulation.

Suspended particle transport is inherent in a wide range of industrial and environmental flows, from energy generation to manufacturing and from marine to atmospheric systems. Such flows are inherently stratified where varying concentration of particulates changes the mean density of the fluid; however, the role of stratification on particle suspension is poorly understood. Here the suspension of sediments in a channel (plane Poiseuille) flow is resolved using numerical simulation where the flow is stably thermally stratified and the particles passive. This set up enables quantification of stratification controls sediment transport processes. Sediment suspension is resolved for settling velocities of $V_s=0.005, V_s=0.01$, and $V_s=0.02$, made dimensionless by the friction velocity $u_{\tau }$. Our results show that stratification generates flow-scale mixing processes, which invalidate extant models of sediment suspension that have been used for over 100 years. For stratified flows, the dimensionless collapse of flow scalars and turbulent statistics is poor near the core of the channel, where large concentration gradients coincide with large-scale mixing events. Here the differences between vertical turbulent diffusivities of sediment and temperature increase with increasing $V_s$, reaching $15\%$ for $V_s=0.02$. Discrepancies arise due to a breakdown of the linear gradient diffusion hypothesis. Predictions using the gradient diffusion hypothesis are expected to worsen with increasing settling velocity, indicating that classical models poorly predict dilute particle transport in strongly stratified flows, which are common in a range of environmental and industrial settings. Further, in stratified flows a feedback loop is established that generates strong buoyancy forces in the core of the duct, having the profound impact of building a self-reinforcing two-layer sediment concentration profile. These results highlight that classical sediment transport models may underpredict the amount of turbulent mixing, and therefore the capability of flows to suspend material, where flow-scale mixing events occur. They further reveal mechanisms for the formation of a barrier to mixing which significantly reduces suspended load capacity in flows with an internal velocity maximum, such as ducts, pipes, gravity currents, and jets.

One of the most widespread canonical devices for fluid mixing is the T-shaped mixer, in which two opposing miscible liquid streams meet at a junction and then mix along a main channel. Laminar steady and time-periodic flows in T-shaped mixers have been thoroughly studied, but turbulent flows have received much less scrutiny despite their prevalence in applications. We introduce here a novel experimental setup with a hydraulic diameter of 4 cm that enables the optical study of turbulent mixing at small scales. Using this setup, we perform two-dimensional particle image velocimetry and planar laser-induced fluorescence measurements. First, we successfully replicate characteristic flow regimes observed in microscale T-shaped mixers at low Reynolds numbers. We then focus on the turbulent regime and characterize the turbulent kinetic energy and dissipation along the mixing channel. Further, we measure the scalar concentration variance and its corresponding probability density function and spectra. The latter exhibits an incipient Batchelor scaling. We estimate the mechanical-to-scalar timescale ratio and examine the link between the turbulent velocity and scalar fields. The measurement data are compared with model predictions and correlations used in engineering practice, and with our own direct numerical simulations performed with a spectral-element code.

Inspired by the spontaneous behavior observed in filamentous layers—where the balance between flow-induced drag and structural elasticity dictates the equilibrium streamlined posture of the filaments—we perform a series of large eddy simulations to investigate how filament inclination affects turbulent shear flows developing both above and within a canopy of filaments. We examine six distinct filament inclination angles ranging from $0^{\circ }$ to ${90}^{\circ }$. The in-plane solid fraction and filament length are chosen to achieve a fully dense canopy at zero inclination, and these parameters remain constant throughout our study. By setting a nominal bulk Reynolds number of 6000, we provide a detailed statistical characterization of the turbulent flow. Our findings illustrate distinct changes in the flow regime with varying filament inclination. At lower angles, the canopy remains dense and significantly influences the flow, conforming to a classical canopy-flow regime. However, as the inclination approaches ${90}^{\circ }$, the intracanopy region progressively becomes shielded from the outer flow. Remarkably, at ${90}^{\circ }$ inclination, the flow drag reduces significantly, and the total drag becomes lower than that typically seen in an open, filament-free flow. We document this transition from a canopy-dominated regime to a scenario where the canopy becomes largely sheltered from the outer turbulent flow, highlighting key alterations in intracanopy dynamics as filament inclination increases. Our observations are substantiated by an analysis of the velocity spectra, providing deeper insight into the interactions between the canopy and the developing turbulent boundary layer.

