Papers

Stably stratified wall-bounded turbulence governs the dynamics of many environmental and engineering flows. A key challenge is characterizing how stratification modifies mean and turbulent profiles. Monin–Obukhov similarity theory (MOST) is the dominant modelling framework, although it has rarely been rigorously validated against well-controlled direct numerical simulation (DNS) data over a wide range of stratification levels. In this study, we exploit the temporally developing turbulent boundary layer (TTBL) framework to investigate stratified turbulent boundary layers from the weakly stable to the very stable regime, spanning a range of Reynolds and Richardson numbers, and isolating the effects due to buoyancy from other mechanisms such as flow rotation. We demonstrate that the TTBL set-up faithfully reproduces classical similarity theory results and that surface-based scaling of the mean velocity gradient holds over a wider range of $z/L$ ($L$ being the Obukhov length) than previously reported. This result is attributed to the similar decay rate of turbulent shear stress and heat flux in this canonical flow. Next, we show that, as stratification intensifies, the intercept of the mean velocity profile increases, until the separation of scales required for a logarithmic region to exist can no longer be sustained. We propose an empirical closure for this intercept shift in terms of the Reynolds number based on the Obukhov length. Finally, a simple damping of the MOST contribution to the mean velocity profile is proposed and validated, enabling accurate prediction of the wall friction coefficient ($C_f$) across the investigated regimes.

We propose GPU algorithms for high-fidelity simulation of incompressible turbulent flows. Discretization in space is performed with H(div)-conforming high-order Raviart-Thomas finite elements for the velocity and an $L^2$-conforming discontinuous Galerkin approximation for the pressure. In time, a consistent splitting scheme based on higher-order BDF time stepping is used, with convection treated explicitly. In this scheme, a pressure Poisson equation and a symmetric reaction-diffusion-type equation for the velocity need to be solved in each time step. We develop a solution framework with fast matrix-free operator evaluation for all ingredients, combined with multigrid solvers for the Poisson problem, and propose a robust mixed-precision algorithmic framework. A key to mixed-precision efficiency is a least-squares projection to generate accurate initial guesses for the iterative linear solvers, enabling us to work with relative residual tolerances of $10^{-3}$. In this regime, running the solvers entirely in single precision leads to almost no change in overall iteration counts and maintains the crucial turbulence statistics, while showing up to $1.7\times$ speedup over pure double-precision simulations.

The impact dynamics of hollow droplets, while influential in applications such as coating and spraying, remain less explored than their dense counterparts. In particular, the impact dynamics of viscoelastic hollow droplets have yet to be fully explored. This study presents an experimental investigation into the impact of hollow Newtonian (water) and viscoelastic (polymeric solution) droplets on a solid surface at different impact velocities and polymer concentrations. We demonstrate two hallmark features of hollow droplet flattening: the formation of a central counter-jet and the final deposition, both associated with the entrapped air bubble. For Newtonian droplets, the counter-jet exhibits rapid growth and breakup due to capillary instabilities. Introducing polymer additives fundamentally alters this behavior: viscoelasticity affects the counter-jet's height and velocity, delays bubble rupture, and inhibits droplet detachment. Crucially, we observe the emergence of beads-on-a-string structures during filament thinning, a signature of the competition between elastic and capillary forces. By systematically varying the polymer concentration and impact velocity, we identify the conditions under which three distinct outcomes occur: deposition, partial deposition, and detachment. Our results show how inertia, viscosity, capillarity, and elasticity together govern the splashing morphology of hollow non-Newtonian droplets.

A neural turbulence closure defines a new boundary-value problem, $R(U)=N(U)+F(U)=0$, with a coupled Jacobian $J(U)=N'(U)+F'(U)$, where $N$ is the original mean-flow operator and $F$ the learned closure. We establish two consequences of global tangent dissipation. For a monotone original operator, a positive uniform margin supplied by the original operator and closure together guarantees existence, uniqueness and a global inverse-sensitivity bound relating a posteriori solution error to the a priori residual. For a general original operator, a dissipative closure cannot worsen tangent dissipation, but this alone does not guarantee uniqueness. Tangent dissipation depends on both diffusion and reaction. We study two complementary ways to promote it: (1) an exact-integral construction enforcing non-negative tangent diffusion while leaving reaction unconstrained, and (2) a penalty on tangent-reaction violations at sampled states. Tangent diffusion enters the Jacobian, and non-negative secant eddy viscosity alone does not control its coercivity. We conduct tests with channel flow at $Re_\tau=180$–$5200$, which provides a strongly monotone baseline. Both constrained closures reach accurate solutions in all 50 training-seed/Reynolds-number cases. At $Re_\tau=1000$, we conduct tests with 10,000 starts for one fixed network per closure and we find one root for each constrained closure and multiple roots for the other closures. Although this does not prove uniqueness, it provides strong empirical evidence for uniqueness of the tested constrained closures. At $Re_\tau=5200$, the construction and penalty reduce the reported inverse sensitivity relative to the original operator by approximately $372\times$ and $11\times$, respectively.

