Papers

The fingering instability of thin-film flow is a significant obstacle to producing uniform and stable films in industrial processes. In the framework of lubrication theory, we investigate the linear stability of a gravity-driven thin film with an inclined contact line using numerical and asymptotic methods. The contact-line singularity is regularized by imposing the Greenspan slip model. As demonstrated by the results, although the contact-line inclination slightly enhances long-wavelength instability, it significantly suppresses the growth of spanwise finite-wavelength perturbations. Moreover, the most unstable wavenumber shifts toward the long-wave region as the inclination angle increases. The inclination of the contact line introduces complex eigenvalues, leading to traveling-wave modes, in contrast to the standing-wave modes observed for horizontal contact lines. We also performed asymptotic analysis in the limit of small wavenumbers, confirming the enhanced long-wave instability. The physical mechanisms underlying these stability characteristics are elucidated, revealing that the effects of contact-line inclination come from the eigenmode distortion and additional streamwise flux.

Bubbly flows involve strongly coupled bubble motion, deformation, and hydrodynamic interactions, making high-fidelity simulation computationally expensive. We propose a neural surrogate that jointly predicts bubble trajectories and interface deformation in a compact, shared representation, replacing costly mesh-resolved simulation with fast generative inference. Because two-phase flow dynamics is nonlinear and chaotic, we treat forecasting as a conditional generative problem rather than deterministic regression, predicting entire future windows in a single pass. We train and evaluate the surrogate on BubbleSH, a Front-Tracking dataset of rising deformable bubble swarms, assessing performance using trajectory, shape, and distributional metrics over kinematic, morphological, and interaction-based properties. The surrogate reproduces key flow statistics while running several orders of magnitude faster than the underlying DNS solver.

Context: Solar magnetism exhibits long-term variations on timescales of decades to centuries. Aims: The main aim is to study how the supercriticality of the dynamo affects the variability of magnetic fields on timescales relevant to the Sun. Methods: Three-dimensional rotating magnetohydrodynamic simulations in a spherical wedge geometry are used to produce self-consistent convection-driven dynamos. The supercriticality of the dynamo is controlled by varying the magnetic diffusivity. Results: The main result is that long-term variability of the dynamo increases with decreasing supercriticality of the dynamo and that cases nearest to the onset of dynamo action show extended grand minima-like periods of low activity. The simulations fall in three classes where the least supercritical cases show the largest variations of magnetic activity and where the flow including differential rotation is almost unaffected by the magnetic field. In the cases with the highest supercriticality the magnetic field is permanently strong and differential rotation permanently quenched, both having relatively little temporal variation. In an intermediate regime both the magnetic fields and differential rotation exhibit strong anticorrelated fluctuations. Conclusions: The occurrence of grand minima in the Sun has been conjectured to be due to a weakly supercritical dynamo. The current results support this idea and suggest that the absence of grand minima in earlier global dynamo simulations is because their large-scale dynamos were too supercritical. Furthermore, the current results suggest that the effect of the magnetic field on differential rotation is negligible if the average rms-field is less than about 2~kG.

A ghost-cell immersed boundary method is proposed for the two-dimensional shallow water equations with a variable bed (topography), solved with an explicit Godunov-type finite volume scheme (unsplit second-order MUSCL, HLLC flux, hydrostatic reconstruction) on Cartesian grids. Ghost-cell methods leak mass through the wall. To find a robust and conservative treatment, eight constructions of the ghost values and a cut-cell form of the continuity equation were applied to seven test problems, which include wetting and drying on sloping beds and a laboratory dam break. In the resulting scheme, the ghost values are interpolated bilinearly at the image point; solid and dry nodes are excluded, and the weights of the remaining nodes are renormalized. Mass is conserved by solving the continuity equation in cut-cell form, while the momentum equations are left unchanged. The proposed scheme is about as accurate as the ghost-cell method without this modification and preserves a lake at rest whose shoreline crosses an immersed wall. Because only the continuity equation is modified, it avoids the treatment of the momentum equations on cut cells (wall pressure, cell merging) that a full cut-cell method requires.

