The flow near a moving contact line is primarily governed by three key parameters: viscosity ratio, dynamic contact angle, and inertia. While the behavior of dynamic contact angles has been extensively studied in earlier experimental and theoretical works, quantitative characterization of flow configurations remains limited. The present study reports detailed measurements of flow fields, interface shapes, and interfacial speeds in the low- to moderate-Reynolds-number ($\mathrm{Re}$) regimes using particle image velocimetry and high-resolution image analysis. The investigation is restricted to dynamic contact angles greater than ${90}^{\circ }$. In the low-$\mathrm{Re}$ regime, excellent agreement is observed between measured streamfunction contours and the modified viscous theory of Huh and Scriven [J. Colloid Interface Sci. 35, 85 (1971)] that accounts for a curved interface. Interface shapes from experiments are compared against well-known theoretical models, and the experiments reveal the limitations of these models to capture interface shapes over the entire range of length scales. Theoretical models such as the DRG formulation using a single fitting parameter, accurately predict interface shapes even at finite $\mathrm{Re}$. The interfacial speed away from the contact line compares favorably with theoretical predictions, whereas a pronounced deceleration is observed close to the contact line. Complementary volume-of-fluid–based numerical simulations were performed using identical geometric and material parameters to validate and extend the experimental observations. The simulations successfully reproduce the interface topology, flow structure, and the deceleration of the interfacial velocity near the contact line, providing strong support to the experimental findings. We argue that this rapid reduction in speed, observed both in experiments and simulations, is critical to the resolution of the long-standing moving contact line singularity.

We consider shear-driven longitudinal flow of an exterior fluid over a periodic array of rectangular grooves filled with an immiscible interior fluid (the “lubricant”), the grooves being formed by infinitely thin ridges protruding from a flat substrate. The ratio $\lambda$ of the effective slip length to the semiperiod is a function of the ratio $\mu$ of the interior to exterior viscosities and the ratio $h$ of the groove depth to the semiperiod. We focus on the limit $\mu \ll 1$, which is singular for that geometry. We find that the viscous resistance to the imposed shear is dominated by a boundary layer of exponentially small extent about the ridge tips, resulting in the effective slip length scaling as ${\mu }^{-1/2}$—not ${\mu }^{-1}$ as implied by intuitive arguments overlooking the tip contributions (and by proposed approximations in the literature). Analyzing that exponential region in conjunction with an integral force balance, we find the simple asymptotic approximation $\lambda \approx {\mu }^{-1/2}$; using conformal mappings, we also calculate the leading-order correction to that result, which introduces a dependence upon $h$. The ensuing asymptotic expansion breaks down for $h=O\left({\mu }^{1/2}\right)$, upon transitioning to a lubrication geometry. We accordingly conduct a companion asymptotic analysis in the distinguished limit of small $\mu$ and fixed $H=h/{\mu }^{1/2}$, which gives $\lambda \approx {\mu }^{-1/2}H/(1+H)$ as well as a closed-form leading-order correction to that approximation; the intuitive ${\mu }^{-1}$ scaling is accordingly only relevant to the regime $H\ll 1$ corresponding to extremely shallow grooves. We demonstrate excellent agreement between our predictions and numerical solutions constructed using a boundary-integral formulation.

Thin-heavy-flexible disks are observed orbiting at a quasistable radial position from the axis of a strong vortex. Given that the disks are denser than the fluid, it is surprising that they persist in orbit rather than being centrifuged away from the vortex. A 3D reconstruction technique was used to track both the position and deformation of the thin flexible disk, providing insight into the mechanisms underlying the trapping phenomenon. The reconstruction process uses shape-from-silhouette to define an initial 3D reconstruction, which is subsequently refined by minimizing a cost function based on physical and visual criteria. The results of the 3D reconstruction measurements are presented and compared with a phenomenological model. The analysis shows that orbital stability depends on a combination of vortex parameters (strength and core size) and particle parameters (trajectory curvature, surface curvature, angle of inclination, and slip velocity).

