We investigate uncertainty growth and chaotic dynamics in statistically steady, stably stratified three-dimensional turbulence. Using direct numerical simulations of the Boussinesq equations, we quantify the divergence of initially infinitesimal perturbations via twin simulations and decorrelator diagnostics. At short times, perturbations exhibit exponential growth, allowing us to define a (largest) Lyapunov exponent. We systematically examine how this exponent depends on stratification strength, quantified by the Brunt-Väisälä frequency and the Froude number, in a parameter regime relevant to oceanic flows. We find that increasing stratification leads to a monotonic reduction of the Lyapunov exponent, indicating suppressed chaoticity. Despite this reduction, uncertainty growth retains the universal temporal sequence observed in homogeneous isotropic turbulence—initial decay, exponential growth, and saturation. The growth phase is characterized by self-similar decorrelator spectra, but exhibits strong anisotropy: uncertainty spreads much more slowly along the stratification direction than horizontally, with the disparity increasing with stratification strength. An analysis of the decorrelator evolution equation reveals that the suppression of chaos arises primarily from strain-mediated alignment dynamics rather than direct buoyancy coupling. Our results provide a quantitative characterization of predictability and uncertainty growth in stratified turbulence and highlight the utility of decorrelator-based methods for anisotropic geophysical flows.

Collective locomotion of swimming and flying animals is fascinating in terms of individual-level fluid mechanics and group-level structure and dynamics. Here we bridge and relate these scales through a model of formation flight that views the collective as a material whose properties arise from the flow-mediated interactions among its members. We build on and revise an aerodynamic model describing how flapping flyers produce vortex wakes and how they are forced by others' wakes. While simplistic, the model faithfully reproduces a series of physical experiments carried out over the past decade on pairwise interactions of flapping foils. By studying longer in-line arrays, we show that the group behaves as a soft “crystal” with regularly spaced member “atoms” whose positioning is, however, susceptible to deformations and dynamical instabilities. Poking or wiggling a member excites longitudinal waves (flow-mediated phonons, or “flonons”) that pass down the group while growing in amplitude, and indeed the internal excitation from flapping is sufficient to trigger instabilities. Linear analysis of the model explains the aerodynamic origin of the lattice spacing, the springiness of the “bonds” between flyers, and the tendency for disturbances to resonantly amplify. Other properties, such as the timescales for instability growth and wave propagation, seem to involve the full nonlinear behavior. These findings suggest intriguing analogies with physical materials that could be generally useful for understanding and analyzing animal groups. Several properties displayed by our system seem particularly relevant to biological collectives, namely, group cohesion and organization, sensitive detection of and response to perturbations, and transmission of information through traveling waves.

Mosquitoes exhibit unique motion patterns that have attracted growing interest from researchers aiming to understand their underlying aerodynamic mechanisms. However, previous studies have primarily focused on hovering flight. In the present study, we measured for the first time the kinematic and morphological data of mosquitoes Aedes togoi in forward flight using three orthogonally aligned and synchronized high-speed cameras, and numerically computed the forces acting on the wing and the surrounding flow. The results show that mosquito wing kinematics in forward flight exhibit two distinctive features that differ from those observed in most other insects. One feature is that the mosquito's stroke plane remains nearly horizontal; the other is that its wing pitching motion is remarkably asymmetric between the downstroke and upstroke. More specifically, the pitch-down acceleration at the beginning of the stroke and the pitch-up amplitude in the middle of the stroke are highly asymmetric. By establishing the kinematic-fluid-aerodynamic link, two novel thrust-generation mechanisms in mosquito forward flight are revealed: asymmetric pitch-down acceleration mechanism and asymmetric pitch-up amplitude mechanism. The mass-specific power of mosquitoes in forward flight is found to be comparable to that of hovering, and approximately 27% lower than that of the smaller mosquitoes Aedes aegypti, potentially offering larger mosquitoes an energetic advantage in seeking and feeding on hosts. These findings not only deepen our understanding of mosquito flight mechanics but also provide new insights for the kinematic design of micro flapping-wing vehicles in forward flight.

