Papers

Turbulent conjugate heat transfer (CHT) in pipes with azimuthally non-uniform heating is studied theoretically and numerically with a focus on low-$\mathrm{Pr}$ fluids. While the influence of the solid properties is well documented for uniform heat flux, their effect under azimuthally non-uniform heating has not been explored systematically. We address this gap by combining spectral analysis of the problem – which reduces arbitrary boundary conditions to a discrete set of azimuthal wavenumbers – with well-resolved numerical simulations of thermally and hydraulically fully developed turbulent pipe flow at $\mathrm{Re}_\tau \approx 180$ for $\mathrm{Pr} = \{0.025, 0.71\}$, representative of liquid metals and air. Two principal results emerge: (i) the global Nusselt number is independent of the azimuthal heat-flux distribution and exhibits only a minor dependence on the solid properties, resolving an open question for low-Prandtl-number fluids; (ii) CHT nevertheless strongly affects the azimuthally resolved mean temperature at low $\mathrm{Pr}$, where azimuthal conduction in the solid homogenises the interface heat flux, and governs the level of temperature fluctuations through the effusivity ratio (thermal activity ratio) $K$. Finally, an analysis of the turbulent Prandtl number $\mathrm{Pr}_{t}$ shows a strong anisotropy, particularly near the wall, and a dependence on the azimuthal wavenumber.

The Richtmyer-Meshkov instability (RMI) is initiated when a shock wave interacts with a perturbed interface between two materials, imparting an initial velocity to the interfacial perturbation. When the materials are viscoelastic, the subsequent evolution is influenced by the coupled effects of inertia, viscous dissipation, and elastic resistance. The interplay of these effects remains poorly understood and is important for predicting the dynamic response of shock-loaded soft materials, e.g., in blast-induced injury. Using the incompressible Cauchy momentum equation with a Kelvin-Voigt constitutive model, we conduct a linear stability analysis for the early-time post-shock evolution of a single-mode interface perturbation of two viscoelastic materials. We derive an implicit dispersion relation for the temporal growth rates of the perturbation. This relation depends on density, viscosity, and elasticity contrasts between the two materials and an viscoelastic parameter which is a bounded ratio of the viscous dissipation and elastic resistance response rates. Four material cases, spanning symmetric to highly contrasted interfaces, are examined to show how the viscoelastic number affects the growth rate structure as complex-dominated (oscillatory) or real-dominated (monotonic relaxation). The critical viscoelastic number separates these two regimes and is primarily governed by the density and viscosity contrasts. These results provide a theoretical criterion for predicting the early-time response of shock-driven interfaces involving fluids and viscoelastic solids.

We study minimum-time navigation between two points in a known two-dimensional fluid flow for a vessel with fixed-magnitude slip velocity and controllable direction. The navigation policy is parameterized by a neural network and optimized using a genetic algorithm that evolves an ensemble of candidate strategies through Darwinian selection and parameter mutation, without crossover. The method recovers analytical and numerical optimal-control solutions in several benchmark cases, including two-dimensional turbulence, and outperforms Q-learning and one-step actor-critic method. We further show that the learned navigation strategies are robust to variations in the starting position and to unresolved small-scale turbulent fluctuations, provided that the characteristic velocity of these fluctuations remains small compared to the vessel's slip velocity. The proposed approach provides a compact representation of the navigation policy, is readily parallelizable, and eliminates the need for reward shaping, offering an efficient alternative to existing analytical and numerical methods for computing minimum-time trajectories in complex flows.

Large Eddy Simulation (LES) resolves only the large, energy-containing structures of turbulent flows while modeling the effects of unresolved subgrid scales. As a result, the ac- curacy of LES strongly depends on the subgrid-scale closure. This work investigates the online calibration of a spectral viscosity closure for forced two-dimensional turbulence using ensemble Kalman Inversion (EKI). The closure consists of a wavenumber-dependent viscosity function, which is parameterized by a 16-dimensional vector. An ensemble of potential parameter vec- tors is passed through coarse resolution LES simulations, and the resulting kinetic energy spec- tra are compared with a DNS reference spectrum up to the LES-resolved wavenumber range. Then, ensemble statistics iteratively update the spectral viscosity parameters in order to reduce the model-data discrepancy. The convergence of the spectral mismatch is used to assess the accuracy of the calibrated closure by comparing LES with the filtered DNS data in spectral space. The results demonstrate the potential of EKI-based online calibration as a derivative- free framework for constructing data-driven turbulence closures with multiple parameters.