Aim. We try to understand the interaction of eccentricity tide and convection in icy satellites. Method. We use the numerical calculation of rotating convection with eccentricity tide in a spherical shell. Results. We have the following results. (1) Energy scaling exponent about buoyancy force (or tidal force) decreases with increasing tidal force (or buoyancy force). (2) The combined tide-convection flow is not identical to superposition of two pure flows in respect of energy spectrum. (3) Tide controls large-scale of fluid motion but convection is important for small scale, and the mode-mode transition occurs at intermediate scales. (4) Tide suppresses heat transport efficiency. (5) Dissipation of kinetic energy scales as square of tidal force with a very weak dependence on buoyancy force, which has little impact on dissipation but suppresses the tidal influence on dissipation.

The results from [Fluid Dyn 61, 20 (2026)], concerning the generalized Chapman-Enskog method and a nonlocal (i.e., non-diffusive, spatially integral) viscous stress tensor in the Navier-Stokes equation, are extended to the case of arbitrary gradients of not only hydrodynamic velocity but also temperature. The resulting equations simplify the description of tangential discontinuities and separated flows. For the specific case of an incompressible medium, a nonlocal vorticity transport equation is derived that is structurally identical to the Biberman-Holstein equation for resonant radiation transport in plasmas and gases. A power-law form has been determined for the velocity distribution function of long-free-path vorticity carriers that satisfies empirical Richardson t^3 law for the mean square of relative separation of a pair of particles in a turbulent liquid or gaseous medium.

We present two and three dimensional direct numerical simulations of planar intrusions injected from a continuously supplied, narrow source into a linearly stratified ambient at the level of neutral buoyancy. The evolution passes through three phases. A laminar leading vortex dipole first advances at constant speed with a varicose wave train behind it; the trailing jet then undergoes a sinuous instability whose initial growth rate and wavelength agree with inviscid unstratified planar-jet theory evaluated on the local jet; the flow finally relaxes into a buoyancy-controlled wedge whose area grows linearly in time. Three-dimensional simulations show that the transition remains organized by the planar instability, while three-dimensionality reshapes the near-source region into a slowly evolving, actively mixing zone that entrains an additional twenty to one hundred percent of the source flux depending on source width. Rescaled with this measured effective flux, the downstream intrusion collapses reasonably well onto the similarity solution for a wide-source intrusion.

We perform direct numerical simulations of rotating turbulence to investigate the mechanisms responsible for the maintenance of large-scale geostrophic vortices. We confirm that the Reynolds stresses generated by inertial waves are consistent with the Reynolds-Averaged Navier-Stokes balance of the large-scale flow and demonstrate the predicted cyclone-anticyclone asymmetry, with cyclones exhibiting stronger azimuthal velocities and more compact cores. Wave-field analysis provides evidence that geostrophic vortices selectively reflect and absorb inertial waves according to the sign of their angular momentum. Wave absorption occurs either through the formation of a critical layer ahead of the reflection point or through enhanced viscous dissipation associated with increasing local wavenumber. As rotation increases, fewer inertial waves undergo resonant absorption, reducing angular-momentum transfer to the vortices and weakening the geostrophic flow. Consequently, the fraction of energy contained in geostrophic modes depends non-monotonically on the rotation rate, demonstrating that sufficiently rapid rotation can ultimately suppress, rather than enhance, turbulence two-dimensionalization.

A disturbance in steady rectilinear translation along a capillary-gravity interface radiates waves only above a minimum speed $c_{min}$, where it experiences a wave resistance; below this threshold it generates no waves, and the response is merely a localised deformation of the interface around the source, free of wave resistance. Modulating the source amplitude at a frequency $\Omega$ shifts the forcing to the sideband pair $kV\pm\Omega$, where $k$ is the wavenumber and $V$ is the translation speed, opening resonance conditions absent from the steady problem; radiation then sets in below the steady threshold $c_{min}$. Here we derive the mean wave resistance $\langle R\rangle$ of a line source in closed form, and show it to be strictly positive at every nonzero speed $V$: the drag-free below-threshold regime disappears for any $\Omega\neq 0$. Crossing the radiation transitions—where the group velocity matches the source speed—produces integrable resonant peaks in $\langle R\rangle$, whose exponents we derive, including at the cusp where two transition branches merge. Below threshold, where a steadily moving source feels no drag, $\langle R\rangle$ rises from zero as $\Omega^5$ (at fixed $V$). Throughout, surface tension is essential to $\langle R\rangle$: because it controls the short, dominant capillary-scale waves, discarding it misrepresents $\langle R\rangle$ over almost the entire speed-frequency plane.