The skewness of the streamwise velocity is an important parameter in turbulent-boundary-layer (TBL) flows and is intrinsically related to the mechanism of quadratic energy transfer between different scales of motion. In this paper, the skewness in both a canonical and actuated zero-pressure-gradient TBL (${\text{Re}}_{\theta }=1770$) is spectrally decomposed via the real part of the bispectrum. This provides the individual triad interactions contributing to the skewness, and their summation is used to obtain partial sums of the skewness as a function of frequency. The canonical TBL investigated has a Reynolds number that is sufficiently low that no naturally occurring energetic large-scale outer structures exist. The skewness spectral decomposition of the canonical TBL is compared to that in which a plasma actuator introduces large-scale vortices into its outer layer. In this manner, actuation is used as a tool to document the influence of imposed outer-layer large-scale structures on the spectral content of skewness. These measurements are compared for a range of representative near-wall ($y^{+}\le 60$) locations. The bispectral results reveal that there is a close correspondence between the dominant triad interaction frequencies and the near-wall structure frequencies, captured using the variable-interval-time-averaging technique. At $y^{+}=15$, the presence of mostly negative peaks within the lower frequency region of the bispectra indicates the existence of ejection-type events active in the near-wall region. The effect of the artificially induced outer large-scale structures is shown to reach the near-wall region. However, the common features in the bispectra and partial bispectral sums that are associated with the streamwise buffer layer vortices remain largely unchanged. This is evidence of their primary role in the skewness at these wall-normal locations. The bispectral results also show that the effect of actuation remains confined around the lines representing the actuation frequency, which is suggestive of the dominance of the linear inner-layer–outer-layer interaction mechanism over nonlinear interaction for the given configuration, Reynolds number, and actuation parameters. The phase-averaged results indicate that, in an actuated TBL, the outer-layer synthetic structures modulate the strength of the near-wall vortices. It is concluded that in both canonical and actuated TBLs, outer-layer structures do not serve as triggers for the near-wall events.

Reduced order models (ROMs) play a critical role in fluid mechanics by providing low-cost predictions, making them an attractive tool for engineering applications. However, for ROMs to be widely applicable, they must not only generalize well across different regimes but also provide a measure of confidence in their predictions. While recent data-driven approaches have begun to address nonlinear reduction techniques to improve predictions in transient environments, challenges remain in terms of robustness and parametrization. In this work, we present a nonlinear reduction strategy specifically designed for transient flows that incorporates parametrization and uncertainty quantification. Our reduction strategy features a variational autoencoder that uses variational inference for confidence measurement. We use a latent space transformer that incorporates recent advances in attention mechanisms to predict dynamical systems. Attention's versatility in learning sequences and capturing their dependence on external parameters enhances generalization across a wide range of dynamics. Prediction, coupled with confidence, enables more informed decision-making and addresses the need for more robust models. In addition, this confidence is used to cost-effectively sample the parameter space, improving model performance a priori across the entire parameter space without requiring evaluation data for the entire domain.

In this paper, turbulent flow through a longitudinally rib-roughened square duct is studied using direct numerical simulation at a nominal bulk Reynolds number of ${\text{Re}}_b^N=4410$. To understand the rib effects on the velocity field, DNS of a smooth-wall duct flow is also performed, which serves as a baseline case of comparison. The influences of longitudinal ribs on the flow structures, statistical moments of the velocity field, and turbulence kinetic energy budget balance are investigated. Through analyses of the streamwise two-point autocorrelation coefficients of the velocity fluctuations and swirling strength, it is found that ribs can effectively disrupt the growth of turbulence structures. In each corner of the smooth and ribbed ducts, secondary flow appears as a pair of counterrotating vortices. However, in the longitudinally ribbed duct flow case, it is interesting to observe tertiary vortex structures which significantly alter the distributions of the viscous and turbulent stresses. Owing to the shearing effects from the ribs, turbulence transport of momentum is substantially enhanced near the rib edges. By examining the third- and fourth-order statistical moments of the velocity field, it is also interesting to observe that sweep and ejection events are intensified and the turbulence is more intermittent near the rib regions.