Geodynamic simulations involve solving the Stokes equations, where boundary conditions play a crucial role in governing internal dynamics and surface topography evolution. A common approach is to model the interface in contact with air as a free surface. This interface is stress-free and deforms in response to internal force balances, which is essential for understanding processes ranging from rifted margins to subduction. However, a free surface can introduce instabilities and oscillations in the numerical solution, commonly known as the "drunken sailor" instability, forcing the use of small time steps. Geodynamic models therefore often employ stabilization terms based on the gravitational effect of free-surface motion. To date, these terms have been derived primarily on a heuristic basis. Here, we apply variational calculus to the energy-minimization formulation of incompressible Stokes flow. Using the Gateaux derivative, we derive the complete weak form for a deforming free-surface domain and show that the stabilization terms arise naturally from the free-surface assumption. We consider the linear-viscosity case and identify two boundary-integral contributions: one associated with internal viscous deformation and the other with gravitational body force. Two benchmark cases demonstrate the consistency of the derived formulation with previously proposed stabilization approaches. Our results provide a mathematical foundation for the commonly used gravity stabilization and identify an additional viscous boundary contribution.

Standard convolutional neural networks for turbulence super-resolution are restricted to uniform structured grids, preventing their direct application to the non-uniform and non-orthogonal meshes commonly used in wall-bounded flows and complex geometries. We introduce a finite-volume convolution unit (FVCU) that removes this restriction. The key idea is to construct convolutional layers using finite-volume operators that are applicable to non-uniform and unstructured meshes. To this end, we use an exact representation of a 3D convolution as a linear combination of successive axis-wise convolutions. We adopt axis-wise gradient, averaging, and identity operators, as they can be evaluated on arbitrary polyhedral cells using finite-volume discretization. The resulting FVCU is well-defined on general meshes, serving as a drop-in replacement for conventional convolution layers. The FVCU is embedded in a super-resolution neural network and trained to reconstruct 3D velocity fields from $4\times$ coarsened low-resolution fields in turbulent channel flow on a non-uniform mesh, and in circular-pipe flow on a non-orthogonal O-grid mesh. Inspired by the role of the Van Driest damping function in near-wall subgrid-scale modelling in large-eddy simulations, this function is supplied as a conditional input to encode wall proximity. An ablation study confirms that the network interprets this input in a physically consistent manner. In both configurations, the model accurately reconstructs instantaneous velocity fields, Reynolds-stresses and their anisotropy, and energy spectra beyond the Nyquist limit of the low-resolution mesh. On an elliptic pipe unseen during training, the model reproduces the main flow features and local statistics, with a modest overprediction of small-scale energy. These results demonstrate a framework for extending CNN-based super-resolution to general finite-volume grids.

The profound mathematical and conceptual analogy between pressure in fluid mechanics and gravity in general relativity motivates a novel geometric reinterpretation of flows. This article proposes a theoretical framework for geometrizing pressure by establishing a Newton-Cartan geometry and applying a conformal transformation to the spatial metric. The pressure field is reinterpreted as a geometric potential that induces an effective spatial curvature, encoded in the Ricci tensor Rij and the associated Einstein-like tensor Gij. Within this curved effective space, fluid particles under the exclusive influence of pressure follow geodesics, and the classical Euler equation is recovered in the weak-field limit. The pressure Poisson equation emerges naturally as a consequence of the geodesic equation and the Bianchi identity, revealing pressure as an instantaneous geometric constraint rather than an external force. This framework provides a unified geometric interpretation of widely used vortex identification criteria, demonstrating that the prevailing Eulerian and Lagrangian schemes correspond to different geometric invariants or projections of the effective curvature. In the degenerate two-dimensional (2D) limit, the effective spatial tensor vanishes identically, and the global integral of the total curvature vanishes as well. This topological constraint offers a novel interpretation of the dual-cascade scenario in 2D turbulence: the inverse energy cascade arises from geometric condensation of positive-curvature structures toward larger scales, while the forward enstrophy cascade results from geometric dispersion of negative-curvature structures toward smaller scales.

In this study, we revisit Lorenz's pioneering concept of analogues to investigate error growth and predictability in fully developed turbulence using experimental data. By applying the method to a 1D turbulent velocity time series, we successfully identify the three error growth regimes intuited by Lorenz and later formalized by turbulence theory: the chaotic exponential regime, the algebraic regime of spontaneous stochasticity, and the saturation regime. Our analysis reveals that the Lyapunov exponent and the exponent of the algebraic regime depend on the initial error. We interpret this dependence as a statistical bias induced by the intermittency of turbulence, where rare events, characterized by lower Lyapunov exponents and more singular velocity increments, are preferentially sampled when considering larger initial errors. These findings not only validate Lorenz's qualitative intuition but also provide new quantitative insights into the predictability of turbulent flows, paving the way for potential applications in the prediction of extreme events.