Taylor bubble flows with nanoparticle suspensions are regularly encountered in non-isothermal chemical synthesis and microfluidics. Despite this, a complete mechanistic insight into the coupled thermal and hydrodynamic interactions remains unresolved. Here, a Eulerian-Lagrangian framework has been developed to address this, capturing two-way momentum, energy exchange, and nanoparticle interactions under non-isothermal conditions. We find that Brownian motion acts in two opposing ways, enhancing local particle-fluid energy exchange yet driving a thermophoretic drift away from the heated wall that strengthens as particle diameter is reduced below 100 nm. At particle volume fractions of $\phi \sim 10^{-2}$, Taylor flow departs from the Nusselt scaling with dimensionless slug length, $\tilde{L}_s$, observed for particle-free flows. This coincides with alterations to bubble topology that co-benefit nanoparticle momentum and energy exchange with the carrier fluid. Examining both Poiseuille and Taylor flow problems, we observe contrasting, often opposing dimensionless heat transport behaviours, questioning the suitability of traditionally accepted mixture approaches. This work reveals that, in the visco-inertial regime ($Re > 500$), it is the interplay of hydrodynamic, Brownian, and interfacial forces, combined with the Taylor bubble and slug flow topology, which determine positive or negative $Nu$ outcomes. Interestingly, short-range particle forces at the liquid-gas interface work synergistically with the convective motion in the slug to alter local particle concentration and energy exchanges within downstream thin film and near-wall regions. The intensity of this convective flow was found to impact both slug and film transport phenomena, improving the redistribution of nanoparticles when $\tilde{L}_s \leq 1.6$ and with increasing $Re$.

Distributed-input distributed-output (DIDO) systems arise in numerous engineering applications where large numbers of actuators generate spatially distributed physical fields that are monitored by distributed sensors. Developing physically interpretable models that enable real-time optimal control of these systems remains challenging because of the high dimensionality and strong spatial coupling between inputs and outputs. In this work, we propose a physics-based framework for modeling and closed-loop optimal control of DIDO systems from experimental input-output data. First, an effective partial differential equation (PDE) is selected among candidate transport models and discretized on the actuator grid to obtain a minimum-grid representation. Second, the PDE is solved in closed form, which yields an input-output operator with only four physically interpretable parameters. Third, the operator is incorporated into an iterative, constrained quadratic program that accounts for the actuator limits. The framework is demonstrated on the inner 40 x 40 section of the world's highest-resolution Fan Array Wind Generator (FAWG), comprising 1600 independently controlled fans with 36 distributed velocity measurements. The model describes the spatial interaction between the 1600 actuators and the measured velocity field with normalized mean absolute prediction errors of 11-20% for representative actuation patterns. The closed-loop controller reproduces all three prescribed two-dimensional velocity fields with a normalized mean absolute error below 2.3% in fewer than 10 iterations.

We formulate the Generalized Constraint-Controlled Rheological Model (GCCRM) for entangled linear and long-arm-branched polymer melts under sinusoidal periodic shear deformation (SPSD), spanning the linear and strongly nonlinear regimes. Molecular architecture, conformation, chain stretch, flow-active constraints, convective constraint release, dynamic tube dilation, and activated arm retraction define a common upstream molecular state. This state feeds two time-domain constitutive pathways (a configurational stress and a dissipative internal-variable stress) which are recombined before Fourier analysis. For branched polymers, the architecture is described by an entire backbone of molecular weight $M_{bb}$ and $N_a$ long arms of molecular weight $M_a$, with a compliance-weighted representative-constitutive-cell partition. The linear limit is normalized so that the configurational moduli sum to the entanglement modulus, while dynamic tube dilation and stretch drive distinct contributions to dissipative activation. Under reduced closures, GCCRM generates a smooth nonlinear elastic response with an onset of nonlinearity, an approximately logarithmic growth regime, an architecture-dependent maximum, and distinct high-deformation asymptotes. Fourier harmonics, ELR, VLR, and Lissajous curves are treated as post-processing observables of the total stress. The framework establishes a consistent constitutive architecture whose quantitative validation requires one parameter set per material across SPSD and, prospectively, transient shear histories.

