Papers

Lab-scale membrane distillation (MD) modules are commonly used for membrane characterization and developing empirical heat-transfer correlations. Entrance-induced flow structures can introduce geometry-specific effects into measured temperature polarization (TP) and heat transfer. However, the dependence of these effects on module geometry and flow condition remains unclear. We performed three-dimensional computational fluid dynamics (CFD) simulations of direct contact membrane distillation (DCMD) over inlet Reynolds numbers of $\Re_{\mathrm{in}}=10$-$1000$, focusing on side-chamber length and main-channel height. We discovered that counter-rotating streamwise vortices formed near the main-channel entrance across all geometries, but their downstream persistence increased with $\Re_{\mathrm{in}}$. At lower $\Re_{\mathrm{in}}$, the vortices mostly decayed before mid-channel, while at higher $\Re_{\mathrm{in}}$ they persisted farther downstream and produced pronounced spatial variations in TP. Increasing side-chamber length reduced the secondary-flow kinetic energy entering the main channel, and generally strengthened TP, whereas increasing main-channel height reduced the bulk velocity and streamwise kinetic energy, resulting in a thicker thermal boundary layer and stronger TP. For most geometries, the deviation from the straight-channel baseline changed from stronger TP at lower $\Re_{\mathrm{in}}$ to weaker TP at higher $\Re_{\mathrm{in}}$. Entrance effects therefore vary in both magnitude and direction with operating condition and cannot be represented by a constant correction across the Reynolds-number range.

The adverse-pressure-gradient (APG) effect challenges the classical scaling of turbulent boundary layers (TBLs) over a flat plate, and it remains unclear whether outer-layer similarity holds across a wide range of APG strengths.We assemble a benchmark comprising the present direct numerical simulation of a suction–blowing-induced separation bubble and published profiles, spanning Clauser parameters $\beta_e=0.04$–$180$ and Reynolds numbers $Re_\theta=530$–$19000$. Across this broad $(\beta_e,Re_\theta)$ parameter range, existing APG normalizations do not simultaneously collapse the two mean-velocity defects and four Reynolds-stress components, leaving open whether outer similarity persists. Instead of defining new scalings, we normalize each quantity by its value at a common location $y_s$. Results are shown using $y_s=0.5\delta$, beyond the outer stress peaks. For each of the six quantities, the normalized profiles exhibit a common outer shape across the conditions, with collapse emerging for $y/\delta\gtrsim0.2$ for the velocity defects and $y/\delta\gtrsim0.4$ for the Reynolds stresses. The collapse-error analysis shows that outer self-similarity is retained over a broad range of $y_s$ within the outer region and is not restricted to $y_s=0.5\delta$. Furthermore, explicit expressions are provided for the normalized outer profiles. These results support component-wise outer similarity under strong APGs and provide compact references for APG turbulence-model assessment and conditional profile reconstruction.

Homogeneous turbulent flows exhibit recurring multiscale structures across spatially separated regions, suggesting that a single flow realization may contain sufficient information to learn representations of unresolved scales. We investigate this hypothesis through an extreme super-resolution framework in which a wide-activation deep super-resolution (WDSR) network is trained exclusively on overlapping patches extracted from a single high-resolution turbulent realization. Previously unseen flow fields are reconstructed through patchwise prediction followed by Hann-window-weighted overlap-add assembly. The framework is evaluated for two-dimensional homogeneous isotropic turbulence at super-resolution factors of x32 and x64, representing severe spatial under-resolution. Despite the limited training data, the proposed approach reconstructs coherent vortical structures and recovers fine-scale features more accurately than conventional interpolation. Spectral and statistical analyses further demonstrate improved recovery of high-wavenumber energy content and multiscale flow characteristics. To assess the effectiveness of exploiting internal spatial information, we compare the proposed framework against WDSR models trained on 1, 25, 50, and 100 complete high-resolution snapshots without patch extraction. This comparison distinguishes the benefits of localized learning from those associated with increasing the number of training realizations. The results demonstrate that exploiting spatial redundancy within a single turbulent realization enables accurate reconstruction of previously unseen flow fields, even under extreme spatial under-resolution. These findings establish single-realization patch-based learning as a promising data-efficient approach for turbulent super-resolution when high-resolution training data are scarce.

