In fluid experiments, the temporal resolution of velocity fields is typically constrained by the complexity and high cost of measurement systems. Although recent studies have explored the temporal super-resolution of velocity fields using data-driven approaches, they typically rely on large amounts of high-frequency experimental data for supervised training, resulting in high costs and limited generalization capabilities. To overcome this bottleneck, we focus on cavitating hydrofoil flows and propose a semisupervised deep learning framework, DAIT-DNN (Domain-Adaptive Iterative Transfer Deep Neural Network), which completely eliminates the reliance on external high-frequency velocity datasets. The proposed method innovatively employs low-cost, nonintrusive high-speed imaging to capture high-frequency binary phase fields, which serve as inputs to enable temporal super-resolution reconstruction based on its own sparsely sampled, low-frequency velocity field data. The results demonstrate that, under sparse sampling conditions, DAIT-DNN—integrating pseudolabel assistance, domain adaptation, and an iterative optimization strategy—significantly improves the generalization capability of few-shot modeling compared to conventional DNN models. Particularly, for certain highly unsteady conditions or specific moments, DAIT-DNN trained on low-frequency data even outperforms traditional models trained on high-frequency datasets. By integrating low-cost phase information with few-shot velocity data, this work offers an efficient, economical solution for reconstructing complex cavitating flow fields and broadens the potential applications of deep learning to modeling complex physical systems.

Particle image velocimetry (PIV) is a cornerstone of experimental fluid mechanics, yet existing methods present a trade-off between the robustness of cross-correlation and the resolution of variational optical flow. Although modern deep learning models have bridged this gap, they often rely on computationally expensive, architecturally complex black-box modules that limit efficiency and interpretability. In this work, we introduce a different paradigm: a physics-informed variational inference framework that achieves state-of-the-art performance through a transparent and principled design. Our model replaces the conventional learned cost volume with direct photometric error signals and integrates physical constraints, such as brightness constancy and incompressibility, at every level of a multiscale pyramid hierarchy. The entire refinement process is guided by a robust, computationally efficient coarse velocity prior, which stabilizes training and enhances final accuracy. On synthetic benchmarks, our method establishes new state-of-the-art accuracy on the most challenging large-displacement flows, including turbulence and surface quasigeostrophic flow, with improvements of 18% and 40%, respectively, over leading models, while being over 6 times faster. Furthermore, the model demonstrates superior robustness to various PIV-specific disturbances, including particle density, noise, and common optical artifacts. When applied to real-world riverine data without retraining, it shows outstanding generalization, producing velocity fields that align closely with in situ measurements. This work demonstrates that by grounding deep learning in classical variational principles and explicit physical laws, it is possible to create PIV models that are simultaneously more accurate, efficient, and interpretable.

We review recent studies on the hydrodynamic interactions in tandem flapping wing systems, with a focus on the interplay between vortex dynamics and structural flexibility. We examine configurations including rigid wings with prescribed motion, spanwise-flexible wings, and chordwise-flexible wings. For rigid wings, three-dimensional effects are shown to reduce thrust, but they can be mitigated through aspect ratio tuning. Flexibility introduces fluid-structure resonance phenomena that enhance aerodynamic performance. In tandem systems, performance optimization requires careful coordination: forewings benefit from resonance, while hindwings perform best with slightly stiffer configurations to effectively capture upstream wake structures. Finally, in systems of self-propelled flexible flappers, hydrodynamic interactions give rise to coordinated motion and energy savings through flow-mediated feedback.

We present a molecular dynamics simulation of a Mach 5 reactive shock wave in a stoichiometric gaseous ${\mathrm{H}}_2/{\mathrm{O}}_2$ mixture. ${\mathrm{H}}_2$ is compressed slightly ahead of ${\mathrm{O}}_2$ to form two separate shock fronts. Chemical reactions initiate during the ${\mathrm{O}}_2$ compression, followed by a postdetonation flow exhibiting a Zeldovich–von Neumann–Döring-like structure. To analyze the shock substructure, the profiles of state variables near the shock and the postshock particle velocities of molecules are compared with those of a synthetic, inert shock wave. The results indicate that the small ${\mathrm{H}}_2$ to ${\mathrm{O}}_2$ mass ratio causes the separation of shock fronts regardless of chemistry, like those observed in rarefied binary gases, and the velocities of the species relax before leaving the shock region, characterizing the nonequilibrium ${\mathrm{H}}_2/{\mathrm{O}}_2$ shock dynamics so that reactions are present but not as active as they were without the separation.