Colloidal particles at fluid interfaces can enhance the stability of drops and bubbles. Yet, their effect on mass transfer in these multiphase systems remains ambiguous, with some experiments reporting strongly hindered diffusion, while others show nearly no effect, even at near-complete surface coverage. To resolve this ambiguity, we solve the Fick-Jacobs equation for unsteady diffusion, allowing us to treat the particle-laden interface as a locally reduced cross-sectional area for mass transfer. Our numerical solutions reveal two limiting regimes, with the particle layer hindering diffusion only at short times. Guided by analytical solutions for a homogeneous layer with reduced diffusivity, we derive quantitative expressions for the transport regimes and associated transition times for diffusion across the particle layer. This analysis yields a simple criterion for long-term hindrance that accurately distinguishes between conflicting experimental results, providing a unifying framework for mass transfer in particle-laden multiphase systems.

Hydrodynamic interactions driven by particle activity are ubiquitous in active colloidal systems. Although these interactions are strongly influenced by the interfacial actuation mechanism and geometry of the swimming particles, theoretical understanding of how these microscopic design parameters govern collective dynamics remains limited. Here we investigate the collective dynamics of oblate spheroidal microswimmers. Using an approximate kinetic theory and corroborating boundary element method calculations, we demonstrate that breaking symmetries in both particle shape and interfacial actuation enables the emergence of dynamically stable immotile $n$-particle clusters. At larger scales, the clustering process drives the system into a dynamically arrested absorbing state characterized by disordered class I hyperuniform structures. Our analysis highlights the essential role of cluster-sourced long-range flows in establishing this long-range order. Overall, our findings reveal a promising, purely hydrodynamic mechanism for hierarchical self-organization in active matter systems, introducing a strategy for engineering multifunctional hyperuniform materials.

Using discrete simulations of granular flows on smooth inclines bounded by smooth lateral walls, we confirm recent findings indicating that the local effective wall friction can be described by a simple law involving a single Froude-like dimensionless number—defined as the ratio of the slip velocity to the square root of the wall pressure. This relationship has been validated for a fixed gap width $W$ across a wide range of inclination angles and mass hold-up values. Remarkably, it holds in both steady, fully developed regimes and in unsteady flow conditions. We also establish a similar empirical law governing the local packing fraction at the wall. Notably, the Froude number proves to be a reliable proxy for the ratio of the slip velocity at contact to the square root of the granular temperature. Together, these relationships for wall friction and packing fraction provide general boundary conditions for granular flows confined by flat frictional surfaces. Our results also highlight the significant influence of lateral walls, which induce pronounced differences between the velocity profiles near the walls and those at the flow center. Furthermore, the tensorial form of the $\mu \left(I\right)$ rheology generally fails to capture the flow behavior, except near the centerline. In contrast, the kinetic theory of granular gases offers a more suitable framework for describing the observed flow dynamics. Finally, we exploit spatially averaged versions of the wall friction and packing fraction laws to construct a depth-averaged model that successfully predicts the basal-averaged velocity of granular flows on a flat frictional base, laterally bounded by flat frictional walls.