Slender elastic structures that interact with surrounding fluids are common in many biological and engineering settings. Motivated by these applications, we investigate the dynamics of a thin elastic sheet that is initially held in a laterally compressed configuration within a quiescent fluid, and then released from rest. As the sheet tries to recover its minimum energetic shape, its motion is governed by a subtle balance between elasticity, inertia, and fluid resistance. We begin by focusing on the early-time behavior and derive an analytical model in the inviscid limit, capable of predicting the oscillation frequency around the first buckling mode of the sheet and the growth rate near the unstable second mode. These predictions are in close agreement with numerical simulations of the more complex viscous formulation of the fluid, and show strong dependence on the sheet-to-fluid inertia ratio. At later times we analyze the sheet's transition from the second to the first buckling mode. We find that the inviscid model continues to track the system's evolution with good accuracy. In particular, we identify a logarithmic scaling for the transition time, which is also well supported by our numerical results. Altogether, our findings suggest that even in viscous environments, inviscid models can offer valuable insight into transient elastohydrodynamic processes.

Turbulence is a complex system exhibiting both universal statistical features and prominent coherent structures. We model turbulence using coherent vortices distributed within a multiscale statistical framework, termed "woven turbulence." These entangled vortices are generated based on fractional Brownian bridges, with scale-dependent parameters set by dimensional analysis and geometric similarity. By integrating statistical and structural modeling, our approach naturally captures both the universal statistical features of turbulence and its coherent vortex structures. The spatial filling fraction of vortices in woven turbulence, termed "vortex density," is tunable, enabling us to investigate the statistical-structural interaction and uncover two concise physical insights of turbulence. First, the invariance of the hierarchical vortex density across scales corresponds to Kolmogorov's $-5/3$ law in the inertial range. Second, there exists a critical total vortex density at which the intermittency of woven turbulence closely matches that of real turbulence, and this critical density converges to a finite value in the inviscid limit. Deviating from this critical density reveals a negative correlation between intermittency and total vortex density. In addition, woven turbulence also serves as a fast turbulence synthesis method, requiring only the Taylor-Reynolds number as input and exhibiting an extremely low computational cost proportional to the grid size. It generates instantaneous turbulent fields at Taylor-Reynolds numbers of order ${10}^3$ on ${4096}^3$ grid points, with computational cost over five orders of magnitude lower than that of direct numerical simulation.

We present an experimental investigation of free surface deformations and undulations in horizontally driven shallow flows within electrolyte layers—commonly employed laboratory analogs for quasi-two-dimensional flows and oceanic circulations. We characterize deformations as deviations of the free surface height relative to its mean level and undulations as spatial variations in the fluid layer thickness. Using a multicamera imaging setup, we simultaneously track the spatiotemporal evolution of the electrolyte-air interface and the horizontal velocity fields at this free surface across a wide range of Reynolds numbers ($\mathrm{Re}$) in layers with three different mean thicknesses. Across experiments, we show that deformations and undulations remain small for $\mathrm{Re}\lesssim 400$ but become sizable for $\mathrm{Re}\gtrsim 800$, showcasing a strong (approximately quadratic) dependence on Reynolds number and a weak (sublinear) dependence on fluid layer thickness. Consequently, surface deformations and undulations—measured as percentages of the mean fluid layer thickness—repeatedly approach $\pm 20\%$ and $30\%$, respectively, at the highest Reynolds number ($\mathrm{Re}\approx 1190$) in the shallowest (3-mm-thick) layer realized in our experiments. These findings suggest that, similar to observations in soap film experiments, deviations from quasi-two-dimensionality in shallow electrolyte flows must be evaluated also in terms of free surface deformations and thickness variations—an important refinement to current understanding.