We investigate rarefaction effects in compressible turbulent boundary layers by conducting direct numerical simulations by imposing slip boundary conditions at the wall. Such a simulation method is justified by the observation that the Kolmogorov and viscous length scales are an order of magnitude higher than the molecular mean free path. The influences of the slip boundary conditions on turbulent flow statistics are restricted within the viscous sublayer. Despite their minor impacts on the mean velocity and skin friction, the mean wall heat flux, vorticity, and velocity divergence fluctuation intensities are obviously affected.

Recent numerical experiments of dynamo action relevant to the generation of the geomagnetic field have produced different regime branches identified within bifurcation diagrams. Notable are separate branches in which the resultant magnetic field is either weak or strong. Weak-field solutions can be identified by the prominent role of viscosity on the motion whereas the magnetic field has a leading order effect on the flow in strong-field solutions. For a given Ekman number, $\mathcal{E}$ (measuring the ratio of viscosity to rotational effects), the existence of these branches and bistability between them is reliant on a small enough magnetic Ekman number, ${\mathcal{E}}_{\text{m}}$ (measuring the ratio of magnetic diffusion to rotational effects, so $\mathcal{E}/{\mathcal{E}}_{\text{m}}={\mathcal{P}}_{\text{m}}$, the magnetic Prandtl number). Both branches are known to produce large scale dipolar magnetic fields but do not exhibit an expected scale separation between the flow and magnetic field. In this work, by reducing ${\mathcal{E}}_{\text{m}}$, we identify a variety of dynamo states on the weak-field branch beyond the known dipolar solutions. Specifically, hemispherical and nondipolar dynamos were found, in addition to the usual dipolar solutions. Some solutions exhibit clear scale separation between small-scale flow and large-scale magnetic field, despite the large ratio of viscosity to magnetic diffusion. Numerical solutions in this regime have not been observed before and they offer a first connection with earlier theoretical work based on mean-field theory.

Particle-mediated multiphase flow in confined geometries is common in natural processes and industrial applications. Here, we study air-suspension interfacial patterns under the impact of particle dynamics through a combination of experiments and theory in a lifting Hele-Shaw cell where the suspension is undergoing stretching deformation. We observe a transition of interfacial morphology from wavy pattern with noticeable wiggles, to blobby fingering featured by blunt tips, and eventually to dendritic fingering pattern characterized by densely spaced side branching. Three particle effects are identified in the pattern formation, including rheological modification, nonuniform spatial distribution, and particle perturbations. Notably, the emergence of dendritic fingering is rarely observed in pure fluids under comparable conditions. To explain this phenomenon, we quantify the particle-induced perturbations using linear stability theory. The particle-induced perturbations correspond to higher wave-number modes than cell roughness-induced perturbation. Once their amplitudes become comparable, tip splitting is continuously triggered and evolves into side branching during finger propagation, ultimately leading to the formation of dendritic morphology. On this basis, we propose a perturbation amplitude-based criterion to predict the emergence of dendritic pattern, and further establish a regime diagram of interfacial patterns in the parameter space of capillary number and aspect ratio. The proposed criterion and the phase diagram are in good agreement with our experiments. This study elucidates the crucial role of particle dynamics in shaping the interface morphologies of suspensions, offering insights into controlling interfacial instability in relevant engineering applications.

An exact solution is obtained for the Stokes flow around an active circular two-dimensional Janus swimmer whose active face is a free surface and its inert face is a no-slip surface, a conceptual design motivated by recent work on superhydrophobic surfaces. Locomotion is driven by Marangoni stresses associated with the diffusion of insoluble surfactant from one edge of the active face to the other. The dynamical system governing the motion of the swimmer is derived explicitly in terms of the swimmer geometry. It is shown that this Marangoni-driven actuation mechanism results in a translational-rotational coupling causing the Janus particle to swim in circles while spinning about its center. While idealized, the model swimmer exemplifies a set of minimal ingredients needed to set up such translational-rotational coupling.

In recent years, lab-on-chip technology has become a particularly interesting topic in the field of medical diagnostics. In this context, the ability of such devices to sort particles at the micrometric scale without any external forces is quite intriguing. Due to their small length scale, they operate with flows at low Reynolds numbers, typically in the range 1–100. In this flow regime, the particle dynamics is affected by inertial effects, including wall-lift force and shear-gradient lift force. Secondary flow can arise in curved channels due to radial pressure distribution. This study focuses on rigid particle transport in microfluidic devices, employing a computational framework to better understand the complex interplay between channel geometry, cross section, particle characteristics, and flow conditions. The flow solver is based on a lattice Boltzmann method and includes a fluid structure interaction technique. The particle rigid motion is evaluated starting from the computation of the hydrodynamic forces acting on the particle and repulsive forces taking into account any particle-particle or wall-particle interactions. Kinematic and dynamic boundary conditions are imposed at the fluid-solid interface by means of an immersed-boundary treatment. The model is validated against benchmark data: a single sphere settling under gravity, and rotations of spheroidal particles in a three-dimensional Couette flow at low-to-moderate Reynolds number. Finally, simulations of particle transport in serpentine channels with 10 repeating units have been carried out for two particle sizes at different flow conditions, demonstrating the effectiveness of the solver for particle-focusing applications within serpentine microdevices. To the authors' knowledge, the results reported in this paper are the first obtained with fully resolved simulations of fluid-structure interaction applications in microchannels with complex realistic geometry.

