Accurate modeling of harmful pollutant concentrations is an important field of interest for protecting public health and the environment. In this study, physics-informed neural networks (PINNs) are applied to a low Reynolds number, time-averaged cylinder wake, which interacts with a variety of different passive scalar regimes. The PINN reconstructs both the time-averaged velocity and scalar concentration from limited measurements. In addition to satisfying the incompressible Reynolds-averaged Navier-Stokes equations, the reconstructed fields must also obey the time-averaged advection-diffusion equation. This was done to extend the applicability of mean field reconstruction and to lay the foundation for PINNs to be used in more complex passive scalar modeling in future studies, particularly the prediction of pollutant behavior in urban environments. It was found that the PINN could successfully reconstruct the flow fields on a macroscale in almost all scenarios, having considerable success with first-order quantities and managing to accurately infer the spatial structure of the unknown closure term of the advection-diffusion equation in all cases. When reconstructing scalar source characteristics, the PINN could identify the source location and size in many cases. The results allow basic guidelines for optimal sensor placement to be described to inform future studies and suggest ways in which this technique could be developed to contribute to future air quality forecasting models.

We investigate the effect of a dispersed bubble phase on forced homogeneous and isotropic turbulence using high-resolution high-performance simulations based on the lattice Boltzmann method. While the classical Kolmogorov energy cascade is largely preserved when considering the system as a whole, a phase-specific analysis reveals striking deviations from the classical turbulence scaling. In particular, the gas phase exhibits significant departures from Kolmogorov's predictions, whereas the continuous liquid phase retains a turbulence structure consistent with classical expectations up to $24\%$ in gas volume fractions. These findings suggest that, despite the presence of a dispersed phase, the global energy transfer remains close to a universal behavior. At the same time, phase-specific interactions are shown to introduce modifications to the turbulent dynamics at small scales. In particular, the gas phase exhibits a nearly flat spectrum at low wave numbers followed by a $k^{-3}$ scaling at intermediate scales pointing to the presence of patterns of localized bursts uniformly distributed between two finite wavelengths. Our results aim at deepening the understanding of multiphase turbulence, particularly in the context of energy transfer mechanisms and phase interactions in bubble-laden flows. This study provides a framework for future investigations into the fundamental properties of multiphase turbulence and its implications for environmental, atmospheric, and industrial flows.

Langmuir turbulence (LT) plays an important role in enhancing vertical mixing in the ocean surface boundary layer (OSBL). Such enhanced mixing is strongly affected by the diurnally varying heat flux, especially in the early morning when there is a transition from cooling to heating. In this period, turbulence is weakened, yet the surface heat flux is changing rapidly, such that the deviation of transient turbulence from its equilibrium state is large. This may lead to biases in the parametrization of turbulent mixing due to LT in large-scale ocean circulation models, in which an equilibrium of the turbulence state with the surface forcing is often assumed. In this study, we investigate the transient response of LT to an abrupt onset of surface heating using idealized large eddy simulations, and compare it with the transient response of wind-driven shear turbulence (ST). Near the surface, the destabilizing Stokes shear force competes with the stabilizing surface heating, resulting in a gradual decay of the turbulence intensity, in contrast to ST whose intensity decreases rapidly at first and then partially recovers due to the formation of a stronger jet in the surface warm layer. Below the surface, the decay of coherent downwelling plumes of LT occurs faster than shear turbulence, resulting in a quicker response of LT than ST at depth. The vertical velocity variance of LT at depth decays at a rate initially following $t^{-1}$ and later transitioning to $t^{-2}$. We also examine the impact of details of the Stokes forcing on the transient response of LT. These results may help improve vertical mixing parametrizations in the OSBL.

