In this paper we examine how porosity fluctuations affect the hydrodynamic permeability of a porous matrix or membrane. We introduce a fluctuating Darcy model, which couples the Navier-Stokes equation to the space- and time-dependent porosity fluctuations via a Darcy friction term. Using a perturbative approach, a Dyson equation for hydrodynamic fluctuations is derived and solved to express the permeability in terms of the matrix fluctuation spectrum. Surprisingly, the model reveals strong modifications of the fluid permeability in fluctuating matrices compared to static ones. Applications to various matrix excitation models, the breathing matrix, phonons, and active forcing, highlight the significant influence of matrix fluctuations on fluid transport, offering insights for optimizing membrane design for separation applications.

We investigate the multistability and bifurcation behavior in thermal vibrational convection through direct numerical simulations, focusing on the effects of varying initial conditions, vibrational Rayleigh number (${\text{Ra}}_{\mathrm{vib}}$), Strouhal number ($\text{St}$), and the aspect ratio ($\mathrm{\Gamma }$) at a fixed Prandtl number ($\text{Pr}=1$). In this study, the Nusselt and Reynolds numbers remain below the threshold for the fully turbulent regime, yet the system displays intricate nonlinear dynamics. By modulating the initial phase of external vibrations, we identify two distinct flow states: a periodic state with consistent large-scale circulation and periodic variations in the Nusselt number [$\text{Nu}\left(t\right)$] and the Reynolds number [$\text{Re}\left(t\right)$], and a chaotic state characterized by unstable flow structures and erratic $\text{Nu}\left(t\right)$ and $\text{Re}\left(t\right)$ fluctuations. The time-averaged Nusselt and Reynolds numbers are higher in the periodic state compared to the chaotic state. Fourier mode decomposition reveals that the periodic state is dominated by the single-roll ($M^{1,1}$) mode, while the chaotic state involves interplay among all modes. Initial velocity fields constructed from Fourier mode basis functions confirm that high-intensity $M^{1,1}$-dominated conditions yield the periodic state, while others produce the chaotic state. Parametric analysis highlights that bifurcations occur predominantly near $\text{St}=1$, where the vibration frequency matches the system's intrinsic timescale, fostering sensitivity to initial disturbances and multistability, and the bifurcation exhibits hysteresis across various ${\text{Ra}}_{\mathrm{vib}}$ and $\mathrm{\Gamma }$. This work elucidates the mechanisms driving flow state transitions in thermal vibrational convection, offering a novel framework for studying unsteady flow multistability with implications for heat transfer and flow control.

Understanding the coupled dynamics of liquid-solid phase change and fluid flows is crucial in a wide range of geophysical and industrial applications. When freezing occurs in saline water, the newly formed ice is mushy, with a porous structure that traps the brine within the ice. In this work, which combines experiments and theoretical analyses, we investigate the long-term evolution of saline ice, comprehensively accounting for the coupled dynamics of multiscale fluid flow, heat and mass transfer, and phase change. We show that in a closed convective system the rapid formation of a mushy ice layer is followed by desalination (i.e., the expulsion of salt from the ice) processes that might lead to a slow asymptotic decrease of the ice thickness. Desalination of mushy ice reduces its porosity, which alters the dynamic thermal equilibrium and ice thickness by weakening buoyancy-driven convection within the mushy layer. In turn, changes in brine convection and ice thickness affect the further desalination of the ice. The long-term dynamics of the system can be accurately predicted by a one-dimensional model based on appropriate parametrizations of global heat and mass transfer properties. Furthermore, within the same theoretical model we explore the ice dynamics across a broader parameter space. Our findings advance the understanding of the coupled phase-change physics of saline solutions in the presence of convective fluid flows and provide a basis for explaining and predicting real-world phenomena such as the aging of sea ice.

The dispersion of Lagrangian particle pairs is a fundamental process in turbulence, with implications for mixing, transport, and the statistical properties of particles in geophysical and environmental flows. While classical theories describe pair dispersion through scaling laws related to energy cascades, extreme events in turbulent flows can significantly alter these dynamics. This is especially important in stratified flows, where intermittency manifests itself also as strong updrafts and downdrafts. In this study, we investigate the influence of extreme events on the relative dispersion of particle pairs in stably stratified turbulence. Using numerical simulations we analyze the statistical properties of pair separation across different regimes, and quantify deviations from classical Richardson scaling. Our results highlight the role of extreme drafts in accelerating dispersion. These findings have important implications for turbulent mixing in natural systems, including atmospheric and oceanic flows, as well as applications in cloud microphysics and pollutant transport.