Local measurements of gas flow in microscale geometries remain challenging due to the difficulty of micromechanical sensors implantation. Here, we use a levitated nanoparticle as a minimally invasive probe to map, with high spatial resolution, both the local pressure and velocity gas flow for a canonical example - a micropipe subjected to a pressure gradient. This technique enables characterization of nonequilibrium gas transport across several flow regimes, from slip flow to free-molecular flow. We directly observe the emergence of a nonlinear pressure distribution at large pressure ratios and obtain agreement with kinetic-theory predictions and Direct Simulation Monte Carlo calculations. These results introduce levitated nanoparticles as powerful and reconfigurable probes for microchannel gas sensing, with applications in microtechnology, micro-chemistry, and bioengineering.

For the first time, we study the effects of mass transfer on alloy droplet impact, solidification, and solute non-homogeneity or MacroSegregation (MS). For this purpose, a multi-physics model, including fully-coupled hydrodynamics of multiphase flow, wetting, conjugate heat transfer, phase change, and mass transfer, is established and validated carefully across several benchmarks. In addition, a concentration-flux-correction algorithm is proposed to conserve the solute mass within the droplet at the numerical discretization level. The validated model is subsequently used to explore the impact and solidification of an alloy droplet. The results show that accounting for mass transfer and solute transport improves the prediction of the dynamics of a solidifying splat, in a consistent manner with experimental observations, while this effect has been neglected in all previous studies. The analysis demonstrates that this improvement results from the flow sensitivity to the mushy region thickness, which is regulated by local solute concentration through the solidus and liquidus temperatures. Furthermore, analyses of the MS map identify several critical segregation regions most susceptible to defect initiation, such as cracking, including a long negatively segregated vein within the lamella, formed by the severe advective flow through the mush in the middle stages of the impact, a positively segregated region near the rim of the splat, appearing as a result of hook formation, and a major positively segregated zone at the top of the rim, which develops following the accumulation of the solute-rich melt sustained by washout from the lamella.

We investigate whether a physics foundation model (PFM) pretrained for PDE forecasting can be repurposed for closed-loop fluid-flow control. We construct a PFM-based controller by attaching lightweight Gaussian actor and critic heads to frozen pretrained representations and train the policy using proximal policy optimization (PPO). We evaluate the approach on HydroGym's two-dimensional Kolmogorov-flow environment using vorticity observations at \(64\times64\) and \(128\times128\) resolutions and Reynolds numbers \(\mathrm{Re}=100\) and \(200\). Across these settings, we compare the frozen PFM controller against a baseline MLP policy trained with the same PPO framework. The PFM controller achieves consistently higher reward while requiring smaller executed action magnitudes over training, indicating improved control performance with reduced control effort. These results provide initial evidence that representations learned through self-supervised next-frame prediction can be transferred directly to closed-loop fluid flow control. Project page: https://mahindrautela.github.io/morph.

We investigate finite-amplitude waves in a liquid film containing a soluble surfactant as it flows down an inclined compliant substrate. The coupled motion of the liquid and a spring-backed plate is described by a conservative weighted-residual model, which also accounts for surfactant transport in the bulk and at the free surface. The reduction retains viscous terms arising from wall motion, and its pressure closure recovers fluid added mass under uniform translation. Comparison with the coupled Orr-Sommerfeld problem gives a difference of approximately $1\%$ in the peak growth rate of the film mode at $Re=25$. Nonlinear computations are then used to examine travelling states and their dependence on substrate properties and surfactant coupling. Along the prescribed stiffness-damping path, substrate displacement decreases by more than four orders of magnitude, while wave speed changes by less than $1\%$. The extrema of free-surface elevation and liquid thickness vary differently, so surface height alone does not reliably indicate film thinning over a deformable support. In the cases studied, Marangoni coupling reduces surfactant localisation and weakens the wave and substrate response. Moving-frame reconstruction reveals recirculation near the wave crest and distinguishes propagation of the deformation pattern from transverse substrate motion. The load-work budget identifies capillary pressure as the principal net source of substrate work for the two compliant supports considered. A control calculation in which stiffness is varied at fixed damping shows a substantial change in damping loss but a comparatively small change in deformation.