Classical film theory predicts a finite diffusion-limited current at porous electrodes. However, over-limiting currents (OLCs), which exceed this limit, are often observed and have been attributed to surface charge, confinement, or electrokinetic effects. Here, we use a frequency-domain framework to identify a different mechanism governed by the time scale of concentration variation. For perfectly reactive interfaces, the spectral Sherwood number, a frequency-dependent dimensionless measure of interfacial mass transfer relative to molecular diffusion, grows as $\Shnd\sim\omega^{1/2}$ at high frequency, while its phase approaches $\pi/4$. This response corresponds to the semi-infinite Warburg limit of the electrochemical impedance. A scaling analysis shows that the exponent and prefactor are determined by diffusion within a thin layer adjacent to the interface and are therefore independent of the global pore geometry. Numerical results for parallel plates, circular tubes, and twelve porous microstructures confirm this scaling. Geometry, flow strength, and flow direction affect the low-frequency response and crossover frequency, but not the asymptotic scaling in the high-frequency limit. This temporal route to OLCs requires neither surface charge nor confinement and could inform the design of systems for pulsed electrodeposition, mineral recovery and renewable-energy storage.

We present eMOOD, an entropy-guided evolution of the Multidimensional Optimal Order Detection (MOOD) framework for high-order finite-volume methods on unstructured meshes. A novel troubled-cell indicator based on numerical entropy production replaces the classical relaxed discrete maximum principle. Using entropy generation as a physically motivated measure of non-smoothness, the detector targets shocks, contact discontinuities and under-resolved flow features with a compact stencil. Compared with conventional MOOD detection, eMOOD reduces flagged cells by up to 75%, improving efficiency and reducing memory-access overhead. The detector is used within both the classical MOOD cascade of progressively reduced-order schemes and a novel MOOD-CWENO hybrid, which retains inexpensive linear reconstruction in smooth regions and activates nonlinear high-order reconstruction only where needed. Implemented in the open-source parallel solver UCNS3D, the methodology is assessed on the Shu-Osher shock-entropy-wave interaction, double Mach reflection, supersonic forward-facing step, shock-helium-bubble interaction and triple material point problems. These benchmarks encompass strong shock interactions, shock-induced instabilities, multi-material interfaces and vortex-dominated flows, testing robustness, shock capturing and accuracy on unstructured meshes. Results show that eMOOD preserves the accuracy and robustness of reference CWENO and MOOD formulations while achieving speed-ups of up to 20% without loss of solution quality. Its compact detection stencil, reduced memory footprint and improved localisation offer a more scalable and efficient framework for massively parallel high-order compressible-flow simulations. UK Ministry of Defence (copyright) Crown owned copyright 2026 AWE.

Mesoscale combustion plays a vital role in applications ranging from portable power generation to micro-propulsion systems. This study investigates the response of mesoscale flames to upstream acoustic forcing across three characteristic flame regimes: Flames with Repetitive Extinction and Ignition (FREI), Stable Flames (SF), and Propagating Flames (PF). Acoustic forcing is applied over a broad range of pressure intensities at the first harmonic of the combustor tube. At low forcing intensities, all the flame regimes exhibit oscillations at the forcing frequency without qualitative changes in their respective flame behaviours. However, as the acoustic pressure increases, all flame regimes transition to a common unsteady regime characterised by periodic ignition-extinction cycles (resembling FREI) alongside strong oscillations at the forcing frequency. This response is identified as the oscillating FREI (O-FREI) regime, in which increasing forcing intensity leads to a reduction in the mean heat release rate, an amplification of oscillations at the forcing frequency, and a drop in the Strouhal number associated with the ignition-extinction cycle. The response characteristics across all flame regimes are examined in detail and are further complemented using reduced-order mathematical models.

Active flows are often confined by soft, deformable boundaries that they can push against, reshape, and in turn get reorganized by. Motivated by this interplay, we combine theory and numerical simulations to analyze the morphodynamics of an elastic vesicle enclosing a dilute suspension of extensile active particles. We model the two-dimensional vesicle as a weakly extensible elastic ring with bending rigidity, immersed in a Stokesian fluid, and describe the confined active suspension using a kinetic theory. The vesicle and the suspension are coupled hydrodynamically, through the kinematic and dynamic boundary conditions at the interface, and energetically, through a single alignment interaction that simultaneously aligns active particles with the membrane and the membrane with the particles. We show that this interaction reduces to a weak-anchoring boundary condition familiar from passive liquid crystals and derive a closed-form quiescent equilibrium state in which the nematic order in the suspension organizes into a vortex with a +1 defect core. A stability analysis of this state predicts an ordered hierarchy of activity thresholds at which successive shape modes of the vesicle are destabilized, as well as a purely passive, anchoring-driven instability of floppy vesicles. Nonlinear simulations, performed with a volume-conserving immersed boundary method, reveal that each threshold crossing gives rise to a distinct emergent state: a static spindle with boundary-pinned defects, a rotor that tank treads against its own rotation, a fluctuating spinner, and a turbulent state in which the vesicle acts as a self-stirring compartment. Beyond demonstrating how boundary deformability sculpts, and is sculpted by, confined active matter, our results open the door to study hydrodynamic interactions between such active vesicles and to use membrane fluctuations as a probe of activity of suspensions.