Rayleigh–Bénard convection is a canonical system for buoyancy-driven turbulence and heat transport, central to geophysical and industrial flows. Developing efficient control strategies remains challenging at high Rayleigh numbers, where fully resolved simulations are computationally expensive. We use a control framework that couples data-driven manifold dynamics (DManD) with reinforcement learning (RL) to suppress convective heat transfer. We find a coordinate transformation to a low-dimensional system using proper orthogonal decomposition and autoencoders, and then learn an evolution equation for this low-dimensional state using neural ODEs. The reduced model reproduces key system features while enabling rapid policy training. Policies trained in the DManD environment and deployed in DNS achieve a 16–23% reduction in the Nusselt number for both single- and dual-boundary actuation. Physically, the learned strategy modulates near-wall heat flux to stabilize and thicken the thermal boundary layer, weaken plume ejection, and damp the wall-driven instabilities that seed convective bursts. Crucially, the controller drives the flow toward a quasisteady state characterized by suppressed temporal fluctuations and spatially steady heat-flux patterns. This work establishes DManD–RL as a physically interpretable, scalable approach for turbulence control in high-dimensional flows.

This paper reports on the development of a lattice Boltzmann (LB) code for the Euler-Euler, or two-fluid, large eddy simulation (LES) of turbulent dispersed two-phase flow. To correct for the inbuilt pressure handling inherent to the standard LB method, we develop two LB approaches to the Euler-Euler equations. In the first approach, we naturally remove the inbuilt pressure component by invoking the well-balanced LB method proposed by Guo et al. [Phys. Fluids 33, 031709 (2021)]. Subsequently, the correct pressure term is added as an external force in a Poisson equation. The second approach utilizes a mixture model to generate the required pressure field, assuming an incompressible dilute mixture. This is then coupled to an LB equation for the dispersed phase flow. The two proposed models are validated against two test cases: a falling cloud of particles and a Rayleigh-Taylor instability. The results demonstrate the accuracy of the proposed models while identifying their differences. Subsequently, both models are used to simulate a homogeneous isotropic turbulent two-phase emulsion in a LES supported by the static Smagorinsky subgridscale model. The results of these LESs are compared with a full-scale direct numerical simulation solution. The new models reproduce the larger scales of turbulence accurately, demonstrating the robustness and accuracy of the two proposed models in complex and chaotic scenarios.

Traveling wave packets are key coherent features contributing to the dynamics of several advective flows. This work introduces the Hilbert proper orthogonal decomposition (HPOD) to distill these features from flow field data, leveraging their mathematical representation as modulated traveling waves. The HPOD is a complex-valued extension of the proper orthogonal decomposition, where the Hilbert transform of the dataset is used to compute its analytic signal. Two versions of the technique are explored and compared: the conventional HPOD, computing the analytic signal in time, and a novel space-only HPOD, computing it along the advection direction. The HPOD is shown to extract wave packets with amplitude and frequency modulation in time and space. Its broadband nature offers an alternative to spectrally pure decompositions when instantaneous, local wave characteristics are important. The space-only version, leveraging space/time equivalence in traveling waves to swap temporal operations with spatial ones, is proven mathematically equivalent to its conventional counterpart. The two HPOD versions are characterized and validated on three datasets ordered by complexity: a two-dimensional (2D) direct numerical simulation of a laminar bluff-body wake with periodic vortex shedding; a large eddy simulation of a turbulent jet with intermittent, highly modulated wave packets; and a 2D particle image velocimetry experiment of a turbulent jet with measurement errors and no temporal resolution. In advecting flows, both HPOD versions deliver practically identical complex-valued advecting wave-packet structures, characterized by spatiotemporal amplification and decay, wave modulation, and intermittency phenomena in turbulent flow cases, such as in turbulent jets. The space-only variant allows the extraction of these structures from temporally under-resolved datasets, typical of snapshot particle image velocimetry.