Flows at planetary scales are generally driven by buoyancy and influenced by rotation. Rotating Rayleigh-Bénard convection (RRBC) is a practical and simple model that can be used to describe these systems. In RRBC, thermally induced convection occurs, which is influenced by the constant rotation it experiences. We study RRBC in a cylinder in the transition region between rotation-affected and rotation-dominated (also called geostrophic) convection. Experiments are performed to assess the dependence of the Nusselt number $\mathrm{Nu}$ (efficiency of convective heat transfer) on the Prandtl number $\mathrm{Pr}$ (ratio of kinematic viscosity over thermal diffusivity), a relation that is not explored much for geostrophic convection. By using water at different mean temperatures we can reach $2.8\le \mathrm{Pr}\le 6$. We study the relation between $\mathrm{Pr}$ and $\mathrm{Nu}$ at constant Ekman number $\mathrm{Ek}=3\times {10}^{-7}$ (an inverse measure for strength of rotation) for two different diameter-to-height aspect ratios ($\mathrm{\Gamma }=1/5$ and $1/2$) of the setup. The corresponding constant Rayleigh numbers (strength of thermal forcing) are $\mathrm{Ra}=1.1\times {10}^{12}$ and $1\times {10}^{11}$, respectively. Additionally, we measure the relation between the Rayleigh number $\mathrm{Ra}$ and $\mathrm{Nu}$ for $4\times {10}^{10}\le \mathrm{Ra}\le 7\times {10}^{11}, \mathrm{Ek}=3\times {10}^{-7}$, and $\mathrm{Pr}=3.7$. It is found that $\mathrm{Nu}$ exhibits a significant dependence on $\mathrm{Pr}$, even within this limited range. Increasing $\mathrm{Pr}$ by a factor 2 resulted in a decrease of $\mathrm{Nu}$ of about $25\%$. We hypothesize that the decrease of $\mathrm{Nu}$ is caused by the changing ratio of the thermal and kinetic boundary layer thicknesses as a result of increasing $\mathrm{Pr}$. We also consider the anticipated contributions of the wall mode to the heat transfer using sidewall temperature measurements.

A general formula is established for traveling speed of an axisymmetric toroidal vortex with magnetic flux concentrated in a thin core embedded in electrically conducting fluid subject to the Hall effect. We extend Helmholtz-Lamb's method to include magnetic flux. The resulting formula admits viscous diffusion of vorticity and magnetic diffusion. The Hall effect only modifies the distribution of magnetic field. In the other extreme of fat cores, an exact solution is constructed of the ideal Hall-magnetohydrodynamics (HMHD) for a steadily traveling spherical magnetic vortex. This vortex is accompanied by a spherical-boundary vortex sheet as in the MHD case. The toroidal magnetic field acts to enhance the traveling speed, but the Hall effect causes the discrepancy in the traveling speed, whether the magnetic field is parallel or antiparallel to the vorticity, by modifying the distribution of the magnetic field. The traveling speed of a thin vortex ring is increased or decreased for parallel or antiparallel cases, respectively. For the spherical vortex, the opposite trend is brought by the surface vortex sheet. Besides, a particular solution is found for a spherical vortex pertaining only to the HMHD.

We present the results of a theoretical investigation into the existence and evolution of resonant triads of two-layer gravity waves confined to a cylinder of finite height. We consider a stable stratification, for which the lighter fluid lies above the heavier fluid, with the two fluids being separated by an interface and bounded above and below by rigid horizontal lids. We demonstrate that the lateral confinement can excite resonant three-wave interactions, resulting in pronounced interfacial sloshing and highly efficient energy exchange. Such interactions are absent in unbounded domains or rectangular cylinders and consist of a single vertical mode and a single interface. For a cylinder of arbitrary cross section, we prove necessary and sufficient conditions for three spatially correlated wave modes to resonate, with the existence of triads depending critically on the depth and density of each fluid. Upon deriving amplitude equations governing the long-time evolution of a resonant triad, we show that the triad evolution is generally periodic and determine conditions for which energy exchange is most propitious. We also identify a criticality condition exclusive to multilayer flows that describes the decoupling of the triad interaction. Finally, we discuss the implications of our findings on the formation of resonant internal wave interactions in geophysical basins.