Using fully coupled two-way simulations combining the vortex filament model with the Navier–Stokes equations, we discover that quantized vortices in superfluid $^4$He are systematically rolled up into coherent bundles within normal-fluid vortex tubes. Although co-rotating quantized vortices do not aggregate spontaneously, mutual friction with the normal fluid actively drives their bundling, directly inheriting the spatial hierarchy of classical turbulence. Mutual friction excites high-wavenumber normal-fluid vortex tubes adjacent to quantized vortices, while the superfluid forms a nested structure of thick low-wavenumber outer tubes and fine high-wavenumber inner tubes around the vortex lines. A distinct time lag between superfluid kinetic energy and dissipation fuels the energy cascade, giving rise to Kolmogorov's $k^{-5/3}$ spectrum. Crucially, bundle lifetimes are governed by the ratio of the local coupling time scale $t_\mathrm{cl}$ to the Kolmogorov dissipation time scale $\tau_\eta$ ($t_\mathrm{cl}/\tau_\eta < 20$), leading to enhanced thermal stability at higher temperatures. These findings establish a unified mechanism for two-fluid multiscale vortex organization.

Rapid prediction of pressure-driven flow in microfluidic porous media is important for experimental design, tracer-test interpretation, and digital-twin development for subsurface energy and critical mineral applications. High-fidelity simulations resolve geometry-controlled flow but are computationally expensive across large geometry ensembles. Here, we introduce GeONet, a Geometry-Encoded Operator Network that predicts steady-state pressure fields by jointly representing material properties, spatial coordinates, and solid–void geometry. GeONet extends the Branch–Trunk architecture with a dedicated Leaf Network encoding the binary domain mask through multiscale features. The Branch Network represents porosity and permeability, the Trunk Network combines coordinates with local geometric descriptors and random Fourier features, and a gated DeepMixer integrates these representations to predict pressure. GeONet was trained and evaluated using 5,000 PFLOTRAN simulations of heterogeneous Reduced Complexity Platform domains, comprising nearly 30 TB of data. Comparisons with pore-scale Stokes solutions across three geometries yielded Pearson correlations of 0.987–0.991 and $R^2$ values of 0.974–0.982, supporting PFLOTRAN as reference data. Under matched partitions and two-stage hyperparameter optimization, GeONet substantially outperformed a boundary-condition-aware DeepONet baseline. Across three held-out domains, GeONet achieved NRMSE of 0.0381–0.0500, MAPE of 1.76–2.59%, and $R^2$ of 0.9673–0.9822, versus 0.1483–0.2040, 7.81–10.45%, and 0.5658–0.7126 for DeepONet, respectively. On three additional unseen geometries, GeONet achieved NRMSE of 0.0448–0.0676 and $R^2$ of 0.9511–0.9770. These results demonstrate improved accuracy, pressure-range preservation, and cross-geometry generalization through explicit geometry encoding.

We apply large $N$ expansion techniques to derive kinetic equations for strongly coupled, far-from-equilibrium field theories with $O(N)$ symmetry. For large $N$ vector models, the quasi-classical approximation holds. Incorporating arbitrary momentum-dependent interactions, we show the dynamics obey the standard kinetic equation, with the scattering amplitude given by the retarded propagator of the auxiliary Hubbard-Stratonovich field. This has broad applications to systems like spin wave and Langmuir ion-acoustic turbulence. For large $N$ random coupling (SYK-like) models in $d$ dimensions, leading-order melon diagrams induce order-one propagator renormalization and finite spectral width. The corresponding kinetic equation, unlike those for standard weakly interacting systems, does not have a local-in-time collision integral. We find evidence for a stationary, scale-invariant infrared solution, revealing a potentially novel strong turbulence scaling exponent.