Instability of an upward flow in a vertical heated pipe under a unidirectional transverse magnetic field is investigated through both linear global stability analysis and direct numerical simulations. The magnetic effect on the dominant thermal-buoyant instability for the moderate Prandtl number, $\text{Pr}=6$ for water, and the dominant thermal-shear instability for the small Prandtl number, $\text{Pr}=0.0248$ for liquid metal, is revealed. The two plane symmetric spiral modes for both the thermal-buoyant and thermal-shear instabilities are broken into two asymmetric branches with different critical values for the Rayleigh number and wave number. For the thermal-buoyant instability with $\text{Pr}=6$, as the Hartmann number increases, the critical Rayleigh number on one branch changes significantly faster than that on the other branch. The flow can become unstable at much smaller Rayleigh numbers under the action of the magnetic field with a moderate Hartmann number. For the thermal-shear instability with $\text{Pr}=0.0248$, the critical Rayleigh numbers on the two asymmetric branches also show significant differences in changes. The critical Rayleigh number of one branch increases monotonically as the Hartmann number increases from zero, while that of the other branch first decreases and then increases, showing a nonmonotonic change. Energy budget analyses at the critical values are also performed to validate the increasing stabilization effect of the magnetic field with the increase of the Hartmann number. Direct numerical simulations are used to compute the linear growth rate and validate our linear global stability analysis. Furthermore, fully developed nonlinear flow states of the MHD mixed convection are investigated near the critical curves of linear stability. It is found that for water with $\text{Pr}=6$, the thermal-buoyant instability is supercritical and large-scale spatiotemporal structures are maintained within a large range of the Rayleigh number. In comparison, for liquid metal with $\text{Pr}=0.0248$, the thermal-shear instability can be subcritical because nonlinear sustained states are found below the critical Rayleigh number for linear instability. The flow exhibits turbulent behaviors when the Hartmann number is small but turns to nonturbulent regular structures as the Hartmann number increases due to the suppression of small-scale turbulent structures by the magnetic field.

The “Cheerios effect,” which describes the capillary interaction between spherical particles at a liquid interface, has traditionally been limited to simple self-assembling structures. Our study addresses the need for more complex assemblies by exploring specific particle geometries. We introduce a theoretical model to describe the interaction potential between quadrupolar objects at the mesoscale, which reveals that both side-by-side and end-to-end long-range attractions can be achieved under specific capillary and geometrical conditions—a phenomenon we term the “Pringles effect.” We experimentally validate our model's predictions by encoding this specific capillary information into 3D-printed curved ellipses, which mimic the surface geometry of Pringles crisps. This approach showcases the potential for complex self-assembling mesoscale structures through precise control over capillary-driven interactions.

Diffusioosmotic flow arises in microfluidic configurations due to solute concentration gradients. In soft microfluidic channels, internal pressure gradients generated by diffusioosmotic flow to conserve mass result in elastic deformation of the channel walls, triggering fluid–structure interaction. In this work, we analyze the fluid–structure interaction between diffusioosmotic flow of an electrolyte solution and a deformable microfluidic channel. We provide insight into the physical behavior of the system by developing a reduced-order model, in which a viscous film is confined between a rigid bottom surface and an elastic top substrate, represented as a rigid plate connected to a linear spring. Considering a slender configuration and applying the lubrication approximation, we derive a set of two-way coupled governing equations describing the evolution of the fluidic film thickness and the solute concentration. Our theoretical predictions show that above a certain concentration gradient threshold, negative pressures induced by diffusioosmotic flow give rise to fluid–structure instability, causing the elastic top substrate to collapse onto the bottom surface. We employ theoretical analysis to elucidate the underlying physical mechanisms for the onset of fluid–structure instability by performing a linear stability analysis of the system and identifying three distinct dynamic regimes. We validate our theoretical results with finite-element simulations and find excellent agreement. The understanding of this instability is of fundamental importance for improving the control and design of microfluidic systems driven by diffusioosmotic flow and containing soft elements.