Condensation on vertical surfaces leads to fluid retention, which limits the efficiency of applications ranging from heat exchangers to atmospheric water harvesters. A common strategy is to structure the surface with grooves, yet whether grooves help drainage or worsen retention remains unclear. Here we use a high-throughput condensation setup to quantify retention on substrates patterned with parallel vertical grooves of fixed geometry ($d/w=1$) while varying the spacing $s$. We uncover two opposite regimes separated by the droplet detachment radius $R_d$. For large spacings ($s>R_d$), droplets grow and slide under gravity while grooves, acting as passive reservoirs, increase retention. For small spacings ($s<R_d$), grooves instead trigger active drainage, confining droplet growth and reducing retention to values even lower than on smooth surfaces. Two asymptotic models, a groove-volume reservoir model and a plateau-packing model, capture this transition and explain the scaling of retention with $s$. These findings show that groove spacing controls whether grooves act as drains or reservoirs, providing a simple geometric design rule for tailoring condensation retention in practical systems.

Superhydrophobic coatings are used to separate surfaces from the surrounding liquid by trapping an air layer called plastron in its microstructures. The durability and therefore the performance of these surfaces lie in the capacity to retain this plastron, which might be destabilized by excessive stresses or dissolution. Plastron monitoring is therefore essential to quantify the amount of gas shielding the surface from the liquid and to determine its temporal evolution. Such air layers, which may blend multiple length scales ranging from nm up to cm, are challenging to probe. In this paper, we develop a versatile technique based on the acoustic resonance of the plastron, which allows passive probing of the total volume of air trapped in the surface roughness. Validation of this technique is performed by comparing the mean acoustic thickness against direct optical observations and shows very good agreement. As this acoustic method uses portable transducers and is sensitive to the air layer's volume regardless of the superhydrophobic surface, we foresee that it can pave the way toward plastron monitoring under more realistic conditions such as complex geometries in different flow regimes. Additionally, this technique is shown to efficiently monitor plastron on timescales of a few milliseconds, enabling real-time characterization necessary to better assess destabilization mechanisms leading to the collapse of a plastron.

Particle-laden turbulence involves highly complex interactions between the dynamics of the dispersed particle phase and that of the continuous turbulent phase. Particles with different physical properties, such as shape, density, and size, are particularly interesting as these can be sensitive to or influence different specific aspects of the flow. In this contribution we focus on the coupling between the angular dynamics of particles and turbulent vorticity in turbulence. To this end, we detail the development and demonstrate the capabilities of a special experimental setup where the angular dynamics of particles can be both measured (via optical image processing techniques) and imposed (via the application of external rotating magnetic fields). We further discuss how particles of different densities and magnetic properties can be manufactured, with specific interest toward light particles as these can be transformed into vorticity probes and localized forcing acting on small-scale vortex filaments. The ordinary optical method for particle tracking velocimetry is here extended to accurately measure the angular velocity of particles with sizes significantly smaller than the Taylor microscale, typically an order of magnitude larger than the Kolmogorov scale of the turbulence in which they are suspended. Remarkably, the optical method employed in this study enables accurate measurement of the full three-dimensional angular velocity vector of particles using only two-dimensional image sequences, thereby requiring only one camera. The present contribution discusses in detail how the different design choices are entangled with each other and which considerations are relevant when designing such an experimental setup. Beyond advancing the study of particle dynamics in turbulence, this approach opens up possibilities for actively studying how to modulate turbulence through externally applied magnetic fields.