Large aperture telescopes are pivotal for exploring the universe, yet even with state-of-the-art manufacturing and launch technology, their size is limited to several meters. As we aim to build larger telescopes—extending tens of meters—designs in which the main mirror is based on liquid deployment in space are emerging as promising candidates. However, alongside their enormous potential advantages, liquid-based surfaces present new challenges in material science, mechanics, and fluid dynamics. One of the fundamental questions is whether it is possible for such surfaces to maintain their precise optical shape over long durations, and in particular under the forces induced by the telescope's accelerations. In this paper, we present a model and a closed-form analytical solution for the non-self-adjoint problem of the dynamics of a thin liquid film pinned within a finite circular domain. We use the 50-m Fluidic Telescope concept as the case study and examine the liquid dynamics of the telescope under both slewing actuation and relaxation regimes, elucidating the role of geometrical parameters and liquid properties. The solutions reveal a maneuvering “budget” wherein the degradation of the mirror surface is directly linked to the choice of maneuvers and their sequence. By simulating 10 years of typical operation, we show that, while the maximal deformation might reach several microns, the spatial distribution and propagation rate of the deformation allow the telescope to maintain its optical functionality for years, with at least a substantial portion of the aperture remaining suitable for astronomical observations. The model provides valuable insights and guidelines into the performance of liquid-film space telescopes, marking a crucial step toward realizing the potential of this innovative concept.

The displacement of air by a noncolloidal particulate suspension between two parallel plates can trigger interfacial instabilities and two seemingly intertwined patterns: deformation of the fluid-fluid interface and dense particle clusters within the suspension, hereafter referred to as plumes. While prior studies have primarily examined the onset and source of this instability, the emergence and coupling of these patterns remain unresolved. Notably, existing investigations have been limited to radial geometries, where continuous outward expansion of the interface weakens plume-plume interactions. Here, we experimentally displace air with an oil suspension in a rectangular Hele-Shaw cell. Confinement within a constant-width channel amplifies interactions between neighboring plumes, giving rise to previously unreported regimes of pattern formation, including plume merging and plume shedding. Image analysis reveals strong coupling between interfacial deformation and plumes and characterizes the interaction between adjacent plumes. Employing the suspension balance model, we demonstrate how net particle flux toward the interface drives particle accumulation and establishes the conditions for pattern formation. Namely, particle clustering at the interface locally slows the advancing interface and produces concave plume tips that become preferential sites for plume initiation. In addition, we develop a simple scaling for the size of the interfacial deformation based on the interplay between upstream pressure, interface concentration, and plume concentration.

A laboratory investigation was conducted to quantify the influence of background rotation on nearly zero-mean turbulence generated within an off-axis mounted isotropic box. High-resolution particle image velocimetry measurements were performed at the box center under varying rotation rates to examine the onset and development of anisotropy. In the absence of rotation, the turbulence exhibits nearly isotropic behavior, with radial and azimuthal velocity fluctuations closely matched and energy spectra consistent with Kolmogorov scaling. As the inverse turbulent Rossby number, ${\text{Ro}}_{\varepsilon }^{-1}$, increases, spectral anisotropy becomes increasingly pronounced, and the range of scales over which the radial and azimuthal spectra diverge broadens. The lower bound of this anisotropic range follows the scaling $({\kappa }_L-{\kappa }_{DI})\eta ={\text{Ro}}_{\varepsilon }^{-1}/40$, indicating a progressive influence of the Coriolis effects. A generalized Taylor transformation applied to spatial and temporal spectra yields characteristic convection velocities $U_r^{*}$ and $U_{\theta }^{*}$, which exceed the local rms fluctuations and scale as $U_r^{*}\sim 3u_r^{\prime }$ and $U_{\theta }^{*}\sim 2u_{\theta }^{\prime }$. Direction-specific turbulent rotation numbers exhibit a linear dependence on ${\text{Ro}}_{\varepsilon }^{-1}$, linking integral-scale rotational dynamics to small-scale anisotropy. The results provide experimental support for theoretical predictions of energy redistribution, quasi-two-dimensionalization, and wave-eddy interaction in rotating turbulence. The empirical scalings may offer compact constraints for turbulence closures in noninertial frames and establish a basis for future studies of scalar transport and dispersion in geophysical and astrophysical flows.

We develop a perturbation-based frequency-response framework for analyzing amplification mechanisms that are central to subcritical routes to transition in wall-bounded shear flows. By systematically expanding the input-output dynamics of fluctuations about the laminar base flow with respect to forcing amplitude, we establish a rigorous correspondence between linear resolvent analysis and higher-order nonlinear interactions. At second order, quadratic interactions of unsteady oblique waves generate steady streamwise streaks via the lift-up mechanism. We demonstrate that the spatial structure of these streaks is captured by the second output singular function of the streamwise-constant resolvent operator. At higher orders, nonlinear coupling between oblique waves and induced streaks acts as structured forcing of the laminar linearized dynamics, yielding additional streak components whose relative phase governs reinforcement or attenuation of the leading-order streak response. Our analysis identifies a critical forcing amplitude marking the breakdown of the weakly nonlinear regime, beyond which direct numerical simulations exhibit sustained unsteadiness. We show that this breakdown coincides with the onset of secondary instability, revealing that the nonlinear interactions responsible for streak formation also drive the modal growth central to classical transition theory. The resulting framework provides a mechanistically transparent and computationally efficient description of transition that unifies nonmodal amplification, streak formation, and modal instability within a single formulation derived directly from the Navier–Stokes equations.