We investigate the generation and propagation of an impulse wave on a particle-laden water bath produced by the subaerial collapse of a granular column. Laboratory experiments were performed by releasing dense granular columns into water covered with a monolayer of buoyant particles. By systematically varying column height, water depth, and particle size, we explored the role of the buoyant particles on wave type and characteristics, and made direct comparisons with waves on a particle-free interface. The coupled particle–wave dynamics were found to markedly reshape both the waveform and the particle distribution. Buoyant particles delayed the transition from nonbreaking to breaking waves, with the magnitude of the delay increasing with particle size. After wave generation, two distinct particle-accumulation regions emerged: a static buildup adjacent to the collapsed grains that buttressed the pile, and a dynamic concentration zone traveling with the wave front that acted to suppress breaking. Despite these differences from the particle-free case, the maximum wave amplitude was found to primarily correlate with the geometry of the collapsed column, enabling the use of a simple model to relate the wave amplitude and initial column configuration. These results suggest that a buoyant surface layer modulates wave generation and propagation, providing potential insights into impulse waves triggered by glacier calving in proglacial fjords laden with ice mélange.

We develop a covariant formulation of classical fluid dynamics rooted in the Lagrangian perspective, using the language of exterior calculus and differential geometry. In this framework, the observer is not limited to rigid frames. In particular, we can consider observers (Lagrangian observers) whose frame of reference comoves with the fluid. For such an observer the geometry of space evolves according to the dynamics. We introduce the concepts of frame circulation and frame vorticity, which generalize inertial effects and allow for a natural classification of observers. For Lagrangian observers, the flow appears motionless while the metric evolves, leading to a set of coupled equations for the metric and frame circulation. Several exact nonlinear solutions are presented, including analogues of trochoidal and internal waves. Finally, we derive a generalized Orr–Sommerfeld equation in quasi-Lagrangian coordinates and apply it to prove the stability of Couette flow at all Reynolds numbers. This framework opens new avenues for the geometric analysis of turbulence, stability, and mixing from a fluid-following viewpoint.

We propose a novel meshless method to achieve super-resolution from scattered data obtained from sparse, randomly positioned sensors such as the particle tracers of particle tracking velocimetry. The method combines K-nearest-neighbor particle tracking velocimetry (KNN-PTV) [Tirelli et al., Exp. Therm. Fluid Sci. 140, 110756 (2023)] with meshless proper orthogonal decomposition (meshless POD) [Tirelli et al., Proc. R. Soc. A 481, 20240526 (2025)] and constrained radial basis function regression (c-RBFs) [Sperotto et al., Meas. Sci. Technol. 33, 094005 (2022)]. The main idea is to use KNN-PTV to enhance the spatial resolution of flow fields by blending data from locally similar flow regions available in the time series. This similarity is assessed in terms of statistical coherency with leading features, identified by meshless POD directly on the scattered data without the need to first interpolate onto a grid, but instead relying on RBFs to compute all the relevant inner products. Lastly, the proposed approach uses the c-RBF on the denser scattered distributions to derive an analytical representation of the flow fields that incorporates physical constraints. This combination is meshless because it does not require the definition of a grid at any step, thus providing flexibility in handling complex geometries. An ablation study on the role of penalties and physical constraints demonstrates their key contribution in regularizing the regression and ensuring physically consistent reconstructions. The algorithm is validated on three-dimensional measurements of a jet flow in air. The assessment covers three key aspects: statistics, spectra, and modal analysis. The proposed method is evaluated against standard particle image velocimetry, KNN-PTV, and c-RBFs. The results demonstrate improved accuracy, with an average error on the order of $10\%$, compared to $12-13\%$ for the other methods. When considering reduced-order reconstructions, the error is even halved. Additionally, the proposed method exhibits a higher-frequency cutoff (based on reaching a noise floor) than the one observed in the competing approaches. A qualitative comparison highlights that the KNN-driven densification of the particle distribution also enhances the quality of velocity derivatives and related quantities.