When a long liquid drop is confined in a Hele-Shaw cell, the pull of surface tension produces a rapid retraction of its tip, causing it to bulge out as it draws up the excess liquid. Using numerical simulations, we demonstrate that this retraction is self-similar at long times, with the speed of retraction slowing like $t^{-1/2}$, where $t$ is the duration of retraction. After showing how this scaling can be understood using force and mass balance, we perform an asymptotic analysis of the Hele-Shaw equations to derive both the shape of the retracting drop, as well as prefactors of the scaling laws. Excellent agreement is found between our simulations and theory, and the experimental consequences are pointed out.

In this work, we develop a unified theoretical framework that constructs Bell-shaped Gaussian quadratures for deterministic Boltzmann solvers. The proposed framework establishes a general class of bell-shaped weight functions together with the corresponding integral transformations, revealing the common mathematical structure underlying existing generalized Gaussian quadratures. Based on this framework, a unified procedure for constructing discrete velocity sets is developed by combining radial quadratures with appropriate directional quadratures in different velocity-space dimensions. Several existing generalized Gaussian quadratures are naturally recovered as special cases, while the proposed framework provides a systematic route for constructing new quadrature rules based on different bell-shaped weight functions. Extensive benchmark simulations over a broad range of flow regimes demonstrate that the proposed framework achieves high integration accuracy and computational efficiency with significantly fewer discrete velocities than conventional quadrature strategies. Overall, the proposed framework not only unifies existing generalized Gaussian quadratures under a common mathematical foundation but also establishes a general design principle for the systematic development of efficient velocity-space quadratures in deterministic Boltzmann solvers.

Engineered transport architectures can improve electrolyte distribution and active-material utilization in porous electrodes, yet their implementation remains limited by fabrication methods that compromise precision, throughput, active-material preservation, or scalability. Here, an integrated embossing-calendering method is introduced to pattern Prussian blue analog (PBA) porous electrodes with embedded, micro-interdigitated flow fields (e$\mu$-IDFFs) for electrochemical desalination. This non-subtractive, roll-to-roll compatible method forms channels by controlling plastic deformation while simultaneously calendering the electrode, preserving active material and reducing patterning time by 100-fold relative to mechanical milling. Indentation experiments and a closed-form model further show that embossing requires 15-fold less force than stamping, while electrode microstructures show local densification beneath embossed channels. PBA electrodes are embossed with novel e$\mu$-IDFFs that use continuous width-tapering with isometric flow paths that promote uniform electrolyte distribution, increase rate capability, and reduce polarization. Compared with e$\mu$-IDFFs patterned using less scalable means and non-isometric flow paths, these e$\mu$-IDFFs desalinate seawater-salinity feeds near to potable levels with 1.5-fold of its thermodynamic energy efficiency and water recovery. Brackish desalination benefits similarly. Tapered, isometric e$\mu$-IDFFs and the embossing method introduced to pattern them are readily translated other electrochemical energy storage and separations systems.

A possible mechanism of tornado generation is associated with the Schwarzschild criterion for convective instability. The supercooled cloud-air mixture near the axis starts to descend and, due to the super adiabatic temperature gradient, the overheated near-surface air mass rises. The complete system of equations for full model includes equations for the stream function, for the azimuthal velocity component, and for the change in density. The refined model considers rotating convection within the framework of ideal hydrodynamics. The simplest model uses a separate equation for the stream function and can be applied to the initial stage of vortex generation. Within the framework of the simplest model, an analytical solution is combined from 8 linear dependencies by height. Rotation increases due to the conservation of angular momentum. Within the framework of the refined model, some unidirectional differential rotation arises, but it depends on boundary conditions (can be local). The full model studies the tornado development as rotating convection from the very beginning to the quasi-stationary stage. Velocity components increase in a coordinated manner. Two cases are considered: a single whirlwind and a two-eyed tornado. Radial flows converge towards the central part of the tornado near the earth surface, and there is an outflow from the "wall" to the axis and to the periphery near the top of the tornado. The maximum vertical velocity component is achieved at a certain radial distance at a certain height. The maximum azimuthal velocity component is achieved in the tornado "wall". Tornado generation criteria are discussed.