The frictional drag of turbulent pipe flow is responsible for enormous energy consumption in water and natural gas distribution systems. Flow straighteners can reduce this drag by suppressing turbulence, but they generally induce a pressure loss that exceeds the reduction; similarly, large-eddy breakup devices installed in pipes have not achieved a net drag reduction. In this study, a grid of NACA0006 airfoils was adopted as a flow straightener to suppress the pressure loss, and its net drag reduction was evaluated by numerical simulations using the $k$-$\omega$ shear stress transport model of the axisymmetric Reynolds-averaged Navier-Stokes equations with periodic boundary conditions. The model was validated against fully developed turbulent pipe flow and a previous experiment on a large-eddy breakup device in a pipe. Under a pressure difference corresponding to a Reynolds number ($\mathit{Re}$) of approximately $10^5$, a grid pattern of concentric rings concentrated near the wall at an axial spacing of 0.5 m increased the flow rate by up to 9.0%, and the flow rate increase remained positive for $5 \times 10^{4} \leq \mathit{Re} \leq 2 \times 10^{5}$. The grid pattern reduced the area-integrated Reynolds shear stress by 29% and brought the velocity profile closer to a laminar one. The effectiveness of the near-wall placement is consistent with the Fukagata-Iwamoto-Kasagi identity, which weights the Reynolds shear stress more heavily closer to the wall.

An exploration is presented of two-dimensional, circular Couette flow of an elasto-viscoplastic fluid described by Saramito's (Bingham) constitutive law. Axisymmetrical base states are constructed. As has been noted previously, such states are not unique, with stresses over any plugs depending on the initial polymer stress, and the shear rate and stress may jump discontinuously across the yield surfaces. We show that base states with continuous stress profiles are linearly unstable at zero Reynolds number when they contain regions with relatively low shear rate. Unstable modes become stronger and localized to the yield surfaces as the azimuthal wavenumber increases. We report numerical simulations exploring the nonlinear dynamics of the instability. The linear unstable modes saturate at finite amplitude to create spatio-temporally complicated states. Polymer stress diffusion is added to ease these numerical simulations, eliminating normal-stress discontinuities and instability at the shortest wavelengths. Instability and transition to complex dynamics occur whenever the base flow contains regions with relatively low shear rate.

The Richtmyer-Meshkov instability (RMI) results from the impulsive acceleration of a density interface where either it or the acceleration is perturbed. Density interfaces may arise due to a change in gas species, isotope, temperature or a combination of these. We computationally investigate the effect of interface type on the plasma RMI, which is relevant for a range of applications, including inertial confinement fusion. We simulate the evolution of single-mode perturbed thermal, species and isotope interfaces in an ideal ion-electron plasma using the multi-fluid plasma (MFP) model. We find that in the MFP model, the evolution of different types of interface differ significantly, in contrast to single-fluid models where they behave similarly if the Atwood number is matched. The thermal and species interfaces produce the most severe response to shock acceleration, experiencing the secondary instabilities and enhanced primary mode growth. The isotope interface evolution is restrained in comparison to the former cases, resembling the response predicted by single-fluid models. The determining factor in the severity of the MFP RMI is the density ratio across the initial interface in the electron fluid, which is unity for an isotope interface. We observe that as the density ratio across the electron interface decreases, so do the magnitudes of the self-generated fields and consequently the severity of the growth amplification. Generally, the evolution of the RMI with different types of interface becomes more similar as the level of coupling between the ion and electron fluids is increased, characterised by reducing the plasma non-dimensional skin depth

Multi-domain physics-informed neural networks (PINNs) flexibly model medium-specific representations to solve fluid–solid conjugate heat transfer (CHT). However, standard multi-domain PINNs enforce governing equations and interface conditions on separately sampled domain supports, which can yield plausible temperature fields but inaccurate end-to-end energy transfer and outlet temperatures. We propose Cova-PINN, a multi-domain PINN framework that aligns conservation support with thermal interaction paths in complex geometries. Cova-PINN jointly optimizes cross-domain composite control-volume balances at the local scale and paired-wall closure at the global exchanger scale. We evaluate Cova-PINN on four triply periodic minimal surface (TPMS) heat exchangers and a geometrically distinct DualMS design against CHT-specific, optimization-oriented, and complex-geometry PINN baselines under a common protocol. Relative to the closest baseline, MUSA-PINN-CHT, Cova-PINN reduces average outlet-temperature and device-level closure errors across the four TPMS topologies by $37.7\%$ and $60.2\%$, respectively, while also improving full-field and heat-duty accuracy, with consistent gains on DualMS.