Pressure gradient-induced separation of swept and unswept turbulent boundary layers, based on the DNS studies of Coleman et al. [J. Fluid Mech. 847, 28 (2018) and J. Fluid Mech. 880, 684 (2019)], has been analyzed for various nonequilibrium effects. The goal is to isolate physical processes critical to near-wall flow modeling. The decomposition of skin friction into contributing physical terms, proposed by Renard and Deck [J. Fluid Mech. 790, 339 (2016)] (short: RD decomposition), affords several key insights into the near-wall physics of these flows. In the unswept case, the spatial growth term (encapsulating nonequilibrium effects) and the TKE production appear to be the dominant contributing terms in the RD decomposition in nonequilibrium zones, i.e., the separated zone and the upstream/downstream pressure gradient zones. Inspection of wall-normal profiles of these terms reveals that only the spatial growth term dominates the energy balance in the inner layer close to the separation bubble. This implies a strong need to incorporate nonequilibrium terms in wall-flux modeling of the unswept separation bubble. Comparison of the streamwise RD decomposition of swept and unswept cases shows that a larger accumulated Clauser-pressure-gradient parameter history in the latter enhances the outer-layer TKE production peak in the adverse pressure gradient zone. The spanwise RD decomposition in the swept case indicates that the downstream spanwise velocity profiles, including those within the separation bubble, largely retain the upstream zero-pressure-gradient characteristics. This seems to ease the near-wall modeling challenge in the separated region, especially for basic models with an inherent log-law assumption. Wall-modeled LES of the swept and unswept cases are then performed using three wall models with varying physical fidelity. Many of the above modeling implications from the DNS are verified by analyzing various LES flow quantities. In particular, extending the RD decomposition to wall models reveals the critical role of the spatial growth term near the separation bubble and demonstrates that the PDE wall model accurately captures this term.

The resistance matrix coefficients of a rigid prolate spheroidal particle immersed in a Newtonian liquid near an incompressible, flat, and unbendable liquid-gas interface are computed by finite element simulations. The effects of the spheroid aspect ratio, the particle-interface distance, and a small inclination of the particle major axis with respect to the interface are investigated. The incompressibility condition applied to the interface reproduces a resistance matrix with translational and rotational components for movements parallel to the interface that resemble those obtained by imposing a slip boundary condition. On the contrary, the incompressible interface behaves like a no-slip rigid boundary for friction components corresponding to a particle motion orthogonal to the interface. These friction components are significantly affected by the orientation of the particle, especially for elongated spheroids at small distances from the interface. A comparison between the numerical predictions and the experimental data available in the literature is also carried out.

Diffusiophoresis of charged particles in the presence of electrolytes has been extensively studied in the literature. However, in these setups, particles typically move in a single direction, either up or down the electrolyte gradient. Here, we theoretically investigate the conditions under which a particle can reverse its diffusiophoretic direction within the same setup, leading to the formation of a focusing band under steady-state concentration gradients. Using multi-ion diffusiophoresis calculations, we simulate particle transport in an acid-base reaction system where salt is added alongside the acid. For a range of salt concentrations, particles focus within the channel. Our analysis reveals that a pH-dependent zeta potential is necessary for this focusing to occur, and determines where the particles focus, i.e., on or off the acid-base reaction front. We consider two cases: (i) modest pH-driven variation in the magnitude of a negative zeta potential, and (ii) sign reversal across an isoelectric point. For modest variations in negatively charged particles, we report qualitative agreement with prior experimental observations and derive semi-analytical conditions governing particle focusing, highlighting the delicate balance between concentration gradients and zeta potential variations. For quantitative analysis, we create focusing phase diagrams for both types of zeta-potential variations and compare their focusing regimes. The work elucidates the crucial physics of pH-dependent zeta potential and opens new avenues for exploring diffusiophoresis in acid-base systems, with implications for microfluidic design and biophysical transport processes.

The growth of ice stalagmites obtained by the solidification of impacting droplets on a cooled substrate ($-50{}^{\circ }\mathrm{C}$ to $-140{}^{\circ }\mathrm{C}$) is investigated experimentally. It is shown that for any combination of substrate temperature and drop flow rate, there is a critical height above which unfrozen water accumulates at the stalagmite's tip, drips, and develops into fingers that give a star shape to the stalagmite. Both the vertical growth and the radial growth of the stalagmite are discussed through the Stefan problem and mass scaling arguments, respectively. Finally, a phase diagram that presents the stalagmite aspect ratio in function of the main control parameters is proposed.