Cloud droplets respond to turbulent motion with finite inertia and settle under gravity, while condensation and evaporation change their sizes. The nonuniform accumulation of cloud droplets in turbulent flows, known as preferential concentration, has attracted sustained interest because it affects droplet collision and coalescence rates. We develop an analytical theory that quantifies the coupled effects of droplet inertia, gravitational settling, and phase change on concentration changes. Applying this theory to simulations of two-dimensional homogeneous thermal convection reveals that phase change markedly enhances preferential concentration in this flow, primarily through spatial differences in settling speed. These differences arise because droplets experience different thermodynamic histories along their trajectories and thus acquire different sizes. Droplet transport further increases this settling contribution by rearranging droplets of different sizes. Fluid deformation partly offsets this enhancement by thinning concentration structures, reducing the preferential concentration measured at a fixed spatial scale.

Turbulent annular Poiseulle flow is commonly encountered in various engineering applications, such as heat exchangers. The effects of the inner wall transverse curvature on the flowfield, characterised by the ratio of inner and outer radii $\eta = R_{i}/R_{o}$, have been studied previously using Direct Numerical Simulations (DNS). Scale-resolving simulations based on a Reynolds-Averaged Navier Stokes framework offer a potentially cheaper alternative to traditional Large Eddy Simulations (LES); however it is not clear if such models are able to capture the turbulence anisotropy in the turbulent annular pipe flow. In the present study, turbulent annular Poiseulle flow at $Re_{D_{h}} = 8900$ is performed with the Partially-Averaged Navier Stokes (PANS) model, a variable-resolution turbulence model that is based on the conventional RANS modelling. The ability of the PANS model to capture the effects of the transverse wall curvature is found to be comparable with DNS and other RANS-based scale-resolving approaches despite its relative simplicity and reduced computational cost.

We propose a model for the one-dimensional isothermal gas flow through a valve in a pipe. The valve aims at keeping the outgoing flow in an assigned interval; moreover, its opening and closing depend on a further parameter. The model is realized by a system of two conservation laws with suitable conditions coupling the ingoing and the outgoing flow. We study the corresponding Riemann problem, where non-classical shocks show up. Although simple, the model allows to study two key oscillatory behaviors of the flow, which are due, respectively, to the chattering of the valve, especially seen in the numerical simulations, and to the stabilizing hysteresis induced by the valve operation. We characterize the states leading to chattering and show how they depend on the parameters of the model. Through several numerical simulations, we study the interplay between the two above phenomena.

Fronts, eddies, jets, and meanders populate the ocean surface and play a key role in organizing transport and mixing across a wide range of scales. From a Lagrangian perspective, frontal structures are conveniently detected as surface filaments that act as barriers to horizontal transport. However, the degree to which these structures maintain coherence below the surface and the relationship between horizontal and vertical motions in their vicinity remain poorly understood. Here we analyze two such filaments in the western Mediterranean Sea, south of the Ibiza Channel, using a high-resolution ocean simulation and Lagrangian diagnostics specifically designed to characterize submesoscale transport. Backward Finite-Size Lyapunov Exponents (FSLE) computed at successive depths reveal nearly vertical, curtain-like structures extending several tens of meters into the water column, with intensity decreasing with depth. Vertical-velocity sections across the filaments show coherent downward motion aligned with the filament cores, while Lagrangian trajectories indicate rapid horizontal convergence of fluid particles accompanied by sustained downward displacement. The barrier effect of Lagrangian Coherent Structures (LCSs) is commonly associated with persistent dynamical features of large-scale flows. Here, however, we demonstrate that FSLE filaments generated by rapidly fluctuating submesoscale dynamics can also act as effective transport barriers. The results demonstrate that the surface signatures of Lagrangian filaments identified through FSLE techniques correspond to three-dimensional transport structures that regulate both lateral aggregation and vertical connectivity in the upper ocean.

Liquid marbles interface is composed by a dense network of grains trapped by capillarity at their surface. The mix of capillarity and granular character make their interfaces remarkable, allowing non wetting, high mobility and strong robustness which are a basis for numerous applications. A canonical experiment showing out of equilibrium nature of granular material is the so called tapping experiment, where a dry granular medium under vertical vibration reorganize an evolve toward a denser final state function of the vibration amplitude In this paper we explore the out of equilibrium nature of densely covered liquid marbles by measuring their shape, compaction and stresses evolution under vertical vibration. We show that liquid marble do indeed reorganize when submitted to taps, leading to higher internal pressure and lower effective surface tension.