How the local energy transfer across scales in turbulence is encoded in the instantaneous deformation of fluid elements remains a fundamental question. We exploit the spherical geometry of the real-space energy cascade at length scale $\ell$. An exact derivation shows that it can be decomposed locally by strain self-amplification and vortex stretching, with a coefficient equal to the specific moment of inertia $2/5(\ell/2)^2$ of a spherical fluid neighborhood. Direct numerical simulations show that this contribution captures the dominant local transfer and defines a statistical boundary separating forward- and inverse-cascade events. A further longitudinal and transverse decomposition reveals that the longitudinal transfer underlying Kolmogorov's $4/5$ law is governed solely by strain self-amplification, whereas vortex stretching enters through the transverse component. These results establish a purely mechanical connection between turbulent energy cascade and the local rotational and deformational dynamics of fluid elements.

The logarithmic law of the wall is one of the most robust scaling laws of classical turbulence, yet whether it survives in a quantum fluid such as superfluid $^4$He (He II) remains unknown. At a solid wall, the viscous normal-fluid and inviscid superfluid components of He II obey fundamentally different boundary conditions, yet their motions can be coupled through quantized vortices. How these competing effects organize the near-wall flow remains an open question in quantum-fluid hydrodynamics. Here we visualize the near-wall velocity field in mechanically driven He II pipe flows at Reynolds numbers up to $1.26\times10^6$ using molecular tagging velocimetry and independently determine the wall shear stress from pressure-drop measurements. We find that the normal-fluid velocity develops a robust logarithmic profile, showing that a law-of-the-wall description persists despite the two-fluid nature of He II. Strikingly, however, the resulting wall law is distinctly nonclassical: the effective Kármán constant is less than half its classical value and remains nearly unchanged across the temperature range studied. This invariance, despite substantial changes in the relative fractions of the two components, indicates strong dynamical coupling between them. These results not only reveal how a universal law of classical turbulence is transformed by quantum hydrodynamics, but also provide valuable guidance for the design and operation of cryogenic cooling systems involving He II transport.

Physics-Informed Neural Networks (PINNs) are a widely used data-free method for solving Partial Differential Equations (PDEs) using machine learning. With recent advances in Generative Adversarial Networks (GANs), adversarial learning has shown strong capabilities for modeling complex data-driven problems; however, the use of GANs in deterministic physics-informed PDE solutions remains limited. In this work, we first identify limitations of standard PINNs for solving PDEs, including spectral bias, loss imbalance, and optimizer stagnation. We then propose Generative Adversarial Physics-Informed Neural Networks (Gen-PINNs), a unified deterministic residual-adversarial framework designed to improve data-free solutions of PDEs with sharp or shock-front behavior. The generator learns the underlying PDE solution using dynamically weighted physics-informed loss components, while separate discriminators evaluate complementary PDE residual features against ideal zero-residual states. The framework further develops and adapts several methodological components, including a Fourier representation for resolving high-frequency spatial content, an orthonormal spectral diagnostic for quantifying frequency-dependent solution errors, and a modified gradient-based dynamic weighting system for physics, initial-condition, boundary-condition, and adversarial loss objectives. Gen-PINNs is tested against standard PINNs on nonlinear and higher-order PDEs, including the Burgers, Allen-Cahn, and Kuramoto-Sivashinsky equations. The results demonstrate substantial improvements in accuracy and convergence across sharp-front, stiff, and higher-order PDE solutions, highlighting the potential of deterministic residual-adversarial learning as an effective approach for solving challenging nonlinear PDEs.