The influence of coherent vortices on the decay of turbulent kinetic energy (TKE) is experimentally investigated in a synthetic-jet-driven turbulence box. For the baseline homogeneous case, a power-law decay exponent of $m=1.41$ is obtained. Six cases with a spatial power gradient in the turbulence forcing create turbulence laden with controlled amounts of coherent vortices, quantified by a Rossby number $\text{Ro}$. In these cases, the TKE decay rate is reduced with a minimum of $m=0.66$ for the case with the strongest power gradient (lowest $\text{Ro}$). Decay values for $\text{Ro}<1$ cases, where rotation is relatively stronger than turbulent fluctuations, are well below expected values based on prior empirical and theoretical works. To investigate the underlying cause, a triple-decomposition-inspired framework based on Proper Orthogonal Decomposition is developed to separate coherent modes from the stochastic component of the velocity field. The method identifies coherent modes as modes that are found across repeated experiments and exhibit slower temporal decay. By omitting these modes, we reconstruct filtered velocity fields that retain the essential stochastic turbulence. The resulting fields yield stabilized turbulence statistics and decay exponents comparable to the homogeneous reference case. The proposed framework enables identification of modes that bias the overall TKE decay rate, potentially resolving observed discrepancies in decay rates across the literature.

Developing reduced-order models applicable to fluid-dynamics problems involving complex geometries and different flow conditions remains a critical challenge for turbulent flows. This study introduces VIVALDy, a machine-learning framework that employs a hybrid $\beta$-variational autoencoder-generative adversarial network architecture with masked convolutions to extract dominant flow features into a compact latent space while preserving fidelity at solid-fluid interfaces. A bidirectional transformer then models the temporal evolution of these features, learning to predict flow trajectories from minimal sensor inputs. This two-stage approach enables the transformer to map sensor measurements to dominant flow variables identified by the autoencoder, advancing reduced-order modeling capabilities for real-time flow prediction. The effectiveness of the framework is demonstrated through application to a problem relevant to vortex-induced vibration energy harvesting systems, reconstructing the turbulent flow around a one-degree-of-freedom moving cylinder. Validated against experimental data spanning fluid-structure interaction regimes of interest, VIVALDy accurately predicts different flow states using only the cylinder displacement. The framework demonstrates adequate performance in both reconstruction accuracy and statistical fidelity across diverse operating conditions, enabling efficient prediction of the turbulent flow phenomena governing vortex-induced vibration.

When a cylindrical droplet containing a solid particle rod interacts with a planar shock wave, the evolution of its internal wave structure becomes increasingly complex due to the presence of the solid particle rod. In this study, the interaction between planar shock waves and cylindrical droplets containing a solid particle rod is numerically simulated, and the evolution of the wave structure is analyzed in detail using the ray analysis method. Compared to a cylindrical droplet without particle, the negative pressure regions within the particle-containing droplet are more distinctly separated. At the same incident shock wave intensity, the minimum pressure inside the cylindrical droplet with a solid particle rod is significantly higher than that in a pure droplet, owing to the transmitted shock wave's inability to be fully focused within the droplet. When the incident shock wave's intensity is sufficiently high, multiple cavitation regions form inside the droplet. Additionally, variations in the eccentricity of the solid particles markedly influence the evolution of the wave structure and cavitation behavior, allowing for control over the location and size of cavitation regions. This investigation into wave structure evolutions and cavitation mechanisms within droplets is expected to contribute to advancements in biomedical applications.

The transfer of energy and other conserved quantities across scales, also known as flux or spectral flux, is a central aspect of out-of-equilibrium systems such as turbulent hydrodynamic flows. Despite its role in the few predictive theories that exist, a dynamical understanding of what determines said flux (and its direction in scale) has yet to be established. In this study we work towards this understanding by investigating how the dynamics of complex Fourier velocity phases influence the flux of conserved quantities in hydrodynamic shell models. The phase dynamics, like energy evolution, are influenced by contributions from all neighboring triads, making the full problem intractable. Instead, we assume that the dynamics of the triad phases are determined solely by the so-called self-interaction term and treat the other neighboring triad terms as noise. This transforms the phase dynamics into that of a noisy phase oscillator, which we solve analytically to predict phase statistics. We validate this assumption with a suite of shell model simulations. Our results give us analytical predictions for the energy flux, when the energy spectrum is given. We prove that all shell models that conserve energy along with a sign-indefinite quadratic quantity (this includes three-dimensional turbulence analogs) undergo a forward energy cascade and further show that the phase dynamics prevent the shell model analog of two-dimensional turbulence from forming an inverse cascade of energy.