When solutions of reactants $A$ and $B$ are stratified in a gravitational field and a second-order reaction $A+B\to C$ generates the product $C$ at the miscible interface, buoyancy-driven mixing between solutions can be affected by the reaction. To study this effect, we analyze how the reaction impacts density profiles. We compare theoretical predictions of convective scenarios based on these reaction-diffusion density profiles with nonlinear simulations of the incompressible Navier-Stokes equations coupled to reaction-diffusion-convection equations for the concentration of species $A, B$, and $C$. We analyze the dynamics in the parameter space $(R_B,R_C)$, where $R_B$ and $R_C$ represent the relative contributions of species $B$ and $C$ to the density of the bulk fluid compared to that of reactant $A$. We examine how varying $R_B$ and $R_C$ influence key flow characteristics, including the onset time of instability, the evolution of the reaction front, the mixing intensity, and the overall reaction yield. We find that the reaction can trigger convection in an initially statically stable stratification and intensify mixing in Rayleigh-Taylor unstable cases. Moreover, the reaction can influence the directionality of fingers and plumes depending on the relative contribution of the product to density compared to that of the reactants.

The interplay between dilatancy and particle alignment in sheared granular materials composed of nonspherical particles leads to morphological inhomogeneity. Dilatancy, driven by interparticle friction, causes the packing to expand, while particle alignment tends to densify it. We examine the influence of friction, particle aspect ratio, and initial packing conditions on the steady-state particle alignment and packing density. Unlike spherical particles, nonspherical particles with higher aspect ratios exhibit either dilatancy or compaction under shear, leading to spontaneous heaping or depression formation. We analyzed the evolution of packing density to identify whether dilatancy or compression prevails within the shear band.

Inertial waves transport energy and momentum in rotating fluids and are a major contributor to mixing and tidal dissipation in Earth's oceans, gaseous planets, and stellar interiors. However, their stability and breakdown mechanisms are not fully understood. We examine the linear stability and nonlinear breakdown of finite-amplitude propagating plane inertial waves using Floquet theory and direct numerical simulations. The Floquet analysis generalizes previous studies as it is valid for arbitrary perturbation wavelengths and primary wave amplitudes. We find that the wave vector orientation of the most unstable perturbations depends strongly on the wave frequency and weakly on the wave amplitude. The most unstable perturbations have wavelengths that are small relative to the primary wave wavelength for low wave amplitudes, but become comparable for large wave amplitudes. We then use direct numerical simulations to follow the nonlinear breakdown of the wave and examine how the wave energy is either dissipated in a forward cascade or accumulated into long-lived geostrophic modes. Simulations reveal that the conversion efficiency into geostrophic modes increases with increasing wave amplitude, as expected for pumping of geostrophic modes by nearly resonant triadic interactions. We also find that the conversion efficiency increases with decreasing primary wave frequency, which may be due to the more efficient coupling of quasi-2D waves to geostrophic modes. These results on the stability and breakdown of single plane inertial waves provide an additional foundation for understanding the role of inertial waves in rotating turbulence, transport properties of inertial wave beams, and inertial wave propagation in more complex environments such as those with magnetic fields or shear flows.

Electrokinetic instability (EKI) emerges when fluids with differing electrical conductivities interact with an applied electric field, resulting in interfacial waves that can either disrupt or enhance microfluidic processes. Previous studies on EKI have primarily focused on Newtonian fluids, though many practical applications involve the mixing of different rheological fluids. This work investigates the effects of Newtonian and shear thinning rheology mixing on EKI using a T-shaped microchannel. We find that adding xanthan gum (XG) polymer to the high-conductivity buffer results in lower threshold electric fields and higher wave speeds/amplitudes than the configuration with XG in the low-conductivity buffer. In contrast, the threshold electric fields for the configuration with XG in both buffers are in between the two rheology mixing configurations. These findings suggest the gradient of rheology interacts with that of conductivity and may itself be able to induce instability in electrokinetic flows. We also perform a scaling analysis to account for the fluid shear thinning effect on the electric Rayleigh number in terms of a power-law model. The critical values of this dimensionless number for the onset of EKI exhibit similar variations to the threshold electric field across fluid configurations and XG concentrations.

