Cilia are ancient cell organelles that generate fluid flow by beating periodically. They play four key roles: swimming, feeding, pumping, and sensing. This study explores how cilia generate flow and perform these functions. Swimming efficiency peaks when the number of cilia scales with body length squared, matching biological scaling. In choanoflagellates, inward flagella enhance feeding, and outward motion aids swimming. In mouse embryos, nodal flow from motile cilia is sensed by immotile cilia to establish left-right body asymmetry. These findings underscore the diverse roles of ciliary flow and the significance of fluid mechanics in biology.

The Quincke effect is a striking symmetry-breaking phenomenon in which a particle undergoes spontaneous rotation when subjected to a sufficiently strong electric field. This study, focused on Quincke rotation of a two-dimensional circular (non-deformable) drop, numerically demonstrates the emergence of bistability as the drop viscosity is reduced relative to that of the surrounding fluid — consistent with experimental observations. It is found that capturing this transition entails resolving the formation of charge-density blowup singularities driven by surface convection.

Discovered stochastic resonance (SR) in viscoelastic inertialess channel flow at a fixed location far from inlet has Wi as control parameter (CP), the ratio of elastic stress to its relaxation. By tracking SR downstream along channel locations at Wi>Wi${}_c$, we find that a SR existence range first broadens in Wi values and then remains constant until the outlet, with perturbation intensity as the second CP defining the range of SR appearance. SR existence should satisfy three conditions: chaotic streamwise and flat, weak intensity spanwise power spectra with extremely small elastic wave intensity. Thus, SR plays the key role in stochastic routes to promote sustained chaotic flow at Wi>Wi${}_c$.

Lagrangian particles in turbulence separate faster backward in time than forward. We provide a kinematic explanation by decomposing separation into speed and velocity-orientation components. Analysis of direct numerical simulations shows that orientation, not speed, drives the asymmetry: when particles approach, their velocities align more strongly toward each other, whereas during separation this alignment is weaker.

Collectively controllable active particle swarms are prospective for object manipulation and payload carrying in fluidic microenvironments, but a theoretical description is missing. Observing the motion of magnetotactic bacteria swarms perpendicular to the applied in-plane magnetic field, we present a torque dipole-based “hydrodynamics with spin” model for active particle swarms, and use it to explain this behavior. The motion direction is given by the left-hand rule, and the velocity magnitude is linear in the magnetic field magnitude. The theory is applicable to a wider class of systems, enabling the control of swarms of various types of active particles via different driving fields.

Tiny obstacles in a Brinkman fluid can dramatically alter how swimming microorganisms like bacteria or micro-algae coordinate their motion. The environmental resistance presented by the particulate delays and, at high enough levels, completely suppresses the collective instabilities that arise due to hydrodynamic interactions between the swimmers. By contrasting our results with those for homogeneous fluids, we highlight how the physical structure of a habitat can control and disrupt whether microorganisms swim in coordinated groups.

We investigate the stability of two configurations: a passive viscous Newtonian droplet immersed in an active nematic liquid crystal, and an active nematic droplet surrounded by a passive layer, both under circular confinement. Our results reveal how capillary, active, elastic, and viscous stresses interact to govern droplet dynamics. These findings may inform our understanding of diverse biological systems featuring interfaces between active and passive fluids, from droplets in bacterial suspensions to subcellular compartments within the cytoplasm and cell nucleus.

A mean-field theory is derived for a dilute suspension of active particles in a nematic liquid crystal. Beyond a critical active Ericksen number or particle concentration, the suspension first comes into alignment, then buckles via a classical bend instability. Rather than entering the fully developed roiling state observed in isotropic fluids, the development is arrested into a steady, flowing state by fluid elasticity. The image shows the fluid’s elastic energy in such an arrested state. If the particles are motile, they can surf along the bent environment of their own creation.