Buoyancy-driven natural convection produces spatial nonuniformities in local heat transfer. For Newtonian fluids, these effects are often simplified into averaged heat transfer measures in the design of passive and microscale thermal systems. In viscoelastic fluids, however, the coupling between geometry, elasticity, inertia, viscosity, and buoyancy further complicates the local heat transfer behavior. This study numerically investigates the role of viscoelasticity in natural convection under the assumption of temperature-independent fluid material properties confined within rectangular cavities of varying aspect ratios ($\text{AR}\mathrm{s}$) and Rayleigh numbers ($\text{Ra}$). Specifically, using a hybrid lattice Boltzmann method, this work demonstrates the complex interplay of $\text{AR}$ and viscoelastic effects on natural convective heat transfer performance in viscoelastic fluids. Generally, viscoelastic fluids show enhanced heat transfer compared to Newtonian fluids, which becomes more pronounced at high $\text{Ra}$ in nonunity $\text{AR}$ cavities, arising from the coupled effects of geometry and viscoelasticity. Moreover, simultaneously increasing the effective shear-dependent viscosity and elastic stress contributions within the FENE-P model reduces the average heat transfer while redistributing the local heat transfer, decreasing it in some regions and increasing it in others. This study provides new insight into understanding the enhancing and suppressive effects of elasticity on local heat transfer, which is crucial for the optimization of cavity geometries and polymer properties to improve convective performance.

We present a particle-resolved simulation method for analyzing the rheology of suspensions consisting of noncolloidal, monodisperse, spherical particles dispersed in an incompressible Newtonian fluid. The method employs the lattice Boltzmann method for fluid flow and the discrete element method for particle dynamics, coupled through the improved smoothed profile approach. Lees–Edwards (LE) boundary conditions are implemented to enable efficient simulations of suspensions under shear flow. Verification tests confirm the correct implementations of the LE boundary conditions and the method for evaluating the apparent viscosity of suspensions. Applications to suspension shear flows over a wide range of particle volume fractions and interparticle friction coefficients show good agreement with previous experimental and numerical results, and capture the transition in the dominant mechanisms controlling suspension viscosity with increasing particle volume fraction, from the suspending fluid viscosity, to fluid–particle hydrodynamic interactions, and finally to particle–particle direct contacts. These results demonstrate that the proposed method provides an efficient, robust, and accurate tool for numerical investigations of suspension rheology.

High-resolution particle image velocimetry was employed to investigate the near-wall boundary layer (BL) in viscoelastic polymeric flows subjected to pressure gradient (PG) effects in a mesoscale water channel. The flow was driven over a converging surface with varying favorable PG (V-FPG), a flat surface with constant FPG (C-FPG), and a diverging surface with varying adverse PG. This study examines the interplay between viscoelasticity and FPG in shaping BL dynamics. Velocity statistics measured on the channel midplane are reported for Newtonian water and non-Newtonian polyacrylamide solutions at concentrations of 200 and 400 p.p.m., with and without PG effects. In fully developed C-FPG polymeric flows, mean streamwise velocity fluctuations increased markedly with concentration, with peak dimensional values enhanced by $\approx 58\%$ and $\approx 87\%$ at the highest flow rates compared to water. Accelerating polymer solution flows exhibited elevated edge-to-mean velocity ratios and relaminarized regions in the converging section due to strong FPGs. Inner-normalized mean velocity profiles deviated from the classical log law depending on the local PG and skin friction. The combination of V-FPG and polymer viscoelasticity strongly suppressed Reynolds shear stresses, with peak dimensional values reduced by $\approx 80\%$ and $\approx 89\%$ in accelerating 200 and 400 p.p.m. flows relative to water. These findings provide new insights into the coupled effects of PGs and viscoelasticity on wall-bounded turbulence, offering guidance for improved numerical modeling and engineering design in complex flow systems.