A compressible fluid column between two thin elastic plates carrying plane Poiseuille flow supports discrete structural-acoustic wall modes. This paper analyses their coupled dispersion and reports a flow-induced instability. Because a no-slip profile has zero velocity at the wall, the convective (Ingard-Myers) term in the compliant-wall boundary condition vanishes identically, so the plate-admittance conditions stay Mach-independent and a Fredholm solvability argument yields a closed-form $O(M)$ correction to every coupled wavenumber, valid for any smooth no-slip shear profile. Above the critical Mach number $M_c=\Omega/\xi$ at which an interior critical layer first appears, the two structural branches behave oppositely. The antisymmetric mode is not absorbed by the critical layer, a null protected by an exact mid-plane pressure node rather than by weak coupling. The symmetric mode, which carries no such node, is convectively unstable. Its growth rate, fixed both by a spatial calculation anchored to the dissipative wall-Stokes term and by a convention-independent temporal one, strengthens towards the inviscid limit, identifying an inviscid critical-layer instability rather than a viscous artefact. A Briggs-Bers analysis classifies it as convective. Its neutral curve follows $M_c(\Omega)$, and its growth rate is proportional to the wall compliance, vanishing for rigid walls, so it is distinct from the Tollmien-Schlichting and Kelvin-Helmholtz mechanisms. Three independent numerical schemes agree to one part in $10^9$, and the closed-form correction matches numerical differentiation across three shear profiles.

Translational and helical symmetries provide idealized descriptions of many flows encountered in nature and engineering. While translationally symmetric flows have been extensively studied within kinetic and continuum frameworks, the corresponding connection between microscopic dynamics and continuum behaviour for helical flows is less developed. Here, we investigate this connection for a dilute gas with time-dependent helical symmetry. Using the objective molecular dynamics framework, we derive a reduced Boltzmann equation that retains radial variations while preserving the classical collision operator under helical symmetry. Formal hydrodynamic expansions then yield the corresponding Euler and Navier-Stokes-Fourier equations. The resulting models describe how cylindrical geometry and axial deformation influence transport, including viscous transport and heat conduction, and how deformation generates unequal stresses along and across the axis in competition with collisional relaxation. Comparisons with direct simulation Monte Carlo solutions examine both spatially uniform and radially varying flows. In the cases studied, the first-order fluid corrections capture the leading stress anisotropy and improve the prediction of radial temperature variations, while larger Knudsen numbers expose limitations of the approximation.

We introduce a method for controlling the lateral motion of droplets bouncing on a vibrated liquid bath by superimposing a small periodic rocking motion onto the conventional vertical forcing. We show experimentally that the lateral velocity varies linearly with the rocking amplitude $\alpha$ and sinusoidally with its phase $\phi$ relative to the vertical forcing, while the response depends strongly on the droplet's vertical bouncing mode. A time-averaged model of a harmonic bouncer yields a time-averaged lateral force $\overline{F}_x=mg\alpha\sin(\Phi_b+\phi)$, where $\Phi_b$ is the droplet impact phase. Periodic rocking thus provides a simple, programmable means of exerting lateral forces on bouncing droplets, enabling controlled manipulation of passive and active droplets in pilot-wave hydrodynamics.

Physics-informed neural networks (PINNs) provide a mesh-free framework for multiphysics modeling, yet fluid flow in axisymmetric cylindrical coordinates remains largely unexplored because the governing operators are singular at the axis and momentum and energy are strongly coupled through advection and buoyancy. We introduce SAGE-PINN, a Singularity-free Axisymmetric Geometry-Encoded Physics-Informed Neural Network for this class of problems. SAGE-PINN removes the coordinate singularity by construction: the parity-preserving variable $s=r^2$ and a modified stream-function representation eliminate explicit $1/r$ terms from the trained residuals and satisfy mass conservation identically. Boundary-fitted analytical ansätze enforce the boundary conditions exactly, while staged momentum-thermal-joint training, residual normalization, Péclet- and Richardson-number continuation, and a physics-scaled drift guard stabilize the coupled optimization. The framework is trained without labelled data, using only physics and boundary constraints, and its predictions are validated against finite-element reference solutions for steady nanofluid flow and heat transfer through a stenosed artery over a wide range of flow and thermal regimes, without case-specific tuning. Mass conservation remains at single-precision round-off, and over the central operating range the axial velocity and temperature are reproduced within $1.6\%$ and $9.1\%$ relative $L_2$ error, respectively. The main deterioration occurs only in the limiting regimes of strongly buoyancy-influenced slow flow and highly advection-dominated heat transfer. Embedding cylindrical geometry, conservation structure, and boundary physics directly into the network provides a robust route to PINN simulation of axisymmetric multiphysics flows.