The nonlinear and chaotic nature of turbulent flows poses a major challenge for designing effective control strategies to maintain or induce low-drag laminar states. Traditional linear methods often fail to capture the complex dynamics governing transitions between laminar and chaotic regimes. In this work, we introduce and investigate the concept of the minimal seed for relaminarization—the closest point to a reference state in the chaotic region of the state space that triggers a direct transition to laminar flow without a chaotic transient. We formulate the identification of this optimal perturbation as a fully nonlinear optimization problem and develop a numerical framework based on a multistep penalty method to compute it. Applying this framework to the nine-mode Moehlis-Faisst-Eckhardt model of a sinusoidal shear flow, which displays coexisting laminar and chaotic states, we compute the minimal seeds for both transition and relaminarization. While both of these minimal seeds lie infinitesimally close to the laminar-chaotic boundary—the so-called edge of chaos—they are generally unrelated and lie in distant and qualitatively distinct regions of state space, thereby providing different insights into the flow's underlying structure. We find that while the optimal perturbation for triggering transition is primarily in the direction of the mode representing streamwise vortices, or rolls, the optimal perturbation for relaminarization is distributed across multiple modes in this model, without strong contributions in the roll or streak directions. By analyzing the trajectories originating from the minimal seeds, we find that both the transition and laminarization behavior for this system are controlled by a common mechanism—the stable and unstable manifolds of a periodic orbit on the edge of chaos. The laminarizing trajectory obtained from the minimal seed for relaminarization also provides an efficient pathway out of the chaotic region of state space to the laminar state and can therefore inform the design and evaluation of flow control strategies aimed at inducing laminarization.

This study investigates the diffusive motion of a semirigid fiber immersed in a dense granular packing. Experiments are conducted in an index-matched medium composed of water-saturated hydrogel beads, which is sheared by means of a rotating paddle. In the quasistatic regime, we first characterize the self-diffusion of individual grains and show that it follows established scaling laws for granular diffusion. We then analyze the motion of a single fiber for various imposed shear rates and for different fiber and grain dimensions. We show that the fiber undergoes a slow and steady settling through the medium, with a sedimentation velocity that decreases as the fiber length increases relative to the grain size. After removing this mean settling motion, we find that the residual vertical displacement of the fiber exhibits a diffusive behavior. The effective diffusion coefficient decreases with increasing fiber length and is primarily governed by the ratio of fiber length to grain diameter. From these results, we derive an empirical relationship for the fiber diffusion coefficient in granular flow, expressed as a function of both fiber and flow properties.

We verify a recent prediction [Eq. (3.50) in Eyink, Phys. Rev. X 11, 031054 (2021)] for the drag on an object moving through a fluid. In this prediction the velocity field is decomposed into a nonvortical (potential) and vortical contribution, and so is the associated drag force. In the Josephson-Anderson relation the vortical contribution of the drag force follows from the flux of vorticity traversing the streamlines of the corresponding potential flow. The potential component is directly determined by the plate acceleration and its added mass. The Josephson-Anderson relation is derived from the quantum description of superfluids, but remarkably applies to the classical fluid in our experiment. In our experiment a flat plate is accelerated through water using a robotic arm. This geometry is simple enough to allow analytic potential flow streamlines. The monitored plate position shows an oscillatory component of the acceleration, which adds an additional test of the Josephson-Anderson relation. The instantaneous velocity field is measured using particle image velocimetry. It enables us to evaluate Eq. 3.50 from the above-mentioned paper and compare its prediction to the measured drag force. We find excellent agreement and, most remarkably, find that the added mass contribution to the drag force still stands out after the flow has turned vortical. We finally comment on the requirements for the experimental techniques for evaluating the Josephson-Anderson relation.