Characterization, control, and calibration of stringiness, the propensity to form long, thin, persistent threads, are key to the design and application of polymer solutions and formulations transferred to substrates by dropwise dispensing, jetting, spraying, or coating, and are used in manufacturing fibers, membranes, or spray-dried products. For Newtonian fluids, enhancing shear viscosity translates into increasing stringiness as can be easily perceived during dripping of water vs. sugar syrups or glycerol-water mixtures. In contrast, even polymer solutions with comparable shear viscosity can display a significant contrast in extensional rheology and apparent stringiness. However, there are no quantitative maps, formulas, or scales for stringiness, which motivates this study. In this contribution, we contrast the stringiness for a series of aqueous polymer solutions by determining the filament lifespan using dripping-onto-substrate (DoS) rheometry and filament length and lifespan in using dripping-into-air (DiA). We investigate the influence of polymer chemistry and molecular weight on stringiness and rely on DoS rheometry to characterize pinching dynamics and extensional rheology response. We show that an increase in stringiness correlates with steady, terminal extensional viscosity, and extensional relaxation time, respectively. Lastly, we provide a framework, which compares the stringiness of different polymer solutions through an extensional Ohnesorge-Deborah ($Oh-De$) plot or $Oh_E-De_E$ map, by computing the two dimensionless groups $Oh_E$ using steady, terminal extensional viscosity and $De_E$ using extensional relaxation time, respectively

This paper introduces the mollified-sharp decomposition, a probabilistic regularization of moving shocks in parametric reduced-order models. Each detected shock location is treated as a random variable with a prescribed probability density. Averaging over this artificial distribution replaces the localized pressure change by a smooth transition whose spatial extent is set by the density width, rather than by direct filtering of the pressure field. Each snapshot is decomposed exactly into a regularized mollified field and a local sharp correction that restores the shock. This probabilistic construction and exact additive split define the general method; the detector, kernel, treatment of multiple shocks, alignment coordinates, and regression are implementation choices. In the present realization, a calibrated indicator detects shocks, a compactly supported Wendland kernel mollifies them, and a peak-normalized and, where necessary, partitioned weight derived from each shock-location probability density defines the centroid, principal axes, and scales of its local alignment domain. Separate POD-GPR models represent the mollified field and aligned corrections, with additional regressions for shock presence and alignment. The method is demonstrated on the transonic airfoil pressure data of Catalani et al. (2023) and compared with a standard POD-GPR model constructed from the same data and POD-energy criterion. The mollified-sharp model reduces the mean test-set relative $L^2$ pressure error by 31.2% and the mean test-set surface-pressure-coefficient error by 33.2%, while also improving the predicted shock locations and pressure changes; the trade-off is a median online evaluation time 2.24 times as long. The construction is applicable in principle to other parameter-dependent fields with moving sharp features, such as moving material interfaces in multiphase flows.

The most energetic coherent structure of a hovering full-scale quadcopter is associated with a self-organizing process in which the individual rotor vortices synchronize their frequencies while undergoing merging events, yielding a globally correlated structure. We identify and characterize this phenomenon by applying spectral modal and conditional analyses to assimilated three-dimensional velocity data acquired via Shake-The-Box Lagrangian particle tracking. The dataset captures a high-Re, turbulent flow further complicated by time-varying rotor speeds stemming from active flight control, low-frequency vehicle drift, finite spatio-temporal resolution, and measurement uncertainty. Most coherent structures recover established single-rotor features such as tip vortices and their subharmonic pairing. The globally synchronized vortex merging manifests as a spectral peak at an incommensurate frequency below the rotor band, which cannot be explained by single-rotor aerodynamics, subharmonic instabilities, or band-to-band triadic interactions. Instead, conditional averaging provides evidence of the aforementioned intermittent, distinctly non-subharmonic vortex-merging process involving all four rotor wakes. Establishing whether or not this phenomenon is observed across different flight conditions and configurations remains speculative; however, the consistent characterization of the globally synchronized vortex merging using complementary frequency- and time-domain analyses despite experimental complexities, in particular rotor speed variations, demonstrates its robustness.