Rapid and accurate prediction of urban wind and temperature fields is important for urban microclimate design and climate adaptation. Large-eddy simulation (LES) effectively resolves these instantaneous fields, but its application is limited in iterative design of urban microclimate applications due to high computational cost. Existing regressive data-driven models offers quick outputs, but they produce only deterministic point predictions that inherently fail to represent turbulent stochasticity. This paper adopts a novel generative framework of Conditional Flow Matching (CFM) that uses building geometry and mean flow as guidance to generate plausible three-dimensional instantaneous velocity and temperature fields for urban microclimate in seconds. To overcome the GPU memory bottleneck of pixel space 3D generation, the model operates in parallel on overlapping pixel space through a shared-noise initialization that preserves high spatial continuity of flow structure across the entire domain. Against reference LES data, the CFM surrogate can rapidly and accurately restore the first-order statistics with Normalized Root Mean Square Error (NRMSE) of 2.99% for wind and 1.77% for temperature, second-order turbulence metrics with NRMSE of 7.17% for wind and 8.84% for temperature, turbulent kinetic energy with NRMSE of 7%, probability density function and vertical profiles in representative locations. Wind engineering application of local gust prediction demonstrate that the speed and accuracy of CFM, supporting the use of generative AI for making turbulence-aware resilient urban design and climate adaptation more computationally feasible.

The suitable moments of the Maxwell velocity distribution function recover the conserved variable and flux vectors of the Euler equations of gas dynamics. However, the Maxwellian has infinite support in velocity space, which poses challenges for the numerical analysis of kinetic schemes based on it. Although Maxwellian is a natural choice, it is not the only distribution function that preserves these key moments. In his seminal paper, Perthame (1990) introduced a compactly supported hat function as an alternative. This paper presents the formulation and analysis of a contact discontinuity capturing Boltzmann scheme based on peculiar velocity, constructed using the hat function. Owing to the compact support of the hat function in velocity space, the numerical analysis of the proposed scheme is considerably simplified, allowing for a direct proof of its positivity. The scheme, extended to second-order accuracy without compromising the positivity-preserving property of its first-order counterpart, is tested on several benchmark inviscid flow problems in one- and two-dimensions.

Multiphase flow in porous microstructures is central to CO$_2$ storage, fuel-cell operation, and flip-chip packaging. Predicting these flows remains challenging because wettability and complex pore geometry govern the nonlinear evolution of fluid interfaces. Machine learning holds substantial promise for advancing the field, but progress is constrained by scarce time-resolved 3D datasets and a lack of a unified workflow for training and evaluating models. To fill this critical gap, we introduce PoreML, an open-source framework unifying data generation, model training, and evaluation grounded in pore-scale physics. The framework comprises three core components. (a) A modern GPU-native lattice Boltzmann solver, validated against analytical solutions and published experiments, enables reproducible data generation. (b) A 3.3 TB dataset contains 560 simulation runs and 158,546 stored time steps across four application-driven scenarios. These trajectories span synthetic structures and geometries derived from micro-CT scans of real materials, covering diverse wetting conditions and viscosity ratios. (c) A unified learning framework evaluates one-step prediction and autoregressive rollouts. Its domain-specific evaluation protocols assess predictive accuracy and physical consistency. We evaluate five models of diverse architecture under these protocols. Two complementary challenges assess transfer to larger domains and from synthetic to micro-CT-derived structures. PoreML provides a shared foundation for machine-learning research on multiphase flow in porous media, with the aim of empowering the community to develop reliable predictive models and advance the field.

Chemically active drops release a chemical solute, gradients in whose concentration cause interfacial flows that advect the emitted solute. This non-linear coupling between solute distribution and fluid flow causes the drop to swim via an advective instability, if the system's Peclet number Pe–ratio of advective-to-diffusive solute transport–is larger than a finite threshold. Theoretical analyses often model active drops as diffusiophoresis-driven active particles, primarily to simplify the implementation of boundary conditions at the drop surface. However, physical insights about drop motion that rely on this simplification risk having limited applicability to fluid drops, especially when the drop is interacting chemo-hydrodynamically with its environment. Towards this, we study here the translation of a chemically active viscous drop parallel to a rigid wall, as an example of a common experimental configuration. We consider a propulsion mechanism where the drop swims due to interfacial Marangoni stresses and diffusiophoretic flows, and compare our results to those of the ”isotropic active particle” model, to examine the validity of the latter. Our analysis shows that, for the same confining force, a less viscous drop swims closer to the wall than a more viscous drop. This results in faster swimming, due to stronger concentration gradients driving the drop's motion. It is also shown that for moderate Pe, the swimming speed of the drop depends weakly on its mobility ratio (relative strength of diffusiophoretic and Marangoni flows). This weak dependence provides a quantitative justification for studying diffusiophoresis-driven active particles to infer the motion of Marangoni-stress-driven active drops.