We investigate the influence of insoluble-surfactant elasticity and Boussinesq-Scriven surface viscosity on the parametric instability of an interface separating two viscous fluids. The two-fluid Floquet formulation of Kumar& Tuckerman (J. Fluid Mech., vol. 279, 1994, pp. 49-68) is extended to include surfactant transport, Marangoni stresses and surface viscosity. For the parameter range considered, both mechanisms increase the onset acceleration relative to the clean interface state, but through distinct responses: Marangoni elasticity produces a non-monotonic threshold, whereas surface viscosity yields a monotonic increase towards saturation. Analysis of the corresponding unforced gravity-capillary modes shows that both mechanisms modify modal damping and natural frequency. Wavenumber selection reduces the detuning from subharmonic resonance by approximately an order of magnitude relative to that evaluated at the clean interface critical wavenumber. Along the selected branches, variations in the onset acceleration closely follow those in modal damping, with residual detuning playing a secondary role. Despite their distinct interfacial stress mechanisms, both Marangoni elasticity and surface viscosity suppress tangential interfacial motion in the strong-rheology limit, approaching a common tangentially immobilized condition.

Stiff chemical kinetics is a major computational bottleneck in reacting-flow simulations, while data-driven solvers remain sensitive to training-state coverage and chemical dynamics. This work combines conditional diffusion sampling with a thermochemically constrained multiscale Laplace neural operator (TC-MLNO) for chemistry ODE integration. The diffusion model learns the equivalence-ratio-conditioned joint distribution of temperature and species from low-dimensional flame data, augmenting the state space without independent perturbations. TC-MLNO represents transient, non-periodic responses through pole-residue Laplace layers and assigns fast, medium, and slow species to separate branches. Thermochemical constraints are imposed through losses for mass and elemental conservation and heat release rate. The framework is evaluated in 1D premixed flames, a 2D developing jet, and a 3D turbulent burner flame. With equal-sized datasets, diffusion sampling reduces the 95th-percentile distance to the base flame manifold by up to 37.5% and the a posteriori full-species macro-average error by up to 92.7% versus random sampling, especially for minor species and radicals. TC-LNO yields smaller errors than the DeepONet baseline for 84.9% of retained modes and reduces the 95th-percentile error for the most attenuated modes from 0.372 to 0.081. In multidimensional flames, TC-MLNO better preserves reaction-zone locations, heat-release structures, and chemically sensitive species than DeepONet. Errors of representative radical and nitrogen-containing species in the 3D flame decrease by 88.0%-88.9%. Compared with direct CVODE integration, TC-MLNO reduces mean chemistry and total solution times by 90.1% and 62.6%, respectively. These results show that distribution-aware sampling and Laplace neural operator learning provide an accurate and efficient alternative for stiff chemical ODE integration.

Despite widespread enthusiasm, applying artificial intelligence and machine learning (AI/ML) to turbulence modeling has yielded only modest progress, primarily due to a lack of situation-aware deployment. Data-driven Reynolds-averaged Navier–Stokes (ML-RANS) closures frequently fail to generalize across diverse flow regimes, while scale-resolving simulations (SRS) remain computationally prohibitive. As a result, ML-RANS is often misapplied outside its domain of validity, and ML-SRS is unnecessarily deployed on flows fully amenable to RANS. To guide optimal AI/ML deployment, we propose a turbulence taxonomy map parameterized by degrees of freedom ($Re$) and the degree of non-equilibrium ($SK/\epsilon$). By applying Weaver's well-recognized complexity framework, we classify turbulence into distinct physical regimes. This categorization identifies where local ML-RANS surrogates can generalize, clarifies where explicit scale resolution is physically mandatory, and highlights where physics-informed neural networks (PINNs) are most effective. Ultimately, this perspective establishes a physics-grounded framework for the flow-aware, successful deployment of AI/ML in turbulence.