Controlling water motion on surfaces is critical for applications ranging from thermal management to passive water harvesting to self-cleaning coatings. Yet stabilizing continuous water films, desirable for their high surface coverage and drainage capacity, remains challenging with pure water, due to its high surface tension. Existing strategies rely on extreme wettability achieved by coating or fine-scale patterning, which are costly, fragile, or complex to scale. A robust, purely geometric solution is still lacking. We demonstrate that a pair of laser-engraved grooves on a moderately hydrophilic vertical substrate can laterally anchor water and stretch a continuous thin film, without any other surface treatment. Once stabilized, the film extends vertically over 100 capillary lengths ($>30\mathrm{cm}$), with thickness tunable via both flow rate and groove geometry. At the groove extremities, the end of anchoring triggers a cyclic instability, characterized by film rupture, retraction, and droplet release. The thickness of the film and retraction height obey predictive models, while droplet mass varies systematically with spacing and surface tension. This groove-based method offers a straightforward and scalable approach to creating, sustaining, and controlling thin water films. It opens new directions for passive liquid control in condensation, surface cleaning, and 2D millifluidic systems.

We develop a reduced-order theoretical framework for inertial spheroidal particles in turbulent Navier-Stokes flow, representing their orientation with a single unit vector (the director) instead of using a full rotation matrix. This symmetry-based simplification, analogous to Jeffery's classical description of neutrally buoyant spheroids, yields a compact set of evolution equations with fewer degrees of freedom. In the limit of small inertia, the director obeys Jeffery's equation which we consider as the equation on direction of distance between two infinitesimally close trajectories of a chaotic system. This implies that the particle's director is uniquely determined by its position, defining a director field that, in turn, induces a smooth, weakly compressible effective flow through which the spheroids move. This effective flow is distinct from the underlying incompressible turbulent flow, thereby generalizing Maxey's result for spheres. In homogeneous, anisotropic turbulence with zero mean fluid flow, the effective particle flow can acquire a nonzero mean; for example, in rotating turbulence, particles drift uniformly along the rotation axis. We show analytically that prolate spheroids align with the major Lagrangian stretching direction of the turbulent flow, whereas oblate spheroids align with the major Lagrangian compression direction. In spatially inhomogeneous flows (e.g., a wall-bounded channel flow), particle anisotropy can alter turbophoretic drift, possibly reversing the usual migration toward quiescent regions. We also show that inertial spheroids exhibit preferential concentration. Finally, when gravity is included, we derive analytic expressions for the mean settling velocity in the weak-gravity regime. This settling velocity increases monotonically with the particle aspect ratio, from $8/9$ of the Stokes settling velocity of an equivalent sphere for disklike particles to $4/3$ for rodlike particles. In the strong-gravity limit, the driving of spheroids by the Navier-Stokes turbulence can be effectively described as white noise. We show that very small oblate spheroids settle edge-first, but small ones settle broadside-on. The orientation-dependent settling velocity field is spatially varying and weakly compressible, providing a new mechanism for multifractal preferential concentration. Thus, this director-based framework provides a unified, physically transparent generalization of Jeffery's and Maxey's theories, yielding multiple new analytical predictions for the transport of nonspherical particles in isotropic, anisotropic, and stratified turbulent flows and environments.

We experimentally study the breakup of water-glycerol liquid bridges on nonconductive surfaces and find that spontaneous charge deposition at the receding contact line, slide electrification, can have a substantial influence. Compared to bridge breakup on conductive surfaces, electrostatic forces slow down the dynamics during, and cause spontaneous motion of satellite drops after the bridge breakup. We present a model for electrostatic contact line dissipation that aligns with our experimental observations. Our findings demonstrate that slide electrification plays an important role in dewetting beyond drop-related scenarios.

The size of a pendant drop detaching from a capillary is classically set by the balance between gravity and surface tension, as described by Tate's law, implying only a weak dependence on nozzle size. I show that purely geometric confinement provides a simple and robust means to tune the detachment volume well below this classical limit. By placing a capillary between two superhydrophobic plates forming a shallow wedge, I demonstrate experimentally that drops detach at significantly reduced volumes. A scaling argument reveals that the wedge induces a capillary pressure gradient that assists gravity, yielding a simple relation between drop volume and confinement geometry that collapses all measurements. For completeness, I also consider the complementary case of drops resting on an inclined superhydrophobic surface, which enables volumes above the classical limit through a similarly simple geometric control.