In a recent paper, a mathematical analogy was found between two physically distinct classes of two-dimensional free boundary problems in inviscid fluid mechanics. One class involves free surface flows with constant vorticity in the bulk but without boundary surface tension, the other comprises free surface flows without vorticity in the bulk but with non-zero boundary surface tension (capillarity). Several examples were given of pairs of physically-distinct free boundary problems that amount to solving the same mathematical problem, albeit with the possibility of a single constraint arising for the capillary flows. The present work shows that this analogy extends to another pair of physically-distinct problems: a hollow vortex equilibrium in a shear flow with a third order irrotational strain and a steady bubble with surface tension in a simple straining flow. For both problems, we construct an isolated exact solution when a parameter $\gamma=0$ and provide numerical solutions for non-zero $\gamma$. An interesting feature is that non-trivial conformal mapping identities emerge from the class of problems with capillarity that apply equally for the hollow vortex problems when the parameters are appropriately constrained.

Molecular communication (MC) is a communication paradigm in which information is conveyed through the release, propagation, and reception of molecules. Many envisioned healthcare applications of MC are expected to operate inside the human body, where the cardiovascular system (CVS) may serve as the physical propagation environment and molecular transport is governed by diffusion and blood flow. Although blood flow is inherently pulsatile, most analytical MC channel models assume steady flow. In this paper, we develop a time-variant analytical model for dispersive MC channels with pulsatile flow. We derive the straight-duct response as a Normal distribution with time-variant mean and variance, capturing the combined effects of diffusion and pulsatile flow, and extend it to closed-loop channels through a wrapped-Normal representation. The model is validated against three-dimensional (3D) particle-based simulations (PBSs) for synthetic and physiologically motivated velocity waveforms. We further derive a closed-form first-order approximation for the first-arrival peak time and introduce the nondimensional indicator $S_{\mathrm{Rx}}$ for assessing the applicability of the reduced one-dimensional (1D) model. Our results show that pulsatility has the strongest influence when molecular transport is predominantly advective and the temporal flow variations are not averaged out, whereas stronger diffusion and faster pulsations reduce its impact on the received signal. Moreover, a PBS-based parameter sweep supports $S_{\mathrm{Rx}} \ge 2$ as a practical criterion for the applicability of the proposed analytical model. Finally, relating the analytical assumptions to representative blood-vessel classes shows that model applicability depends not only on the transport conditions but also on physiological properties such as vessel rigidity, geometric uniformity, and blood rheology.

Astropauses can be defined via magnetic or fluid separatrices. For the boundary layer between the stellar wind and the local interstellar medium, two separatrices can occur, the magnetopause and the hydropause. The question is whether they are identical. To address this, we investigate under which conditions the null points of the magnetic and velocity field, which define the corresponding separatrices, coincide spatially. We analysed the case of a non-monotonous pressure distribution driving stationary counterstreaming ideal HD flows and demonstrate that the existence of an extremum of the pressure in the 3D case together with a non-degeneracy condition on the velocity field implies that this point is also a stagnation point. Turning to ideal MHD and considering the regularity of all fields, we formulated the momentum equations, revealing their quasi-linearity. This allowed us to prove the occurrence of null points by examining the rank of the Jacobians of the vector fields. We found that for a given null point of either the velocity or the magnetic field at the pressure extremum, the pendant vector field has a co-located null if the Jacobian of this field is non-singular. We extended the analysis to resistive MHD and further to MHD with general non-ideal terms and proved that if at least one of the first-order momentum equations is ideal, the stagnation point and the magnetic null point are co-located. Even for general fluid theory, the two null points co-locate as long as the curl of the generalised non-ideal terms is zero at one of them or can be represented by a linear operator in the magnetic and velocity field. In general, it is not excluded that the velocity and magnetic nulls are dislocated. However, this would require specific properties of the curl of the non-ideal term, which would reduce the probability of a relaxed quasi-stationary configuration.

We develop a hybrid pore-network model (PNM) for discrete microbubble transport coupled to connected two-phase flow in porous media. We apply the model to simulate flow in the porous transport layer of a rotating proton exchange membrane (PEM) electrolyser. At sufficiently large apparent gravitational forces, bubbles growing at the catalyst layer can detach at sizes smaller than the characteristic pore size and move through liquid-filled pores via buoyancy and advection. The model couples a dynamic two-phase PNM to a Lagrangian bubble tracker. Pore-scale Stokes simulations in square throats provide closures for the bubble buoyancy velocity, the hydraulic resistance of bubble-occupied throats, and the reciprocal coupling between liquid flow and bubble motion. Verification tests assess conservation, pressure-flow coupling, bubble growth, advection, merging, trapping, and transfer to the connected gas phase. The network simulations show that increasing apparent gravitational forces shifts a larger fraction of the produced gas toward discrete-bubble transport. The increase mostly comes from a reduced detachment radius, which decreases bubble size and lets them move more freely through the network.