It is often assumed that general stationary solutions to the wave kinetic equation are described solely by conserved fluxes and temperature. The families of solutions parameterized by these quantities are referred to as warm cascades, and are derivable from differential models of wave kinetics. These models rely on the assumption of local interactions, and we demonstrate by a time scale argument that the nonlocal effect of thermal damping on the cascade may result in dependence on an additional parameter, the UV cutoff, calling into question the validity of warm cascade solutions. This is shown for systems with both three-wave and four-wave interactions. We then consider the depletion of the cascade by this damping, and present a numerical demonstration of this nonlocal and nonuniversal behavior.

We stabilize the linearized 2-D Poiseuille channel flow at arbitrary Reynolds numbers, and assign the decay of every wavenumber to any user-prescribed rate. The actuation is as in Vazquez–Krstic (IEEE TAC, 2007), VK'07 below: the two velocity components at only one wall. This is the first Fredholm backstepping design for a Navier–Stokes system. In VK'07 the wall-normal input renders the plant spatially causal, after which the tangential input closes a Volterra backstepping loop. Here the normal input carries a finite-rank feedback of arbitrarily small gain, whose sole role, in the sense of Heymann's lemma (TAC, 1968), is to give the plant simple spectrum and make every mode controllable from the tangential velocity. The tangential input then applies a stabilizing feedback, obtained through an invertible Fredholm transform to a Stokes target PDE, shifted left by an arbitrary decay. No simplicity of eigenvalues of the Orr–Sommerfeld operator is assumed and the exclusions of plant coefficient values that have accompanied Fredholm backstepping are removed. We state the comparison with the Volterra design without embellishment: the Fredholm architecture is powerful, but its gain is spectral where VK'07 is closed-form, the simpler of the two, and one from which the Fredholm approach takes its model, its actuation, and its target. What is demonstrated here is the reach of the Fredholm method on its most demanding plant to date. The feedback is tested at Reynolds number $30000$, with the dominant part of the closed-loop spectrum assigned so that it amounts to slowing the flow about twentyfold.

Understanding the efficient transport of fluid droplets in confined geometries has been a domain of interest for industrial applications in recent times. In the present work, we focus on designing control strategies that optimally steer droplet motion. Here, we apply optimal control framework to the droplet transport problem in a microchannel based on lubrication theory that minimizes viscous dissipation. Two complementary modeling routes are adopted: a reduced-order ordinary differential equation (ODE) model optimized via Pontryagin's Maximum Principle, and a full nonlinear partial differential equation (PDE) model optimized using a Covariance Matrix Adaptation-Evolutionary Strategy. By parameterizing target displacement, droplet size, and capillary number, we uncover two distinct optimal transport regimes: a "translate-relax" strategy for short distances and a "compact-translate-relax" strategy for longer targets. In continuum mechanics, the competition between surface forces and cumulative viscous dissipation decides the optimal transport strategies. We further show that the displacement range over which the reduced-order controller transfers to the continuum model is governed by capillary stiffness. We finally address closed-loop stability by adapting a control Lyapunov function (CLF) framework to the reduced-order dynamics. We demonstrate that the terminal cost which penalizes deviation from the target, serves as a cost-compatible CLF on the physical domain, and prove that the CLF-compatible feedback exponentially stabilizes the target state.

The ensemble Kalman filter is commonly used to perform sequential data assimilation in science and engineering because of its robust performance and scalability when the state space dimension is high. However, the standard EnKF generates spurious oscillations when applied to compressible flows with shocks; the cause is the uncertainty, across the ensemble, in the shock location. This paper develops the level set EnKF, which overcomes this challenge by employing a nonlinear mapping from the original state space into a latent space in which the analysis step is undertaken. The latent representation comprises a level set function that encodes the discontinuity location and smooth state extensions, defined over the full physical domain, that represent the solution on either side of the discontinuity. We first formulate the level set EnKF as a specific instance of a more general approach of performing data assimilation in a latent space. We then demonstrate the feasibility of the level set EnKF for several one-dimensional compressible flows and a two-dimensional blast wave.