The dynamics of microswimmers’ undulatory swimming near a wall in lyotropic liquid crystal polymers is investigated. Using asymptotic analysis and numerical study, we observe that the infinitely long sheet exhibits orientation-dependent behaviors and speeds up as it approaches the wall, accompanied by a notable increase in swimming efficiency. For the stiff finite-length swimmers, they would reorient themselves and be trapped when close enough to the wall, due to a net hydrodynamic torque induced by the asymmetric distribution of the flow field.

Heavy fluid sinks while light fluid rises – these are the very basics of convection. Here we derive a set of reaction-diffusion equations from the governing dynamics of convection, whose solutions reveal complex flows that display both order and chaos. By tuning the strength of buoyancy (Rayleigh number), a series of transitions between conducting, circulating, and reversing flows appears, leading to an enhanced heat transfer (Nusselt number). This model also reveals a ¼ power-law scaling between the Nusselt and Rayleigh numbers that is verified by both numerical simulations and asymptotic analysis, bringing us one step closer towards understanding the complex physics of convective heat transfer.

While theory has studied the large amplitude single-mode shape oscillations of gas bubbles, this is an idealized case. Real-world scenarios typically involve the excitation of many modes. This study probes the nonlinear shape oscillations produced through coalescence, introducing magnetic levitation for the first time to freely suspend air bubbles in water, 5–6 mm in diameter, with negligible distortion. These experiments, along with simulations, reveal that while the bubble’s shape generally agrees well with theory, the coupling of multiple oscillation modes significantly alters its frequency response, highlighting a key aspect of bubble dynamics not captured by single-mode theory.

This study provides a plausible explanation for the longstanding discrepancy between experiments and simulations of electroconvective flows by systematically incorporating Navier-slip boundary conditions. It demonstrates that partial slip can significantly lower both linear and nonlinear instability thresholds and enhances electric transport efficiency. A previously unreported transition from convective to zonal flows is also uncovered, offering a physical mechanism for the saturation of electric transport observed in experiments. These findings establish a predictive framework linking boundary slip to the stability and turbulent transport characteristics of electroconvective flows.

For a long time, weather forecasting was based on empirical correlations, producing sayings like “Rain before seven, fine by eleven”. The modern weather forecast uses supercomputers and many ground observations. How does it work? Why is our weather app displaying scores for predictions over more than 3 days? Why is it failing sometimes even for shorter periods? Will it improve if we use larger computers and artificial intelligence? The answer to all these questions is now available, thanks to recent progress in mathematics, and involves possible singularities of the inviscid limit of the primitive equations.

The work considers the normal mode stability of plane Poiseuille flow under stable density stratification. The problem is analyzed at low Peclet numbers representing liquid metal flows of interest in advanced nuclear reactor designs. The eigenvalue problem is solved numerically, and a perturbation series is also developed for small stratification. Numerical and perturbation series results indicate that stratification has a purely stabilizing effect on the normal modes. All normal modes are found to be stable when a modified Richardson number, R = Ri $\times$ Pe, is greater than about 0.33.

The stability of viscoelastic jets is essential for industrial processes like printing and coating, but the choice of fluid model can yield vastly different predictions. This study investigates how the popular Oldroyd-B and Giesekus models affect the onset of convective instability, where disturbances grow downstream, versus absolute instability, where they grow locally. We demonstrate a key trade-off: Giesekus jets are more convectively unstable, while Oldroyd-B jets are more prone to absolute instability. These findings clarify how different fluid properties govern distinct instability pathways, guiding better process control.

We examine the fundamental fluid dynamical mechanisms dictating the generation of bioaerosols in the human trachea during intense respiratory events, such as coughing and sneezing. Using a ‘cough machine’ and numerical simulations, we observe that when subject to intense shear from the airflow, the mucosalivary-mimetic fluid lining forms bag-like structures. These structures rupture through the appearance of retracting holes on the bag surface, generating droplets via the unstable retraction of liquid rims bounding these holes. Viscoelasticity of the mucosalivary-mimetic fluid promotes the formation of larger, thus thinner bags, leading to the production of smaller droplets upon rupture.