Counter-rotating vortex reconnection is a topology-transforming event that leads to strong vorticity amplification and is often associated with the most irregular regions of the velocity field. Detecting such events directly in turbulent flows is a major challenge due to the ambiguity inherent in the definition of a vortex and the rapid proliferation of intense small scale vortices. We develop a novel methodology by combining two tools. The first is a local in scale, space and time regularity indicator that isolates spatio-temporal regions of interest. The second is a reconnection indicator that exploits a well-known property of vortex reconnection namely, that the enstrophy (volume integral of the square of vorticity) flows from the symmetry to the collision plane. To examine the flow of enstrophy in the correct reference frame, a new method inspired by orientational order parameters in liquid crystals is developed. We then show a proof of concept for our reconnection indicator by comparing it with diagnostic methods available in the literature. The method is validated on experimental datasets from a turbulent von Kármán flow at two different resolutions, one of which allows us to probe the flow below the Kolmogorov scale, $\eta$. Our findings suggest that counter-rotating vortex reconnection could be a potential mechanism for the creation of motions at scales below $\eta$.

The motion of inertial particles suspended in a carrier fluid, together with the dynamics of the underlying vortical structures, is investigated in a square microfluidic T-junction. The coherent structures forming near the branching strongly affect the particle distribution and may promote particle trapping around the T-region. Single-phase numerical simulations of the unperturbed base flow are combined with integration of the particle force balance equation, which, unlike most previous studies, includes the Basset-Boussinesq (BB) history force. The flow topology is analysed for $Re=500$ and $570$, while particle properties are varied through the Stokes number $St$ and the particle-to-fluid density ratio $\rho$. At $Re=500$ the base flow exhibits a steady vortex pair, whereas at $Re=570$ a Hopf bifurcation gives rise to a helical oscillation of the primary vortex pair characterized by periodic breathing. The BB history force has a non-negligible impact over the whole range of $(\rho, St)$ pairs investigated. It acts as an additional viscous force which, together with the drag of the relative motion, opposes the pressure-gradient force, widening particle spiral trajectories radially and elongating them axially. Its inclusion reduces the basin of attraction, indicating that memory effects promote particle displacement away from the vortex core and weaken trapping. At $Re=570$, spectral proper orthogonal decomposition characterizes the breathing of the primary vortex pair. Particles injected at a given location interact with the vortical structure at different phases of the cycle depending on the injection time, producing substantially different trajectories. This phase dependence is reflected in the shape and extent of the basin of attraction, quantified through the trapping probability over the inlet section and the probability density functions of the force components.

A plate withdrawn from a bath of partially wetting liquid entrains a film above a critical velocity. Here, we show that this critical threshold can be substantially increased by the presence of a laminar gas flow opposed to the plate velocity that exerts a tangential shear stress on the liquid-gas interface. Using two-phase immiscible Navier-Stokes simulations and confining the gas to a narrow channel, we derive a closed-form expression for the interfacial stress, which combined with lubrication theory relates the thickness of the film and the contact line velocity to the applied shear stress. As the gas velocity is increased, the film thins and the contact line velocity slows down, until the imposed shear overcomes the drag of the moving plate and entrainment is arrested. As in the quiescent case, the velocity mismatch between plate and contact line is independent of the plate velocity and is set by the applied shear alone. We find that one set of varying gas flow simulations, with constant critical plate velocity, therefore determines the critical gas flow for every smaller plate velocity.