Orientation relative to gravity is rarely considered when assessing hemodynamics in intracranial aneurysms (IAs). Because head posture is readily adjustable during daily life and in clinical care yet is typically overlooked in studies, understanding gravitational effects bears direct translational significance. We investigated the effect of gravity on IA hemodynamics using an in vitro study. Flow through two patient-specific aneurysm phantoms, a basilar tip aneurysm (BTA) and an internal carotid artery (ICA) aneurysm, were measured using volumetric particle tracking velocimetry (PTV); velocity fields with each IA in a vertical orientation (i.e., patient upright) and horizontal orientation (i.e., patient laying down) were captured. The same pulsatile inflow flowrate was maintained across both orientations. Subsequently, turbulent kinetic energy (TKE), time-averaged wall shear stress (TAWSS), oscillatory shear index (OSI), and velocity-gravity alignment probability-density functions were computed. Our findings revealed that geometry dictated the gravitational response. In the coaxial BTA, the mean centerline velocity was 21% higher in the vertical orientation. Further, for the BTA, the vertical orientation produced a Bland-Altman bias of $+0.019\mathrm{m}{\mathrm{s}}^{-1}$ (95% limits –0.033 to 0.070 m ${\mathrm{s}}^{–1}$), nearly twice as large TAWSS (1.08 vs 0.70 Pa) and reduced OSI (0.135 vs 0.158), shifting the sac from a thrombus-prone low-shear/high-oscillation regime to a high-shear state associated with acute wall erosion. Horizontal rotation reversed these trends and yielded elevated TKE, confirming a gravitational toggle between inertia- and buoyancy-dominated flow. The helical-neck ICA showed minimal orientation sensitivity ($<0.11$ Pa change in TAWSS; $<0.05$ in OSI), indicating that intrinsic curvature overwhelms gravitational forcing. These findings demonstrate that gravity is an active, morphology-dependent load: posture can drive clinically relevant shear-polarity switches in gravity-aligned bifurcation aneurysms yet is secondary in curvature-dominated side-wall lesions. Incorporating sac-axis orientation into imaging and computational pipelines may refine patient-specific risk stratification and inform gravity-aware therapeutic strategies.

In nature, many unicellular organisms are able to swim with the help of beating filaments, where local energy input leads to cooperative undulatory beating motion. Here we investigate, by employing reinforcement learning, how undulatory microswimmers modeled as a discretized bead-bend-spring filament are actuated by torques which are constrained locally. We show that the competition between actively applied torques and intrinsic bending stiffness leads to various optimal beating patterns characterized by distinct frequencies, amplitudes, and wavelengths. Interestingly, the optimum solutions depend on the action interval, i.e., the timescale of how fast the microswimmer can change the applied torques based on its internal state. We show that optimized stiffness- and action-interval-dependent beating is realized by bang-bang solutions of the applied torques with distinct optimum time-periodicity and phase shift between consecutive joints, which we analyze in detail by a systematic study of possible bang-bang wave solution patterns of applied torques. Our work not only sheds light on how efficient beating patterns of biological microswimmers can emerge based on internal and local constraints, but also offers actuation policies for potential artificial elastic microswimmers.

Thin flame dynamics in a turbulent flow remains debated with various parametrizations proposed for the typical flame propagation velocity. According to the classical Damköhler's model based on Huygens' principle, a flame front should advance at a constant velocity normal to the interface between reactants and products, with a turbulent acceleration induced by the wrinkling and surface increase of the interface. However, combustion experiments often deviate from this model due to intertwined thermal and turbulent effects, complicating flame acceleration characterization. In this study, we use an autocatalytic reaction that generates a thin reactive front in an aqueous medium, enabling clearer isolation of turbulence effects. Using oscillating grids to generate turbulence in a closed tank, we examine two configurations: a single-grid setup with a spatially decaying turbulence and a dual-grid system with, in the middle, a nearly homogeneous, isotropic turbulence. Particle image velocimetry and laser-induced fluorescence measurements capture both the velocity field and the front propagation, revealing two different regimes: the expected Huygens' propagation regime, but also a reactive mixing regime, where the turbulent advection of the products inside the reactants initiates multiple, dispersed reaction locations. Additionally, we show that even the small density difference between reactants and products plays a crucial role in the front dynamics. This work advances our understanding of autocatalytic fronts in turbulence, emphasizing the critical interplay between chemical kinetics and flow dynamics.