Viscosity-stratified flows are prone to instabilities that influence industrial transport processes such as oil recovery, pipeline lubrication, polymer deposition, and extraction. This study investigates the onset and growth of instabilities in miscible layered channel flows using an initial value problem framework. By capturing the full time-dependent evolution of the base state, the work reveals how transient dynamics affect instability onset and energy amplification, offering new insights beyond traditional quasi-steady analysis.

Particle rafts — fluid-fluid interfaces covered with particles — form wrinkles and folds when compressed, like a crumpled piece of paper. Nevertheless, composed of discrete particles, rafts under compression can also fail by expelling single particles, which cannot be explained by existing continuum models. We develop a composite model that incorporates the contact line dynamics of individual particles to fully describe both the elastic and granular responses of the compressed particle rafts. By using this new model framework, we also demonstrate the control of raft behaviors by tuning the physicochemical properties of individual particles.

Binary fluids with miscibility gap exhibit property variation in response to a stimuli, making them useful for applications like targeted drug delivery, protein extraction, and others. We present a novel phase-field approach to track the continuous evolution of such fluid pairs from initially immiscible/partially miscible state to miscible state with a tunable miscibility framework. The model is used to investigate classical single mode Rayleigh-Taylor instability. Three qualitatively distinct growth patterns of the imposed perturbation are found based on the Atwood and Weber numbers. A secondary instability of Kelvin-Helmholtz rolls is found to be dependent on system temperature.

Stability of a liquid film containing colloidal particles flowing along the exterior of a vertical cylinder due to gravity is studied. The effect of colloidal concentration on diffusion coefficients, bulk viscosity, and surface tension is considered. The Marangoni stress at the interface stabilizes the curvature-driven instability at moderate Marangoni numbers, but introduces another unstable mode driven by surfactant at larger values. The pattern for the curvature mode indicates in-phase waves for film thickness and surface concentration, while a phase-lag is observed between the two waves for the surfactant mode.

In 1922, Jeffery solved the problem of cylinder-pair counterrotation in a viscous fluid and found that it is impossible to satisfy velocity decay at infinity. Following recent interest in this so-called ‘’Jeffery paradox,’’ the present paper sheds some light on the counterrotation and corotation problems in the limit where the separation between the cylinders is vanishingly small.

Internal Boundary Layers (IBL) form when turbulent flows encounter sudden changes in surface roughness. The IBL introduces new length- and time-scales to the flow, characterizing the turbulent motions within. We introduce an alternative scaling for velocity profiles within the IBL using IBL-based parameters: the IBL height and edge velocity. Using our numerical simulations and two experimental datasets, we demonstrate the capability of these new scaling parameters for a variety of flow and surface conditions, offering a simpler, more unified way to understand the behavior within this spatially developing turbulent region.

This study explores conditional one- and two-point velocity fluctuation correlations relative to the turbulent/non-turbulent interface (TNTI) in a temporal jet. By comparing classical and TNTI-conditioned averages, it reveals new spatial correlations, scaling behaviors and peculiar turbulent production regions which may affect turbulence models. The analysis uncovers distinct correlation peaks tied to the TNTI’s variability that point to large-scale turbulent motions influenced by the interface and that may be missed by conventional one-point or unconditioned analyses.

Three dimensional rotating turbulent flows can sometimes transfer energy from the injection scale to the largest scale available in the domain, generating large coherent structures in the process. For intermediate values of the Rossby number, however, a flux–loop mechanism can be achieved, in which the energy transferred upscale is arrested at a scale smaller than the domain size. This mechanism also produces coherent structures similar to the vortex crystals usually found in many physical systems. In this work we study these structures via direct numerical simulations, focusing on their evolution and morphology, and we identify their key controlling parameters.