We present a methodology to modulate immiscible fluid-fluid invasion patterns in patterned porous media during drainage in the capillary fingering flow regime. A 2D patterned porous medium is generated by a sequential deposition algorithm of disks/grains of two distinct size ranges (dual-porosity media). To attain patterned porous media, selected regions are packed with small grains, elsewhere packed with larger grains. By tuning the ratio of viscous to capillary forces, as defined by the capillary number ($Ca$), we control the degree to which the underlying microstructure affects the invasion morphology in the patterned porous medium. A decrease in $Ca$ amplifies the influence of the underlying pore structure, resulting in a more pronounced alignment of the flow pattern with the porous medium's geometry. For these “structured” flows, the drainage within zones packed with smaller grains (having relatively smaller pores) is less than 10%. In contrast, an increase in $Ca$ promotes more “random” displacement patterns with significant invasion in fine (more than 10%) and coarse pores. The possibility to modulate multiphase flows using patterned porous media can have practical implications in engineered membrane designs for fuel cells, selective transport, and filtering applications.

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

The dilute-gas equation-of-state imposes exact nonlinear relations between variances and correlations of the fluctuations of thermodynamic variables. Correlation coefficients in particular satisfy a nonlinear compatibility relation. Applying the positivity of variances and the covariance inequalities on these exact nonlinear relations yields inequalities that constitute realizability constraints for the thermodynamic turbulence structure, valid for any compressible turbulent dilute-gas flow. These relations are illustrated using direct numerical simulation data for compressible turbulent plane channel and boundary-layer flows. At the limit of moderately compressible turbulence, the exact nonlinear identities and inequalities can be linearized yielding approximate relations that are practical in approximately mapping the thermodynamic turbulence structure in terms of two independent structure parameters. The nonlinear terms that determine the range of validity of the linear moderately compressible regime are assessed in terms of fluctuation amplitudes and order-3 correlation coefficients and correlated with the external flow Mach number.

An improved mathematical model is developed to study the electroosmotic flow (EOF) of multivalent electrolytes through a conical nanopore embedded in a polarizable material and to elucidate the lacuna between the experimental hypothesis and the existing theoretical analysis. The present model accounts for hydrodynamic steric interactions and electrostatic correlations among finite-size ions, which manifest for nondilute ionic concentrations of multivalent electrolytes. We have also considered the permittivity as well as viscosity of the suspension medium, and hence ionic diffusivity, to vary with local ionic concentration. The bulk electrolyte concentration of monovalent or trivalent salts is varied up to 500 mM and the intrinsic membrane surface charge density is considered up to $-200{\mathrm{mC}/\mathrm{m}}^2$, so that the strong coupling of finite-size ions manifests. The membrane is considered as low-dielectric and high-dielectric (perfectly conducting) material. The polarization of the membrane, and hence the induced surface charge, depend on the ionic concentration at the electric double layer (EDL). The geometrical asymmetry of the pore and valence asymmetry of the electrolyte leads to an asymmetric-induced surface charge density arising through the dielectric polarization of the membrane. The ion saturation due to the ion steric interactions, electrostatic correlations, and the dielectric decrement affects the counterion distribution in the EDL, which modifies the solid polarization of the membrane. The impact of short-range Columbic as well as non-Columbic interactions is elucidated based on numerical computation of the full set of governing electrokinetic equations supplemented by an asymptotic analysis. Through the present continuum-based approach, we have demonstrated the nonclassical pattern of the EDL, i.e., layered structure of ions, counterion saturation, overscreening of surface charge, and reversal in EOF. Based on the present modified model, we have established qualitative agreement with several experimental observations, which the standard models fails to envisage. The short-range effects on ion transport and their impact on membrane polarization are quantified in this study.