Swimming dolphins generate fully developed turbulence. In the present study, we demonstrate that the hierarchy of multiscale vortices existing in the turbulence is key to understanding how dolphins swim. For this demonstration, we conduct direct numerical simulations of a self-propelled dolphin using a simple model, and examine the role of multiscale vortices in propulsion. By decomposing the turbulent flow into different scales, we elucidate how the dolphin generates the hierarchy of multiscale vortices. Large vortex rings, which are shed due to the oscillation of the caudal fin, produce significant propulsion, while smaller vortices are created through the energy cascade, contributing little to the propulsion. We also demonstrate that the role of these vortices in the propulsion remains robust regardless of the Reynolds number.

Springs can be found in many applications and biological systems, and when these are soft, they easily deform. At small scales, capillarity can induce a force leading to spring deformations when the elastocapillary number is small. We demonstrate through experiments the nontrivial equilibrium-shape liquid droplets adopt in these soft springs, which form an annulus, eruciform, and spherical shapes. When these droplets are set in motion, they display different flow regimes with significant dissipation generated by the internal rotational flow. The static and dynamics of droplets in such a capillary slinky are also used to demonstrate how surface tension can actuate springs by stretching/compression, while providing a way for active flow control in soft springs.

Hydrodynamic flows and swimming trajectories of microswimmers are strongly influenced by nearby surfaces and geometric confinements. The far-field hydrodynamic flow of a microswimmer in bulk can be effectively represented by a force dipole due to the swimmer's propulsion and drag forces, where the source dipole due to body-size effect is subdominant. In contrast, the source dipole becomes the dominant flow contribution when the microswimmer is confined strongly in two dimensions, irrespective of the propulsion mechanism of the swimmer. Recent experimental works demonstrated that this understanding is not completely correct. For microswimmers under slightly weaker confinement, its flow field has a strong dependence on the spatial arrangement of the swimmer's propulsion and drag forces as well as the swimmer's geometry. In this case, the modified far-field hydrodynamic flows of the swimmer should be approximated by placing Stokeslets and source dipoles at proper positions of the swimmer. Here we employ this flow field modification and investigate how the spatial arrangement of Stokeslets and source dipoles influences the dynamics of a microswimmer in a confined liquid film. We observe versatile swimming trajectories, including boundary collision, boundary sliding, centerline sliding, amplified oscillation, and damped oscillation, depending on the relative strengths and positions of the Stokeslets and source dipoles at different confinement heights. These results highlight the enriched dynamics of microswimmers due to the diversity of flow fields in confined geometries.

An antibubble is an object in which a liquid core is separated from a surrounding liquid by a thin spherical gas shell. Such structures can be generated when a droplet crosses a soap film with sufficient kinetic energy to become wrapped by the film, which then merges upon contact with a liquid bath. When droplets fall through multiple soap films, multilayer antibubbles can be generated. In this paper, the conditions required to successfully generate monolayer and multilayer packed droplets are studied in order to optimize the formation of monolayer and multilayer antibubbles. In particular, the geometrical factors and the composition of the liquid that makes up both the droplets and the soap films are discussed. The stability of antibubbles generated using this method is also investigated as a case study. The robust formation of monolayer and multilayer antibubbles is a key to open opportunities in drug delivery without the use of either oil or solid compounds. Moreover, this method allows for the production of monodisperse, millimetric, and multilayered antibubbles.

Optical images of transparent three-dimensional objects can be different from a replica of the object's cross section in the image plane due to refraction at the surface or in the body of the object. Simulations of the object's image are thus needed for the visualization and validation of physical models. We report ray-tracing image simulations that achieved high physical fidelity, reproducing optical behaviors and image features not rendered in previous studies. We replicated brightfield microscopy images of drops with complex shapes and images of pressure and shock waves traveling inside them. For high physical fidelity, the simulations must replicate the spatial and angular distribution of illumination rays, and both the experiment and the simulation must be designed for accurate optical modeling. The simulations are highly sensitive to the properties of the drops and can be used to diagnose and refine fluid dynamics models. The simulated images can also be optimized to extract multiple 3D properties from experimental images. Compared to specialized single-shot 3D imaging methods, this approach has the advantage that it preserves the experimental simplicity, the high resolution, and the visual interpretability characteristic to basic optical imaging. The techniques introduced here are directly applicable to optical microscopy, so they can be used in other fields, such as microfluidics and biology, to expand the type and the accuracy of three-dimensional information that can be extracted from basic optical images.