Empirical observations show that turbulence exhibits a broad range of scaling exponents, characterizing how the velocity gradients diverge in the inviscid limit. These exponents are thought to be linked to singular solutions of the Euler equations. In this work, we propose a dynamic approach to construct concept of these solutions directly from the fluid equations, using a reversible framework and introducing the efficiency $\mathcal{E}$, a nondimensional number that quantifies the amount of energy stored within the flow due to an applied force. To circumvent the computational burden of tracking singularities at finer and finer scale, we test this approach on fluids on log-lattices, which allow for high effective resolutions at a moderate cost, while preserving the same symmetries and global conservation laws as ordinary fluids. We observe a phase transition at a given efficiency, separating regular, viscous solutions (hydrodynamic phase), from singular, inviscid solutions (singular phase). The singular solutions experience self-similar blowups with exponents corresponding to nondissipative solutions. By applying a stochastic regularization, we are able to go past the blowup and show that the resulting solutions converge to power-law solutions with exponents characterizing dissipative solutions. Overall, the range of scaling exponents observed for log-lattice solutions is comparable to those of ordinary fluids.

Using a combination of theory, experiments, and numerical simulations, we investigate the stability of coherent structures in a suspension of strongly aligned active swimmers. We show that a dilute jet of pullers undergoes a pearling instability, while a jet of pushers exhibits a helical (or, in two dimensions, zigzag) instability. We further characterize the nonlinear evolution of these instabilities, deriving exact and approximate solutions for the spreading and mutual attraction of puller clusters, as well as the wavelength coarsening of the helical instability. Our theoretical predictions closely match the experimentally observed wavelengths, timescales, and flow fields in suspensions of photophobic algae, as well as results from direct numerical simulations. These findings reveal the intrinsic instability mechanisms of aligned active suspensions and demonstrate that coherent structures can be destabilized by the flows they generate.

We report the pinching of an elongated liquid droplet confined in a rectangular microchannel. A local variation of the channel topography induces the droplet pinching and can lead to its breakup. The modification of the channel topography is caused by either a reversible local dilation of the channel bottom wall or a confinement gradient irreversibly printed in the channel. Interestingly, in both cases, channel height contraction of a few micrometers leads to the droplet's pinching in the direction of the channel width. If this pinching is such that the droplet is no longer confined at the level of its deformation, i.e., the liquid thread becomes three dimensional, the droplet splits in two. By minimizing the surface energy of the droplet under the channel confinement gradient, we can predict its pinching or breakup, if any. The dynamics of the droplet deformation are then captured by a semianalytical model that relies on the observation that the deformation is self-similar and assumes that most of the viscous dissipation occurs in the gutters at the corners of the channel. Conversely, we show that this kinetic model can be used to extract the channel's average topographic variation, down to a few micrometers, by measuring the droplet pinching dynamics under a classical optical microscope.

We study low Reynolds number turbulence in a suspension of polar, extensile, self-propelled inertial swimmers. We review the bend and splay mechanisms that destabilize an ordered flock. The suspension is always unstable to bend perturbations. Using a minimal 1D model, we show that the splay-stable to splay-unstable transition occurs via a supercritical Hopf bifurcation. We perform high-resolution numerical simulations in 2D to study the varieties of turbulence present in this system transitioning from defect turbulence to concentration-wave turbulence depending on a single nondimensional number, denoting the ratio of the splay-concentration wavespeed to the swimmer motility.

Large-eddy simulation (LES) is one of the high-fidelity turbulence simulations by resolving large-scale motions while modeling the effects of unresolved subgrid scales. However, the predictive accuracy of LES is largely dependent on the subgrid-scale (SGS) model. Traditional SGS models, based on assumptions such as isotropy and scale similarity, have been successfully applied to canonical turbulent flows but often fail in complex flows. Recent advances in machine learning, especially neural network (NN), have opened a new paradigm for SGS modeling by learning complex, nonlinear relationships directly from high-fidelity data. In this paper, we review the limitations of traditional SGS models and examine the development of NN-based SGS models and their strengths and limitations. Toward universal NN-based SGS model development, we discuss critical issues related to extrapolation to high Reynolds numbers, generalization to untrained flows, physical consistency, and computational cost. By combining data-driven methods with physical intuition and principles, NN-based SGS modeling has the potential to enhance the fidelity and versatility of LES.