We present IB-Flows, an open-source, multi-GPU solver for the direct numerical simulation of incompressible fluid-structure interaction (FSI) problems. The code couples a second-order finite-difference fractional-step Navier-Stokes solver on a staggered Cartesian grid with two immersed boundary methods: a Lagrangian method based on moving least-squares (MLS) interpolation and an Eulerian sharp-interface method. Rigid bodies are advanced with a quaternion-based Newton-Euler solver, while deformable surfaces embedded in three-dimensional flows are described by a structural solver based on the interaction potentials; a predictor-corrector scheme provides either loose or strong fluid-structure coupling. Non-Newtonian fluids with shear-thinning or shear-thickening rheology are handled through a strain-rate-dependent viscosity, and the same framework accommodates subgrid-scale eddy-viscosity models for large-eddy simulations of turbulent flows. The solver is written in CUDA Fortran with MPI domain decomposition, so that the fluid, interpolation and structural kernels are all executed on the GPUs, while the distributed transposes required by the Poisson and implicit solvers are further accelerated by the cuDecomp library through GPU-aware communication. Strong- and weak-scaling tests show near-ideal intra-node scaling and good multi-node efficiency. The solver is validated against a set of benchmark problems spanning wall-bounded turbulence, rigid-body and deformable-body fluid-structure interaction, and a biomedical application. IB-Flows is intended as a reproducible reference implementation for immersed boundary FSI simulations on modern GPU clusters and as a transparent platform to be used for tackling multiphysics problems.

Three-dimensional CFD-DEM simulations were used to investigate the influence of fluidizing medium on the hydrodynamics and mixing of a binary fluidized bed containing equal-density 3 and 4 mm particles. Water and air were compared using identical geometry, particle properties, and initial conditions over matched normalized superficial velocities of 0.5-3.0 times the minimum fluidization velocity. The numerical framework was validated against published liquid-solid bed-expansion data and benchmarked against an established gas-solid CFD-DEM case. At matched normalized superficial velocities, water fluidization produced a comparatively dense and homogeneous bed with stable bed height and pressure drop and weak velocity fluctuations. Air fluidization resulted in greater expansion, persistent oscillations, void- and bubble-like structures, stronger circulation, and greater spatial heterogeneity. Mixing, quantified using the Lacey mixing index, increased with superficial velocity in both media but developed more rapidly and reached higher levels in air. Particle trajectories and mean-square displacement further showed greater particle mobility and transport in air. The results demonstrate that normalization by the minimum fluidization velocity does not collapse the hydrodynamic or mixing behavior across fluidizing media because fluid properties strongly influence the underlying particle-transport mechanisms.

We propose a two-dimensional benchmark for fluid-structure-contact interaction consisting of a deformable elastic disk falling under gravity within a viscous incompressible fluid and rebounding in the vicinity of the bottom wall. Solid deformability is essential, as rigid solids do not rebound in this framework. Besides this, the setting is deliberately kept simple to facilitate reproduction. The configuration is particularly challenging due to the well-known no-contact paradox, which can lead to a contactless rebound and forces numerical methods to resolve a vanishingly thin fluid layer in the near-contact region, making the dynamics highly sensitive to the spatial and temporal discretizations. In addition to no-slip boundary and interface conditions, a reduced porous modeling of surface roughness, either on the disk boundary or on the bottom wall, is also considered; this circumvents the no-contact paradox and enables genuine contact. An energy balance law is derived theoretically for all three cases. Eight numerical methodologies, developed by five research groups and spanning different model formulations, numerical methods, and codes (including both fitted and unfitted discretizations), are applied to the benchmark at several levels of spatial and temporal refinement. Quantities of interest of varying complexity are collected and compared, showing close agreement during the falling phase and increased sensitivity in the near-contact and rebound regimes. The setting and the results provide a suitable reference for the systematic assessment of fluid-structure-contact interaction solvers. The time histories of all quantities of interest for every approach and refinement level are provided as supplementary material.

Endovascular implants prevent intracranial aneurysm rupture by altering the mechanical and hemodynamic environment at the aneurysm neck. Yet many in silico workflows prescribe or reconstruct the post-deployment geometry before computing flow, leaving unresolved the mechanics that create the clinically relevant interface. Here we review braided intraluminal flow diverters, intrasaccular devices, and emerging flow-disruption concepts across deployment mechanics, inter-wire and wire-wall contact, superelasticity, wall apposition, pore geometry, computational fluid dynamics, and fluid-structure interaction. We connect these modeling choices to neck coverage, malapposition, migration, deformation, and durability, and distinguish established evidence from mechanistic inference and prospective hypotheses. We argue that model fidelity should match the clinical question: prescribed or fast placement may support screening, whereas questions of coverage, apposition, compaction, and migration benefit from mechanically plausible deployment states. An interface-resolved mechanics-to-flow framework, supported by measurable validation targets and standardized reporting, could improve device design and enable more reliable patient-specific treatment planning.