We experimentally investigate the effects of finite-system size on the dynamics of weakly nonlinear random gravity-capillary surface waves. Experiments are conducted in rectangular tanks with varying aspect ratios, in which the fluid surface is perturbed locally and erratically by small, partially submerged magnets. Driven by an oscillating vertical electromagnetic field, these magnets generate a statistically homogeneous and isotropic random wave field. This setup enables us to probe finite-size effects without the dominant influence of global forcing present in horizontally oscillated tanks. Spatiotemporal measurements of the wave field reveal multiple branches in the wave-energy spectrum along the unconfined direction, corresponding to sloshing modes in the confined direction. We show that the spectral properties of these modes can be tuned by varying either the wave steepness or the confinement. Signatures of discrete wave turbulence in the confined direction and mesoscopic continuous wave turbulence in the unconfined direction are observed. As the confinement is gradually relaxed, we further demonstrate a smooth transition from discrete to continuous wave turbulence, consistent with the nonlinear-to-discreteness timescale ratio. Using high-order correlation analysis, we also show that finite-size effects alter wave dynamics by depleting two-dimensional three-wave resonant interactions along the confined direction.

Small bubbles rising in a chain can self-organize into regular patterns upon reaching a liquid's free surface. This phenomenon is investigated through direct numerical simulations. By varying the bubble release period, distinct branching patterns characterized by different numbers of arms are observed. These macroscopic patterns are found to stem from localized interactions between the bubbles, the free surface, and the surrounding liquid flow. A heuristic model is proposed that quantitatively relates the number of arms to the bubble release period and predicts the probability of observing specific arm counts. This study provides insights into broader nonlinear pattern formation and self-organization phenomena.

Cavitation around marine propellers is a multiscale, multiphase phenomenon that significantly affects hydrodynamic performance and structural response through pressure pulsations. This study experimentally investigates the dynamic relationship between multiscale cavitation structures and their corresponding pressure responses under nonuniform inflow conditions. A multifield synchronous measurement system was employed to capture the evolution of cavitation morphologies along with pressure signals. In addition, a digital inline holography (DIH) system was introduced to quantify the spatial and statistical characteristics of microbubbles in the cloud clusters. The experiments reveal a sequence of cavitation regime transitions, progressing from noncavitating flow to tip vortex cavitation, to the coexistence of sheet and tip vortex cavitation, followed by the onset of cloud cavitation, and ultimately the collapse of vortex structures. Each regime exhibits distinct pressure spectral signatures, with the cloud bubble cluster regime displaying the strongest multiscale interactions. Within this regime, cavitation evolves through four consecutive stages: inception, initial vortex shedding, secondary shedding, and final decomposition. Phase-resolved DIH measurements demonstrate that microbubble size distributions follow an exponential probability density function, exhibiting strong phase-locking and inter-revolution consistency. An equivalent single bubble model was developed to estimate pressure pulsations based on reconstructed bubble statistics, accurately reproducing mid- and high-frequency spectral components associated with bubble collapse. These results offer insights into the multiscale mechanisms of cavitation-induced pressure generation in marine propulsors.

Anomalous dissipation, the persistence of a finite mean kinetic energy dissipation rate as the Reynolds number tends to infinity, occurs in flows with sufficiently spatially rough velocity fields. Compressible turbulence adds further anomalous dissipation mechanisms, which we investigate in this work. To this end, the Duchon-Robert framework (DR) for anomalous dissipation is extended from the incompressible to the compressible Navier-Stokes flow case. We obtain three integral dissipation terms, two anomalous and a viscous, which arise from the pressure-dilatation and density variations, differently from the incompressible case. Subsequently, fully compressible one-dimensional flows with traveling and mutually crossing shock waves are analyzed in detail. In such flows, DR reveals a local maximum of anomalous dissipation at the shock front. Furthermore, DR is compared with a coarse-grained cascade theory of compressible turbulence due to Aluie (AL) and the relevant dissipation flux terms of both frameworks are identified and compared with each other. The comparison shows that each contribution related to the compressibility effects in DR has an analog in AL. Finally, a piecewise linear shock-type velocity profile, which approximates the crossing of two shock waves from the simulations, is used for an analytical analysis of the anomalous dissipation terms of DR to investigate the dependence of the terms on the local Hölder exponent. Our work is a first step towards a comparison of coherent flow structures in higher-dimensional compressible turbulent flows and related anomalous dissipation.