We present an experimental investigation of the mutual synchronization between hydrodynamic and thermoacoustic oscillations in a turbulent lean-premixed bluff‐body flame. By fixing the equivalence ratio ($\varphi =0.65$) and Reynolds number ($\mathrm{Re}=5.4\times {10}^3$) and systematically varying the combustor length, we sweep the acoustic chamber eigenfrequency through the hydrodynamic vortex-shedding frequency. As the combustor length increases, the system evolves from a pure hydrodynamic vortex-shedding mode, through a thermoacoustically self-excited combustor mode, to a hybrid quasiperiodic state in which both modes coexist, and finally to a 1:2 mutually synchronized state in which both modes lock together, amplifying both the heat release rate (HRR) and pressure oscillations. Temporal analyses–Hilbert‐transform metrics, recurrence quantification, and Pearson correlation–reveal the route from desynchronization to phase and generalized synchronization, the latter coinciding with a significant amplification of the HRR and pressure amplitudes. Spatiotemporal analyses—local frequency and HRR amplitude maps, Rayleigh index fields, phase-locking distributions, and modal decomposition of ${\mathrm{CH}}^{*}$ chemiluminescence images—reveal the bluff‐body recirculation zone as the dominant energy-injection site for thermoacoustic instability. Finally, two flame blow-off pathways are identified: (i) isolated pinch-off events that cause global extinction when $\varphi$ drops below the lean flammability limit and (ii) coupled pinch-off/wall-quenching events driven by high-amplitude thermoacoustic forcing. These findings clarify the interplay between hydrodynamic and thermoacoustic modes, guiding control strategies for next-generation low-emission combustors.

Swirl switching refers to the temporal rotation of the plane of symmetry of the cross-sectional vortices about the equatorial plane of the curved pipe and may induce significant vibrations in piping systems. The origin of this phenomenon is not yet understood, and its relationship with turbulent fluctuations in the upstream straight section is still debated in the literature. To assess the effect of upstream turbulence, direct numerical simulations are performed for spatially developing bent pipe flows under both laminar and turbulent inflow conditions. Additionally, the influence of the bending angle on swirl switching and time-averaged flow characteristics is investigated. Proper orthogonal decomposition (POD) is applied to three-dimensional velocity fields to extract spatially coherent structures responsible for swirl switching. The phenomenon is observed for both inlet velocity profiles and bending angles, although it does not correspond to the dominant mode in the case of laminar inflow conditions. A reduced-order reconstruction using the most energetically relevant antisymmetric POD modes indicates a link between swirl switching and the shear layer within the bend. We therefore infer that swirl switching could arise because of a symmetry-breaking shear layer instability, representing a stage in the bifurcation cascade that leads to turbulence.

We develop a robust numerical method for thin plates falling in inviscid fluid that allows for leading-edge vortex shedding. The inclusion of leading-edge shedding restores physical dynamics to vortex-sheet models of falling bodies, and large-amplitude fluttering and tumbling are observed in inviscid simulations. Leading-edge shedding is achieved by introducing a quadrature rule and smoothing procedure for the Birkhoff-Rott equations. The smoothing error is controlled by a projection procedure similar to fencing. We find a transition point between fluttering and tumbling that is consistent with previous viscous simulations and experiments, and other falling motions such as looping and autorotation are also observed as the plate density increases. The dipole street wakes behind the fluttering plates resemble those in experiments. We consider plates bent into V shapes and study the effects of density and bending angle on the qualitative falling dynamics. At small densities, increasing the bending angle stabilizes the falling motion into fluttering, while at large densities, decreasing the bending angle stabilizes the falling motion into autorotation. In the autorotation regime, the magnitude of angular velocity increases as time cubed before it reaches a terminal angular velocity, and in the fluttering regime, the fluttering frequency scales as the $-1/2$ power of $R_1$, the plate density.

Liquid films coating vertical cylinders can form annular liquid collars which translate downwards under gravity. We investigate the dynamics of a thin viscoplastic liquid film coating the interior or exterior of a vertical cylindrical tube, quantifying how the yield stress modifies both the Rayleigh-Plateau instability leading to collar formation and the translation of collars down the tube. We use thin-film theory to derive an evolution equation for the layer thickness, which we solve numerically to examine the nonlinear dynamics. Instability and collar formation occur when gravity is sufficiently strong to make the fluid yield initially. We use matched asymptotics to derive a model describing the quasisteady translation of a slender liquid collar when the Bond number is small. The structure of the asymptotic solution for a viscoplastic collar shares some features with the Newtonian version, but there are several novel asymptotic regions that emerge at the two ends of the collar. The global force balance, which determines the collar's speed, is modified by a leading-order contribution from viscous drag in the collar when the liquid is viscoplastic. We use the asymptotic model to describe slow changes in collar volume when the film thicknesses ahead of, and behind, the collar are unequal. When the film thickness ahead of the collar is less than a critical value that we determine, viscoplastic collars adjust their volume and reach a steadily translating state. This contrasts with the Newtonian problem, where the only state in which steady translation occurs is unstable to small changes in the film thickness.