Surfactant Replacement Therapy (SRT) is a well-established intervention for Neonatal Respiratory Distress Syndrome, yet its translation to adults with Acute Respiratory Distress Syndrome (ARDS) has yielded inconsistent results in clinical trials. Using a three-dimensional, zero-dimensional biomechanical model of surfactant bolus transport through the pulmonary airway tree, we demonstrate that, while the tree-like branching architecture of the lung gives rise to discrete flow regimes that result in spatially heterogeneous and inefficient drug delivery, surfactant viscosity is a key determinant of delivery homogeneity: below an analytically derived critical viscosity, gravity causes complete surfactant exclusion from entire lung subregions regardless of dose volume. A clinically compatible tenfold to thirtyfold increase in viscosity above current formulations drives all bifurcation splitting factors toward the ideal even-split value of 0.5, enabling near-complete and spatially uniform coverage of terminal bronchioles in both infant and adult lung models. Principal component analysis across approximately 24 million simulations confirms that viscosity exerts the strongest positive influence on delivery homogeneity among all injection parameters, with dose volume being the primary determinant of efficiency. These findings provide a mechanistic rationale for reformulating exogenous surfactants with higher viscosity to improve SRT outcomes in adults.

At the fluid surface, an asymmetric wave field generated by an oscillating body produces thrust in what is known as wave-driven propulsion (WDP). Although this thrust is directed forward, the vertical oscillations inevitably produce waves radiating outwards in all directions. The effect of these side waves is not accounted for in simplified models focused on the fore–aft wave field. In this work, we take a two-dimensional shallow water approach, deriving thrust and power expressions that account for surface waves emitted in any direction. Supported by an analytically driven approach, we pose a numerical optimisation problem to maximise thrust, imposing appropriate Sommerfeld boundary conditions across subcritical and supercritical velocity regimes. The two-dimensional set-up allows us to understand how the side waves emitted by the body contribute to thrust and efficiency. Furthermore, we explore how maximal thrust depends on the shape of the body beginning with a square followed by ellipses of varying aspect ratios. Using these learnings, we include the shape of the body as a control variable to demonstrate how an optimised shape can lead to further thrust and efficiency gains.

Understanding how particles such as microplastics and plankton spread, or accumulate in localized regions below the ocean surface is crucial both for the development of sea pollutant control strategies and for marine ecology. Yet the role of vertically inhomogeneous turbulence, due to the vertical structure of density stratification in the ocean, remains poorly understood. We study, by means of direct numerical simulations, the dynamics of weakly inertial, quasi-neutrally buoyant particles in an idealized two-layer fluid model aimed to represent the ocean convective mixed layer and the more stably stratified upper thermocline beneath. We find that particles eventually rise at the surface if their density matches the mean value of the fluid at a selected depth within the mixed layer. Interestingly, however, for all other values of density, they accumulate around their neutral-buoyancy depth within the thermocline, where stratification hinders vertical transport. Our analysis shows that the thickness of the accumulation layer results from the competition between buoyancy-driven confinement, internal-wave motions, and turbulent fluctuations penetrating from the mixed layer. Smaller particles, which respond more rapidly to flow fluctuations, form broader layers; layers also broaden as their equilibrium depth approaches the mixed layer. We then derive a reduced stochastic model that explains the dependence on particle inertia and reference depth of such spreading around the equilibrium position. These results show how the coupled action of stratification and decaying mixed-layer turbulence controls subsurface particle-layer formation, which may be relevant to ocean-biology oriented studies and to improve the sampling of plastic pollution in the sea.

This study examines how the chemical-reaction timescale alters hypersonic wall-model predictions of heat and momentum transfer. A one-dimensional finite-rate-chemistry wall model for high-enthalpy air is evaluated over 3 <= Ma_e <= 25, 2 <= p_e <= 100 kPa, and a broad range of edge and wall temperatures. All forward and reverse reaction rates are multiplied by a common factor Gamma, which changes the chemical timescale while preserving the equilibrium constants and thereby connects the frozen and fast-chemistry limits within the same governing equations. Taking a 1 percent difference in wall heat flux between the frozen and finite-rate solutions as the threshold for retaining finite-rate chemistry, two quantities obtained from the frozen solution provide practical selection criteria: Da_fr = t_shear / t_ch >= 1.93 x 10^3 and T_max >= 3760 K. The wall heat flux does not generally vary monotonically with reaction rate; instead, it can decrease below both the frozen and fast-chemistry predictions before recovering at higher rates. The two limiting chemistry solutions therefore do not generally bound the finite-rate heat-flux response, and interpolation between them can be misleading. At Ma_e >= 20, the median wall-heat-flux errors of the frozen and fast-chemistry limits are 7.1 percent and 27.6 percent, respectively. Chemistry also produces substantial changes in wall heat flux and shear stress, whereas the Reynolds analogy factor responds much less because the momentum- and enthalpy-side wall-law shifts nearly cancel. These results show that finite-rate wall transfer cannot in general be inferred from its frozen and fast-chemistry limits and provide frozen-state indicators for determining when finite-rate chemistry should be retained in hypersonic wall modelling.