The Kelvin-Helmholtz (KH) instability is a fundamental signature of the natural world, manifesting in phenomena ranging from atmospheric clouds to the iconic turbulence of Jupiter's Great Red Spot. While the linear dynamics of this instability is well-understood, the ultimate fate of the fluid — the final stationary state to which it relaxes — remains a formidable challenge. In this paper, we present a general non-equilibrium statistical mechanics framework that allows us to predict the asymptotic vorticity distribution of a sheared 2D Euler fluid. By constructing a self-consistent ansatz for the solution of the Vlasov equation, we determine the stationary stream function without explicitly solving the time-dependent Euler equations. We demonstrate that the relaxation leads to a population-inverted core, where high-energy states are fully occupied, surrounded by a tenuous halo of vortices in the lower-energy regions of configuration space. This result establishes the core-halo structure as a robust statistical consequence of the system's evolution, offering a universal framework for understanding the saturation of shear-induced turbulence in inviscid 2D fluids.

Solidification is expected to suppress fingering by removing mobile liquid. Here we report an unexpected re-emergence of fingering in impacting molten-tin drops: cooling first weakens peripheral fingers, but stronger undercooling restores them. At weak undercooling, fingers originate from a decelerating liquid rim and solidification reduces the effective acceleration that drives Rayleigh–Taylor-like amplification. At strong undercooling, solidification structures develop while liquid is still spreading, creating lateral mobility contrasts that redirect the residual flow. Comparison between the kinematically estimated solidification time and the experimentally measured fingering-onset and growth-termination times reveals a reversal in temporal ordering across the temperature range. A physics-based reduced-order model combines solidification-modified rim deceleration with mobility-gradient growth, captures the characteristic onset dynamics and accounts for the final finger length within the same physical framework.These findings establish solidification as an active means of regulating interfacial flow and morphology, with broad implications spanning metal-based additive manufacturing and debris mitigation in semiconducting industry.

These notes summarize the content of a one-week course given by Luis Vega on the binormal flow model applied to describe the dynamics of three-dimensional vortex filaments in incompressible fluids following the Euler equations. This topic touches connections between the binormal flow, the Schrödinger map and the 1d cubic nonlinear Schrödinger equation, providing a rich casuistry linked to the physical and numerical phenomenology. This course was part of the $2^{\text{nd}}$ Advanced Summer School held at the Institut d'Etudes Scientifiques de Cargèse (IESC), at Cargèse (Corsica), from $20^{\text{th}}$ to $30^{\text{th}}$ June 2023. These notes have been written and completed by two of its attendees, Elena Danesi and Pablo Merino.

Reduced order modeling provides an efficient alternative to high fidelity simulations for the rapid prediction of fluid flows in many query settings. Among non intrusive approaches, Operator Inference (OpInf) enables the identification of reduced dynamical operators directly from data while preserving a prescribed mathematical structure. The present work extends physics structured OpInf to the construction of parametric Reduced Order Models for transient incompressible flows governed by the Navier-Stokes equations. The velocity and pressure fields are represented using separate global reduced bases, and their reduced operators are identified directly from temporal and parametric POD coefficients. The identification procedure is formulated as a sequence of uncoupled least squares problems, leading to an efficient offline stage while avoiding the explicit projection of the governing equations. The approach is first evaluated on a lid driven cavity flow in a periodic regime to assess temporal extrapolation and prediction at previously unseen parameter values. Its applicability is then demonstrated for transient flow through a porous medium with a square obstacle, for which the nonlinear terms are not directly amenable to a standard Galerkin projection. The results demonstrate that the approach can accurately reproduce both velocity and pressure fields while providing computationally efficient predictions for unseen parameter values.