We present direct numerical simulations (DNS) of particle deposition in a turbulent channel flow, incorporating a viscoelastic soft-sphere collision model with van der Waals adhesion. Particle-wall contact is governed by an adhesion number that varies with temperature, enabling exploration of a wide range of deposition behaviors. Deposition is strongly heterogeneous, especially for inertial particles, where rolling and sliding enhance nonuniformity. Spanwise radial distribution functions reveal that deposited particles form streaks with characteristic spacing set by near-wall two-point velocity correlations. A clustering metric confirms that high-inertia, low-adhesion particles deposit in elongated, anisotropic patterns due to spanwise particle creep driven by velocity fluctuations. Finally, it is shown that this heterogeneity in deposition leads to localized wall wear rates exceeding 10 times the mean, with the most severe wear associated with particles that are carried to the wall in clusters by sweep events.

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.

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 dynamic averaging algorithm combined with a high-order spectral (HOS) model is introduced for wave reconstruction and prediction using radar data from stationary or moving ships. The algorithm enables gradual reconstruction of waves entering the radar's blind zone and improves accuracy by reducing the effects of shadowing modulation, particularly under steep wave conditions. The effects of nonlinearity on wave prediction accuracy are examined across a range of sea states with varying wave steepness and directional spreading angles. Results show that the HOS model, which includes third-order nonlinear effects, outperforms both linear and second-order models. Its advantage is especially clear in steep or narrowly spread wave fields, where simpler models fail to accurately predict the timing and height of large waves, leading to wave prediction errors at the ship's position up to three times higher than those from the HOS model. Additionally, when the ship slows down in head waves or speeds up in following waves, the relative velocity between the waves and the ship decreases. This reduction in relative speed extends both the time required for accurately reconstructing waves in the blind zone and the length of the predictable wave field ahead of the ship.

Drying of fluids undergoing sol-gel transition in porous media, a process crucial for the consolidation of damaged porous structures in cultural heritage, often leads to skin formation at the surface. This phenomenon significantly hinders evaporation, yet its precise impact on drying kinetics remains poorly understood. To uncover the governing mechanisms, we develop a novel pore network model that closely replicates quasi-two-dimensional experimental porous media in a previous paper [Le Dizès Castell et al., J. Phys. Chem. Lett. 15, 628 (2024)], incorporating spatial gradients in pore size distribution, with smaller pores near the evaporation side. We demonstrate that this pore distribution dictates the air invasion path and extends the constant-rate period of drying in Newtonian liquids, reproducing the experimental drying curves for water. We further extend our model to capture the interplay of capillary-driven liquid flows, space-dependent viscosity increases, and localized skin formation. To incorporate skin formation, we implement a viscosity-dependent vapor pressure rule derived from experimental data on evaporation-induced sol-gel transition within a capillary tube. We identify a simple relationship: vapor pressure decreases once the meniscus fluid viscosity exceeds a critical threshold. By accounting for localized skin formation through reduced evaporation pressure at high-viscosity throats, our model successfully captures the slowdown of drying kinetics, achieving remarkable agreement with experimental drying curve.

Ice melting is a complex, dynamic, and multiscale process involving many feedback effects. An essential but poorly understood factor for floating ice is the potential to overturn, as dramatically demonstrated by capsizing icebergs. Here we study the melting-induced reshaping of ice coupled to its free rotation dynamics and find that periods of stable equilibrium are punctuated by spontaneous capsize events. Laboratory experiments on floating ice show that melting produces faceted and angular shapes whose tendency to orient to the waterline is repeatedly upset by rolling over. Similar geometries and motions are reproduced in simulations that drive the shape development via differential melt rate over the surface and which solve for the rotational dynamics subject to shape-dependent forcing from gravity, buoyancy, and hydrodynamics. Melting gradually drives the structure toward postural instability while also priming other orientations that prove stable when reached by abrupt flipping. These findings show how the shape and motions of ice are inextricably linked at fundamental scales, and they reveal mechanisms that may be operative for natural conditions.