In the present study, the consistent and conservative Phase-Field method is extended to the six-equation model for compressible multiphase flows. Based solely on the conservation laws and the second law of thermodynamics, the six-equation model with the Phase-Field mechanism is first derived. In addition to satisfying Galilean invariance and consistency of reduction, the model is general to admit an arbitrary number of phases with different formulations of the Phase-Field mechanism. The isobaric closure by the pressure relaxation and the incompressible limit of the proposed model are analyzed. The derivation and analysis identify additional terms arising from the Phase-Field mechanism, which are absent from previous studies. The consistent and conservative numerical approach is adapted to the proposed six-equation model with moderate modifications, retaining the interfacial equilibrium condition, conservation, and flexibility and robustness of incorporating different formulations of the Phase-Field mechanism with bound preservation. As the new component of solving the six-equation model, both the pressure and pressure-temperature relaxations are theoretically analyzed in a general multiphase setup, with a proof of the existence and uniqueness of a thermodynamically admissible solution for these two relaxations. Various two-phase compressible flow benchmarks are performed to demonstrate the method, and good agreement with exact solutions is achieved.

Since Taylor's seminal work on the dispersion of soluble matter, the modeling and control of solute dispersion have received considerable attention. This study investigates the solute dispersion in polymer solutions driven by unsteady magnetohydrodynamic-oscillatory electroosmotic flow within a microtube, aiming to reveal the transport mechanisms in complex rheological media through microscale flow. Firstly, based on the Debye-Hückel approximation, analytical solutions for the electric potential and velocity distributions of mixed magnetohydrodynamic-electrohydrodynamic flows are rigorously derived. Subsequently, using Sankarasubramanian & Gill's generalized dispersion model, mathematical models are developed to systematically investigate the temporal evolution of hydrodynamic dispersion. By investigating the synergistic modulation of electrokinetic and magnetic fields, we identify three distinct flow regimes, namely the electric-field-dominant, competitive transition, and magnetic-field-limited regimes, and quantitatively define their boundaries and evolution with oscillatory Reynolds number $Re$ and Deborah number $De$, thus allowing accurate flow regime classification. Moreover, a non-monotonic critical response governing solute dispersion is observed over a wide range of oscillatory Reynolds numbers, which provides a novel control paradigm for microfluidic mixing and separation. Additionally, through a comparative analysis of fractional Maxwell, classical Maxwell, and Newtonian fluids, we show that microscopic structural relaxation plays a crucial role in macroscopic solute transport under multi-field coupling. Our findings help to reveal flow mechanisms for precise mass transport control in electro-magnetically coupled systems, advancing the development of microfluidic devices and biomedical detection technologies.

Large-amplitude entrywise corruption can distort flow-field data and contaminate extracted modes. Robust principal component analysis (RPCA) separates low-rank flow content from a sparse corruption component, but recovery deteriorates when corruption occupies a large fraction of measurements. We introduce library-learning-assisted robust principal component analysis (LLA-RPCA), which restricts the recovered spatial basis to combinations of functions from a fixed candidate library and prescribes the available modal capacity. Here, the library contains standard trigonometric functions and graph-Laplacian eigenfunctions. The decomposition is solved via augmented-Lagrangian alternating minimization. The method is evaluated on a post-stall NACA0012 wake, oscillating-cylinder wake video data, and particle image velocimetry (PIV) measurements of a flat plate undergoing a transverse gust encounter. For the first two cases, synthetic large-amplitude entrywise corruption is imposed over fractions from 0% to 90%. LLA-RPCA retains coherent wake structures and recovers dominant linear modes at corruption levels where standard RPCA retains residual corruption, attenuates the reconstructed field, or collapses to a one-dimensional reconstruction. For the experimental gust-encounter case, standard RPCA exhibits a trade-off between attenuating coherent flow content and retaining naturally occurring PIV artifacts as its tuning factor increases. Conversely, LLA-RPCA suppresses artifacts while consistently preserving coherent velocity and derived-vorticity structures. These results indicate that a library-constrained reconstruction with prescribed modal capacity improves denoising and modal recovery when the prescribed representation adequately captures the relevant spatial content.