A finite Rossby number induces cyclone–anticyclone asymmetry in surface quasi-geostrophic turbulence under thermal wind balance. Using freely decaying simulations, we demonstrate that this asymmetry systematically enhances large-scale frontolysis. By extending energy-transfer theory to incorporate horizontal divergence, we further reveal that divergence during frontolysis drives a dominant inverse energy cascade in the balanced submesoscale flows.

The statistical behavior of a scalar passively advected by a Navier-Stokes flow resulting from a two-dimensional turbulent inverse energy cascade is strongly intermittent, displaying anomalous multiscaling, which violates Kolmogorov’s self-similarity predictions. Recently, the concept of hidden symmetry (HS) has been introduced to define a new set of dynamically rescaled (projected) variables for which scale invariance is restored and allowing to calculate from the projected equation of motion the anomalous scaling of the structure functions. Hidden symmetry has been validated numerically in the context of the shell models. In this work we validate HS for the case of the passive scalar.

Dimples – localized indentations in otherwise smooth surfaces – have attracted attention in both numerical simulations and experiments due to their practical applications. Direct numerical simulations have been performed to examine the flow in a zero-pressure-gradient boundary layer over a single deep circular dimple. The flow is characterized by the presence of a tornado-like vortex pair within the dimple, followed downstream by a quasiperiodic shedding of hairpin vortices forming a vortex street. Downstream of the dimple, both sinuous and varicose streak instabilities develop, contributing to the generation of hairpin vortices and the periodic meandering of these vortices, respectively.

While splitter plates are typically employed to suppress flow-induced vibration in bluff bodies, this study reveals an opposite outcome. In a new configuration, attaching a splitter plate to the windward side of a circular cylinder leads to amplified rotational vibrations. Numerical simulations at low Reynolds numbers uncover several regimes, including large-amplitude oscillations, chaos, and symmetry breaking — driven by vortex-structure interactions. The findings highlight the role of leading-edge vortices and demonstrate synchronized structural oscillations with enhanced energy transfer between fluid and structure, offering potential applications in energy harvesting.

This study examines extreme vortex gust-airfoil interactions at Reynolds number 5000 using large-eddy simulations and nonlinear machine learning. We show that aerodynamic responses remain primarily two-dimensional up to gust ratios |G| ≤ 3 but transition to three-dimensional dynamics beyond |G| ≥ 4. We further reveal the low-dimensional nature of extreme aerodynamic flows for cases where the interaction dynamics are primarily two-dimensional throughout nonlinear observable-augmented autoencoder compression. These findings provide a foundation for modeling and control of small-scale aircraft operations under highly gusty environments.

When a disk suddenly moves toward or away from a solid wall, the resulting vortex ring behaves in ways that differ from the unbounded case. Experiments and numerical simulations show that the circulation and core radius of the vortices obey new scaling laws that depend not only on disk diameter, stroke length and time but also on the distance to the solid wall.

Wave-powered propulsion using flapping foils is a relatively new idea with great potential, but the performance of these systems depends strongly on foil geometry and pitch control. Using high-fidelity fluid–structure simulations, this study examines pitch-limiting strategies and foil shapes that can maximize thrust across a range of sea states. A simple pitch angle-limiter offers performance benefits especially in low amplitude waves, while a thin elliptical foil outperforms other foil shapes. These results provide practical design guidelines for efficient wave-powered flapping foil propulsion systems.

This study describes the wake behind a multi-wake model using three mean velocity components, obtained using stereo-particle image velocimetry, at a Reynolds number of $5.64\times {10}^5$. The near-wake is dominated by a separation bubble that forms immediately downstream of the model. Shear layers detached from the model periphery morph into a single connected bound vortex that stays inside the separation bubble. The far-wake dynamics are dominated by four corner vortices that originate from each slant edge, and they remain coherent several body lengths behind the vehicle. The surface slant angles significantly influence the evolution of the wake and have important implications for drag reduction.