This study considers rapidly modifying the wake shedding frequency of the flow around an airfoil using sparse sensor information, subject to constraints on the lift coefficient fluctuations. This is achieved by combining phase-amplitude reduction with nonlinear machine-learning-based sparse sensor reconstruction. We derive time-varying phase and amplitude sensitivity fields that identify the optimal spatial locations and timing for actuation from merely three sensors. Through the sensitivity fields, we analytically obtain the optimal waveform for fast synchronization of wake shedding frequency while minimizing amplitude deviation of aerodynamic responses. The proposed approach is evaluated using flows over various NACA airfoils at several post-stall angles of attack, all of which exhibit unsteady periodic vortex shedding. With the identified optimal forcing, the wake frequency is altered much faster than with a standard sinusoidal actuation. Furthermore, the amplitude-penalized forcing achieves $20\%$ suppression of the lift coefficient fluctuation compared to the optimal forcing without amplitude penalty. The current amplitude-penalized technique may offer an efficient path for fast flow modification without causing detrimental fluctuations in periodic aerodynamic and aeroelastic systems with fluid-structure interactions.

acousticHelmholtzFoam is an OpenFOAM application that computes time-harmonic acoustic pressure fields in heterogeneous gas-liquid media on unstructured polyhedral meshes. The complex pressure is stored as real and imaginary volume fields, the material coefficients are constructed from a volume-of-fluid phase fraction with geometric face-fraction averaging, and open boundaries are truncated by Cartesian perfectly matched layers (PMLs) whose damping tensor is generated by the companion utility setPMLFields. The two coupled real-valued equations are discretized with the cell-centred finite-volume operators of OpenFOAM and assembled explicitly, including processor couplings and boundary contributions, into a distributed PETSc matrix that is solved by default with the MUMPS sparse direct solver. The solver writes pressure amplitude, complex velocity, acoustic radiation pressure and time-averaged momentum flux for acoustic-force evaluation. This paper documents the implemented equations, the case interface, the assembly and solution algorithm, the build procedure and the test infrastructure. A layered gas-liquid-PML case with an analytical solution serves as an end-to-end regression: on 8000 cells the whole-domain relative complex-pressure error is $1.197\times10^{-3}$, and serial and MPI solutions on up to eight ranks agree to within $10^{-12}$ in relative $L_2$ norm. A single-axis acoustic-levitator height sweep with constant-volume spheroidal drops demonstrates the two-phase material input and the force output, and strong- and problem-size-scaling measurements characterize the direct-solver workflow. The numerical formulation and its verification are presented in a companion paper (arXiv:2610.01593).

The problem of incompressible fluid mixing is long-studied, yet many questions remain open. This paper aims to address the question “what do efficient flow fields for mixing look like, and how do they behave?” Inspired by the dynamic and geometric approach to optimal mass transport, we formulate a version of the fluid mixing problem as an optimal control problem for transport of a passive scalar, in which the dynamics are given by the continuity equation together with an incompressibility constraint. We then develop a geometric framework around this problem which parallels that of classical optimal transport: the optimal control problem induces a metric on the set of reachable states (analogous to the Wasserstein metric), and this metric carries a formal Riemannian structure when the optimal control objective is induced by an inner product. Using this structure, we decompose our problem into a series of more fundamental geometric problems and derive (formal) necessary conditions for optimality, geodesic equations, and gradient flows for mixing. Specializing the control objective to the kinetic energy recovers the incompressible Euler equation, connecting our framework to the geometric hydrodynamics of Arnold. The resulting problem appears to be ill-posed, however, suggesting that the kinetic energy is an unnatural measure of mixing effort. Specializing instead to the enstrophy, which we argue is better suited to mixing, yields the Euler-Poincaré (EPDiff) geodesic equation for the right-invariant homogeneous $\dot{H}^1$ metric on the group of volume-preserving diffeomorphisms, and we present numerical simulations of both geodesics and gradient flows in this case. Along the way, we generalize the classical Helmholtz decomposition of vector fields, rederive the Clebsch representation of incompressible flows, and develop a parallel to the Otto calculus of optimal transport.