Young's law on a rigid solid and the Neumann balance at a three-fluid junction describe different admissible motions. We connect them through an ordered continuum construction. An affine viscoelastic third phase first acquires permanent deformation memory in the no-relaxation limit at fixed modulus. Independently specified material-surface laws distinguish surface free energy from mechanical surface stress. On the deformable support, displacement of solid material and migration of the wet-dry partition give separate equilibrium conditions. Stiffening an anchored support suppresses displacement at a fixed macroscopic observation distance but leaves reversible migration possible. The surviving variation gives Young's law; the constrained mechanics remains as a reaction carrying normal and, in general, tangential capillary loads. Two complementary results substantiate this reduction. A clamped finite-strain model with circular liquid interfaces yields uniform convergence of reduced energies and recovery of the spatial Young angle for global almost minimisers. A separate quadratic half-space model gives convergence of stationary migration derivatives and a nonzero limiting traction distribution. The results explain how a local Neumann-like ridge can coexist with a Young angle measured against the distant wall, while distinguishing geometric convergence from the control of migration and reaction forces.

Liquid droplets deform from spherical shape due to aerodynamic variation of pressure along the surface as the droplet moves through a gas. The deformation is predicted for axisymmetric droplets translating through a gas with low Weber numbers, We < 1, and Reynolds number Re = O(10). That deformation analysis is based on the relations between local pressure jump and the two radii of curvature. A thin boundary layer on both sides of the gas-liquid interface is considered with a surface-velocity jump due to pressure-gradient-driven flow with a large density jump and a pressure jump due to surface tension. A near-ellipsoidal shape is predicted using $We$ as a perturbation parameter. Then, the quasi-steady internal liquid-phase stream function and velocity field are predicted, describing internal circulation and a vortex ring structure with vorticity distributed through an inviscid liquid. The gas-phase flow over the oblate droplet is described using a ring doublet as an image within the droplet. The ring-doublet radius is related to We. Gas potential flow results are presented and compared using both the exact analytical solution and a perturbation analysis based on the square root of We. The perturbation analysis provides a lower computational cost. Three analyses for local curvature, liquid circulation, and gas potential flow are matched to yield the velocity and pressure fields. The appropriate radius for the image ring doublet is matched to the square root of We. Liquid-phase stream function, two velocity components in each fluid, and gas potential field are predicted. S Some comments on droplet drag are presented.

We study the effects of conductivity variation on the Ponomarenko dynamo. Taking monotonically increasing/decreasing and sinusoidally varying radial profiles, we study the kinematic dynamo problem. The threshold of the dynamo, given by the critical magnetic Reynolds number Rm$_c$, is found to strongly depend on the form of conductivity variation near the discontinuity of the velocity field where the shear is dominant. For monotonically varying profiles in the limit of sharp variation, this threshold maps to the problem of the dynamo with a jump in conductivity, while for the sinusoidal profile with large variations/wavenumbers, the threshold increases due to effective diffusivity arising from the rapid changes in conductivity. Far from the threshold, it is found that the growth rate depends only on the local gradient of the conductivity near the discontinuity, with the opposite sign of shear and conductivity gradient leading to a larger growth rate, thereby aiding the dynamo instability in regenerating B$_{\phi}$ from B$_r$. We calculate the expression for the growth rate in the limit of large Rm$(\gg 1)$ and find that the conductivity variation leads to a modification proportional to the local gradient of conductivity times Rm$^{-1/2}$. This correction is found to depend only on the local gradient of the conductivity at the discontinuity. Similar dependencies are found for realistic, smooth velocity profiles and for different magnetic boundary conditions.

Capillary forces are commonly regarded as an energetically closed channel in multiphase turbulence, redistributing kinetic energy across scales without net gain or loss. Here we show that this picture breaks down in bubble-laden turbulence when short-range near-contact interactions are active. A spectral analysis of the kinetic-energy budget reveals that the cumulative capillary power does not vanish at statistical stationarity, but instead retains a finite negative residual. This apparent imbalance is exactly compensated by the work of short-range repulsive forces, which is negligible at large and intermediate scales and becomes positive only at small scales. Near-contact interactions therefore open a distinct small-scale pathway in the interfacial energy transfer, rather than acting as a mere regularization of unresolved thin films. The proper scale-by-scale description is thus an extended interfacial transfer, combining capillary and near-contact work, rather than a purely capillary one.