The process of breaking in surface gravity waves can be characterized by two distinct stages. Breaking onset is defined as the first visible surface manifestation of breaking. This is preceded by breaking inception, which is characterized by the initiation of an irreversible process within the crest that inevitably leads to breaking. Breaking inception diagnostics formulated using the local energetic, kinematic, and geometric properties of the wave crest have recently been proposed that appear to provide generic parametric threshold estimates and may facilitate the effect of wave breaking on larger-scale processes to be parametrized. In a recent numerical study [McAllister et al., J. Fluid Mech. 974, A14 (2023)], a breaking inception diagnostic was proposed based on a threshold value for the maximum local interface angle $\mathrm{\Theta }$. Utlizing an ensemble of breaking wave packet numerical simulations, we extend these findings to include surface tension effects, which are an inescapable feature of ocean surface waves and are known to have a non-negligible effect on wave geometry. The ensemble consists of narrow bandwidth, short wavelength $(\sim 1\mathrm{m})$ gravity wave packets with varying packet size, water depth, and wind speed forcing. For this data, we show that ${\mathrm{\Theta }}_{\text{th}}={60}^{\circ }$ is a robust threshold value for the initiation of breaking inception; twice the magnitude of that for waves in the absence of surface tension. We explore this result in the context of the kinematic inception parameter $B$ [Barthelemy et al., J. Fluid Mech. 841, 463 (2018)] and show that the kinematic and geometric methods are related through the relative flux of energy into the wave crest.

We present three-dimensional helicity maps of fully developed turbulence obtained through chirality tomography, a Lagrangian voxel-based method that reconstructs helicity density from particle trajectories. Our approach builds on an empirically established relation between helicity and trajectory linking, converting local counts of signed crossings $\mathcal{K}$ into volumetric maps of dimensionless helicity, $\mathcal{H}\left(\mathit{x}\right)$. We demonstrate that the entanglement of particle trajectories, quantified by the mean signed crossing number, provides a robust proxy for helicity, not only at the global scale, but also locally in space and time. Our method can reveal local spatial heterogeneities in helicity and relate them to large-scale flow organization, enabling the reconstruction of spatially resolved chiral structures. Applied to von Kármán experiments and Taylor-Green direct numerical simulations, the method reveals iso-helicity surfaces and coherent chiral features, while time series of $\mathcal{K}$ accurately track the evolution of domain-averaged helicity. The proportionality between $\mathcal{K}$ and $\mathcal{H}$ remains robust across different voxel geometries and different values of particle inertia, but is not held in laminar or time-modulated flows. This study shows that chirality tomography provides a practical helicity diagnostic in turbulent flows, while establishing a direct bridge between trajectory-level topology and a fundamental dynamical invariant of turbulence.

Inertial particles (IPs) in vortical fluid flow cluster strongly, forming singular structures termed caustics for their resemblance to focal surfaces in optics. Here we show that such extreme aggregation onto low-dimensional submanifolds can arise without mechanical inertia for self-propelled particles (SPPs), through a formal correspondence between the dynamics of IPs and SPPs in a generic background flow. We establish that a singular perturbation underlies caustics formation by SPPs around a single vortex, and numerical studies of SPPs in two-dimensional Navier-Stokes turbulence reveal intense caustics in straining regions of the flow, peaking at intermediate levels of self-propulsion. Our work offers a route to singularly high local concentrations in a macroscopically dilute suspension of zero-Reynolds-number swimmers. Caustics generate burstlike encounters through large relative velocities between neighboring swimmers, with potentially significant implications for communication and sexual reproduction. An intriguing open direction is whether the active turbulence of a suspension of swimming microbes could serve to generate caustics in its own concentration.

Capillary suspensions are commonly encountered in a wide array of applications, but their stability in flow is not fully understood. Here, we investigate the stability of a two-particle capillary cluster in extensional flow using a combination of theory and experiments. A linear stability analysis reveals the existence of a critical capillary number ${\text{Ca}}_c=(8/45)cos\theta$ that depends only on the contact angle $\theta$. For $\text{Ca}>{\text{Ca}}_c$, clusters are unconditionally unstable, regardless of initial conditions. For $\text{Ca} < {\text{Ca}}_c$, a nonlinear analysis shows the existence of a $\text{Ca}$-dependent minimum interparticle separation beyond which breakup occurs. The analytical model further supports the experimentally observed slowdown in relaxation dynamics. Theoretical predictions are supported by precise flow experiments using a Stokes trap, where active flow modulation is used to stabilize an initially unstable cluster in extensional flow. Overall, these results provide a quantitative understanding of capillary suspension stability in flow.