Setting up, running, and assessing a computational fluid dynamics (CFD) simulation requires substantial manual effort, from meshing and solver setup to diagnosis and interpretation, and repeating it across design variants slows engineering iteration. We present CFD Forge, an agentic framework built around OpenFOAM that carries an engineering request through case construction, meshing, solver execution, diagnostics, and reporting. A large language model interprets the request, reads the simulation evidence, identifies likely causes of problems, and proposes actions from a closed set. Automation is only useful if its results can be trusted, so acceptance is not left to the model: deterministic checks, registered for each type of flow, measure explicit criteria and decide. We demonstrate the framework on a converging-diverging nozzle and a two-dimensional forward-facing step, including geometry and operating changes requested in text. A turbulent cube, run outside the agent loop, shows why the checks matter: the solver completed and the mean drag settled, but the lateral-force oscillations were still growing, so a retrospective assessment withheld acceptance. To test this separation, we replayed 36 recorded simulation states, some with deliberately altered diagnostics, through the same model in two setups. Judging from the evidence without the check results, the model accepted 12 of the 13 detectable faults in all three repeats; with CFD Forge's checks deciding, none was accepted. The two setups also differ in prompting, and a fixed rule reached the same verdicts, so the model's value lies in the open-ended work rather than the verdict. Case files, recorded model calls, and decisions are retained for audit. A model that does the work, paired with checks that decide what is accepted, is a step toward automated CFD that can be trusted in high-throughput design and active-learning loops.

Philip L. Roe, the renowned British scientist, passed away on April 26, 2026, at the age of 87, while Professor Emeritus at the University of Michigan. My association with Phil Roe began in 1984, when he joined the Cranfield Institute of Technology, UK, as Professor of Computational Fluid Dynamics, while I was a postdoctoral research fellow at the same institution. For more than four decades, his incisive ideas, physical principles and distinctive approach to research on numerical methods for solving hyperbolic partial differential equations have had a lasting influence on my own approach to research in the field. Here I recount some personal memories and anecdotes emerging from the rewarding experience of interacting with Phil during the Cranfield years and beyond. I also review, quite succinctly in places, some of the main research topics that he pursued throughout much of his academic career. These notes are intended as a modest homage to Roe's impact on the subject, as well as to his influence on the careers of generations of scientists in both academia and industry.

Lymphangions, the valved muscular segments of lymphatic vessels, pump lymph against an adverse pressure gradient. Current models resolve this pumping in one vessel, a short chain or a regional network, and whole-body human models are passive. We extend the passive whole-body network of a companion static study to the active regime on the same anatomical graph, with intrinsic contraction, dynamic valves and a respiration-gated venous outlet on every vessel. Without fitting the waveform or the contraction amplitude, the network settles into a bounded pumping cycle at the lymphovenous junction, at a clinical pressure of 7.5 to 12.3 mmHg and a drainage of 35 to 50 mm^3/s. Respiration adds a swing of 1 to 2.5 mmHg at the junction and contraction about 1 mmHg inside the duct. Pressure generation is limited more by load than by drive, and no single contraction amplitude fits every vessel. Raising the subclavian venous pressure from 3 to 15 mmHg lifts the deep cervical node from 8.6 to 21.1 mmHg at the weakest drive, a transmission of 1.04 that falls to 0.78 at the strongest, so contraction buffers cervical drainage against venous pressure. The same solver gives the human cervical outlet pressure that cerebrospinal-fluid drainage models prescribe.

The lymphatic system returns 2 to 3 L of interstitial fluid per day to the venous circulation and drains the central nervous system. Most models of lymph transport describe one lymphangion or a short chain, so they cannot show how body-wide topology, calibre hierarchy and the venous outlet set pressure and flow. We build a passive steady hydraulic model on an anatomically derived graph of the human lymphatic system, with 1010 vertices and 1126 edges expanded to 89,060 sub-edges. Radii follow a Murray cube law, derived both from minimum work and from wall-shear-stress homeostasis. Pressure and flow follow from nodal hydraulic balance over Hagen-Poiseuille conductances, with an exponential wall law, hysteretic valves, Starling leak, node retention and a Windkessel outlet. Active contraction is off, and only the inflow scale is calibrated. Two quantities that are not fitted land in clinical range at the same operating point. Radii fall inside the vessel-class range, from 1.50 mm in the thoracic duct to 0.16 mm in the cervical collectors, and pressures stay below the 50 mmHg cuff scale on all sub-edges. About 49% of the gross load is removed before the outlet, nearly independent of the outflow scale and of the outlet parameters. On the route that drains the central nervous system, 30% of the superficial cervical load reaches the vein, at 10 to 18 mmHg along a segment that cervical-scale models replace with a prescribed outlet pressure. The model is a passive whole-body baseline for contraction-driven and clinical extensions.