Micron-sized particles moving through a fluid are subject to viscous resistance and thermal fluctuations. Beyond steady Stokes friction, colloids also exhibit hydrodynamic memory effects arising from conservation laws of the surrounding fluid. Although fluid-flow problems in complex geometries and confinements are often highly involved, numerical or approximate solutions can be obtained; translating these solutions into closed-form equations of motion for individual colloids, however, is rarely possible. Here, we develop a theoretical framework that provides both underdamped and overdamped colloidal dynamics from the solution of an arbitrary flow problem: (i) Using the Lorentz reciprocal theorem, we express the colloidal equation of motion in terms of the geometry's Green's function and the fluid-flow profile. This formulation yields both the corresponding Stokes drag as well as a Basset-like hydrodynamic memory contribution. (ii) As colloid inertia is often negligible, we furthermore derive the corresponding overdamped (colloid-inertia-less) limit, which inherits the Stokes and Basset-like resistances and additionally gives rise to a spurious drift. We propose applications of this framework to passive and active particles subject to involved confinements and problem geometries.

Micron-sized colloid particles diffusing through a fluid experience hydrodynamic inertial and memory effects, the latter causing velocity autocorrelation to decay as a power law. At the same time, many theoretical descriptions treat colloidal diffusion in a fluid using overdamped Langevin dynamics for its convenience, eliminating velocity, omitting inertia, but also ignoring the power-law memory. In this Letter, we show that hydrodynamic memory survives in the overdamped (colloid-inertialess) limit. By identifying the dimensionless parameter controlling the crossover between early- and late-time dynamics, we derive in closed form the overdamped Langevin equation in the presence of hydrodynamic memory. This provides a theoretical framework for realistically describing colloidal dynamics in a fluid, and establishes a rigorous basis for the positional memory observed in high-resolution experiments. Our theory predicts that hydrodynamic memory becomes increasingly pronounced for smaller particles and under stronger external forcing, and offers experimental probes for the crossover from conventional exponential relaxation to memory-dominated power-law dynamics.

The finite-time blow-up construction for the forced Navier-Stokes equations released by OpenAI in Sep. 2026 (OpenAI 2026) has as its object an axisymmetric swirl core in anisotropic similarity variables. Its geometry is that of an exact steady swirl between rotating porous cylinders found by Gumerov and Duraiswami in 1998 (GD1998). We find that the GD1998 boundary value problem does not recast into the similarity variables and that its generalization is a two-dimensional profile problem between porous walls held at fixed similarity radii, second order in the radial variable X and first order in the time-like axial variable $\eta$. We solve it by tensor Chebyshev collocation with a pinned pressure gauge, complex-step Newton and arclength continuation, verify it three ways, and sweep the radial Reynolds number, the wall swirl and a symmetry-breaking datum. Below inflow 9 the solution is one smooth branch; above it the symmetric branch folds at a critical swirl $F^*=0.41V_0^2$. The Dirichlet axis problem has no resolution-stable solution; the core must be a Cauchy problem from the axis. Its moment identities cannot be met by a core symmetric about the dividing plane: the core is an axial through-flow, as its authors chose it; a non-symmetric core meets them to 0.2%. The cone condition is Rayleigh's criterion with axial shear and requires radii of order $10^{20}$. Dynamic rescaling shows the profile to be an attractor at weak inflow and toward the fold, a saddle-node; at moderate inflow and strong swirl the spectrum does not converge in the axial resolution and is left open. A real fluid cavitates (water) or shocks (air) first; the GD1998 chamber is proposed as the experiment. Nothing found suggests the mechanism is reachable in a flow one computes or builds; the forced theorem, and this study, leave the unforced equations of practice as they were. Code, tests and log accompany the paper.

It is shown that the second-order Carleman truncation (C2) captures the steady state of the decaying forced logistic with second-order accuracy in the forcing parameter, provided such forcing remains below a critical value of 1/2. We then investigate the extension of these results to spatially extended systems by means of Carleman Lattice Boltzmann simulations of a two-dimensional periodically forced flow. It is found that C2 correctly reproduces the low-Reynolds-number (between 1 and 10) quasi-linear dynamics, well above the critical value of the forced logistic equation. However, C2 fails to capture more complex steady states characterised by persistent vortical structures at Reynolds numbers around 20. Interestingly, the divergence observed in the latter case shows qualitative similarities with the runaway behaviour of the C2 linearization of the growing logistics, suggesting that suitable closures and/or change of variables may improve the convergence of the C2 procedure.