When a vortex ring collides obliquely with a vortex tube at a Reynolds number of 12,000, a series of vortex structures can form, with the onset of turbulence set by their initial circulation ratio. Weaker vortices often wrap around stronger ones, causing deformation, twisting, and breakdown of large-scale structures into smaller scales. Vortex reconnection may produce more stable configurations; however, changes in vortex topology can trigger secondary reconnections, generating even more twisted structures. As these vortices become unstable, they create numerous small-scale structures, ultimately leading to fully developed turbulence with an energy spectrum following Kolmogorov’s −5/3 law.

Four interacting point vortices can form rigidly moving patterns called relative equilibria, yet a complete understanding of the possible geometrical arrangements has been elusive. Using a parametric formulation and configuration matrices, we mapped the locations of the fourth vortex that form relative equilibria for a fixed triangular arrangement of the first three vortices. The results reveal bounded and unbounded continua of vortex positions, uncovering families of relative equilibria and rich bifurcation structures in the configuration space.

The response of biogeochemically active scalars to small-scale turbulent mixing is not well characterized. Using direct numerical simulation, we explore the evolution of idealized phytoplankton and nutrient scalars in an unstable stratified shear layer. Extending theory from stratified turbulence literature, we examine irreversible scalar fluxes and show that the type of stratified shear mixing matters (i.e. overturning or scouring), especially when physical and biological timescales align.

The efficiency of an array of turbines operating in a channel is influenced by how much of the channel the array occupies, represented as the blockage ratio. In this work, the performance and near-wake flow field of a cross-flow turbine array are evaluated across a range of blockage ratios through laboratory experiments. An analytical linear momentum actuator disk model is found to be predictive of the measured velocity of the fluid that bypasses the array. When the array performance is scaled by the bypass velocity in a manner inspired by Maskell’s bluff-body theory, self-similar performance is observed across blockage ratios, highlighting the salient dynamics of highly-confined turbines.

A coherent vortex column in rotating turbulence forms, bursts apart due to instabilities, and reforms again — a cycle driven by a tug-of-war between the destabilizing effect of elliptical instability and the stabilizing influence of rotation. Using Fourier-space analysis, including ring spectra and mode-to-mode energy transfer, we identify a forward energy cascade and the activation of vertical modes (kz = 2, 3) as precursors to bursting, indicating how spectral energy transfer drives the collapse and reformation of the structure.

Understanding internal wave turbulence in stratified fluids could yield improved parameterizations of the fine scales in global oceanic models. As analytical works lead to diverse predictions, the observation of a developed internal wave turbulence in laboratory experiments constitutes a major milestone to achieve. In this article, we present observations of internal wave turbulence, performed in a large-scale, three-dimensional facility, allowing access to unprecedentedly clear power laws for the energy spectra. While most of our results are in line with the phenomenology of wave turbulence, it remains to be explored whether the energy spectra we report can be explained in this framework.

A novel model-based approach for time super-sampling of turbulent flow fields is proposed, based on POD-Galerkin models. Temporal resolution is recovered by integrating in time the dynamical system obtained from projecting the Navier-Stokes equations onto a low-dimensional space derived through Proper Orthogonal Decomposition (POD). This method enables temporally continuous reconstructions between non-time-resolved Particle Image Velocimetry (PIV) snapshots. Our results demonstrate the capability to accurately reconstruct flow dynamics between available measurements.

We present a method for the simultaneous inference of flow fields and obstacle shapes from sparse measurements in steady-state compressible flows. Such inverse problems are highly ill-posed and require strong regularization. We address this by combining the Optimizing a Discrete Loss (ODIL) technique with JAX-Fluids. ODIL minimizes the discrete residual of the governing equations, preserving both the accuracy and convergence properties of the underlying numerical methods. The employed conservative finite-volume scheme, including shock-capturing reconstruction and a sharp-interface immersed boundary method, is crucial for effective regularization and therefore accurate flow field inference.