A mechanism by which the surface zonal flows of giant planets can be gradually attenuated with depth is explored. The zonal flow is driven by an imposed forcing in a thin layer near the surface. A meridional circulation is set up, analogous to the Ferrel-like cells observed in Jupiter's atmosphere. Acting on a stably stratified thin surface layer, the meridional flow induces a horizontal temperature anomaly which leads to a gradual reduction of the zonal winds with depth, governed by the thermal wind equation. Our model is a Boussinesq plane layer, with gravity acting parallel to the rotation axis. A suite of fully three-dimensional time-dependent numerical simulations has been performed to investigate the model behavior. Below the forced stable layer, convection is occurring, typically in the form of tall thin cells. The fluctuating components of the three-dimensional flow can be driven by either the convection or the Reynolds stresses associated with the jet shear flow. When fluctuations are mainly driven by convection in the form of tall thin columns and the forcing is relatively weak, the horizontal temperature anomaly persists much deeper into the interior than when it is driven by shear flow. The zonal jets can therefore extend deep into the interior, consistent with the Juno gravity data.

In this work, we propose an alternative surface tension adjustment approach in the pseudopotential lattice Boltzmann (LB) model, which is not only decoupled from the density ratio but also independent of the collision operator. This is achieved by incorporating a generic source term obtained from the difference between a modified moment equilibrium and an original moment equilibrium distribution function in the LB equation. The explicit form of the source term is obtained through a third-order Chapman-Enskog analysis of the LB equation, aiming to recover the targeted governing equations from a modified Landau free-energy theory using a hybrid density-pseudopotential form. The source term can be easily and straightforwardly incorporated into different widely used collision operators, such as single relaxation time, multiple relaxation time and entropic-MRT operators. The proposed method is validated by three benchmarks: (i) the liquid-gas coexistence density, (ii) surface tension adjustment via the static droplet case, and (iii) droplet deformation via oscillations. It is shown that thermodynamic consistency is restored in a large range of temperature ratio, and, moreover, a remarkable tunable surface tension range of 140 times can be achieved. Benefiting from the proposed surface tension adjustment method, we have successfully modeled the droplet impact and splashing dynamics with a Weber number up to 10 500, achieving one order of magnitude higher than LB simulations reported in the literature.

The aim of this paper is to provide a description of high-Reynolds-number thermally stratified surface-boundary-layer flows consistent with given turbulence models and to study their implications on Lagrangian stochastic approaches. The emphasis is first put on the relations between the selected turbulence models and the resulting universal functions used to describe the first- and second-order moments for temperature and velocity. To this end, a methodology for deriving model-consistent mean profiles that agrees with the Monin–-Obukhov theory is presented. This methodology is based on the derivation of algebraic solutions for the thermal and dynamic second-order moments, and on an iterative resolution of the turbulent dissipation rate. With adequate models for the dissipation rate, it is shown that the derived universal functions for the first- and second-order moments retrieve the correct asymptotic behaviors for both the stable and unstable limits. Based on these formulations, the consequences on Lagrangian stochastic models are then investigated since the turbulent model corresponding to the Lagrangian description must be consistent with the one used in the moment approach. For example, when using wall-function formulations, we highlight the importance of applying an-elastic wall-boundary conditions for both velocity and thermal instantaneous properties. Finally, an application to the case of linear-source dispersion is analyzed in the frame of hybrid moment–probability density function methods. It is shown that these methods can adequately account for stability effects and that models of instantaneous thermal quantities have a great impact on both buoyant plume rise and dispersion.

Self-oscillating gels are chemically responsive hydrogels coupled to an oscillating chemical reaction of a stimulus solute. In response to the oscillating solute concentration field, responsive gels periodically swell and deswell, expelling their adsorbed water as they transition to a drier state, and reswelling once they return to a hydrophilic state. This volume phase transition occurs when the local stimulus concentration crosses a critical value, about which the hydrophilicity of the polymer chains changes abruptly. These gels have been used to make surface crawlers or other pulsatile machines, but here we show that a very simple system comprising two oscillating gel spheres linked by a rigid rod can also swim in the inertialess Stokes regime—albeit rather slowly. Developing a full continuum-mechanical model for a gel that employs a reaction described by the Brusselator model to generate oscillating chemical concentrations that couple to gel and fluid dynamics, we quantify the rate of shrinkage and swelling and associated flows as the gels pump out or draw in water. Herein, we derive analytical results for the swimming velocity of these swimmers, and upon placing them in a solute bath, identify two modes of behavior upon encountering propagating reaction-diffusion waves: “bobbing” and “surfing.” Though somewhat slower than flagellated swimmers, the relative simplicity of the system, with no hinges or moving components, lends itself well to large-scale production.