High-fidelity three-dimensional turbulent flow fields are essential for scientific and engineering analyses, yet obtaining them through direct numerical simulation or high-resolution measurements remains expensive. Super-resolution reconstruction from coarse-grained data therefore offers a promising alternative, but remains fundamentally challenging because fine-scale structures are intrinsically three-dimensional and dynamically coupled across scales. Existing data-driven approaches still struggle to recover multiscale volumetric structures and their coherent temporal evolution. To address these limitations, we propose a turbulence-aware framework for time-resolved three-dimensional flow reconstruction. The framework couples a multiscale neural operator, designed to recover volumetric structures, with a state space model to promote temporal consistency in the reconstructed dynamics. In addition, Navier-Stokes residuals are incorporated as soft constraints to regularize the reconstruction toward physically plausible dynamics. A mixture-of-experts mechanism is also introduced to support unsupervised adaptation to unknown coarse-graining. Across evaluations on canonical turbulent systems and atmospheric reanalysis data, the proposed framework reduces reconstruction errors relative to learning-based and classical baselines, while better preserving multiscale spatial structure and coherent temporal evolution. These results validate the effectiveness of the proposed framework in reconstructing high-fidelity three-dimensional flow fields from coarse-grained data.

Rayleigh-Bénard convection (RBC) is a model for turbulent flow and challenging to simulate by direct numerical simulation (DNS). Adequate resolution of all relevant length scales requires very fine grids in space and stability restrictions can dictate small step sizes. In this paper, we investigate the use of parallel spectral deferred correction (SDC) as a high-order time-stepping method to reduce wall-clock times of direct numerical simulation of RBC. Performance results on JUSUF (CPUs) and JUPITER (GPUs) with two different codes show parallel SDC can offer some concurrency along the temporal axis plus larger maximum stable time steps. Taken together, this allows for a reduction of wall-clock time required for simulations over one free-fall time by having to compute fewer steps and being able to mitigate the higher cost per time step through temporal parallelization.

Although weak at normal gravity, gas radiation sets the gravity at which a co-flowing hydrogen jet diffusion flame stops flickering. Flamelet-based simulations with unity Lewis numbers, which reproduce the flicker frequency measured by femtosecond coherent anti-Stokes Raman scattering within 4%, are combined with local stability analysis. At one tenth of normal gravity, the adiabatic flame flickers, the radiating flame does not, and switching the emission off restores flicker. Radiation acts through two mechanisms that do not weaken at reduced gravity. The hot outer layer loses buoyancy in proportion to the gas residence time, and a disturbance that displaces the flame also displaces its emission, which damps the disturbance on the lean flank (displaced-emission damping). Freezing the radiative source, which removes only its response to disturbances, slows the downstream recession of the oscillation more than tenfold. Both mechanisms slow the upstream spreading of disturbances. This spreading, competing with the co-flow, sets the onset location and the critical co-flow. Without radiation, the spreading speed scales with the square root of gravity; its radiative reduction does not. At reduced gravity, the flicker limit therefore becomes a straight line relating the square root of the co-flow Froude number to a radiation number, the ratio of buoyant to radiative time scales. The calibrated line places the critical gravity for the experimental co-flow at 0.13 times normal gravity, 2.6 times the adiabatic value. It correctly predicted whether two further flames keep flickering. Beyond the limit, transient wave packets can mimic flicker throughout a short drop-tower test.

A tidal bore is a nonlinear step like surge propagating on the top of a river counter-current. The scientific literature reports that the passage of the tidal front may induce local flow reversals and, in some cases, a global reversal of the river current. Here, combining Particle Image Velocimetry (PIV) measurements and 2D numerical simulations based on a Weakly Compressible Smoothed Particle Hydrodynamics (WCSPH) method, we show that the flow classification of tidal bores must explicitly take into account the frame of reference. When the river flow does not reverse after the bore passing, this is a consequence of the perspective imposed by the background current (itself resulting from the previous tide and the natural river discharge toward the sea). Depending on the relative magnitudes of the river current and the velocity field induced by the bore, one may observe a global reversal, a local reversal (or both), or no reversal at all. When the tide is spatially inhomogeneous, with a tidal range that varies along the estuary rather than a simple step in water depth, transitions between bore types may occur during the bore passing.

Cylindrical or spherical windows often appear in experiments and real applications. Measuring through those windows requires projecting 3D points to pixels, which is different to compute due to refraction. A point may have multiple projected images but cannot be efficiently determine with the existing projection algorithms. Using the ray's conserved momenta, we reduce this projection to closed-form equations with a concave structure. As a result, we can successfully determine whether a 3D point has a single projection or multiple and compute those locations. In simulations, with one single search, we can recover images that iterative methods miss even with many restarts. A wand calibration based on it can reach the precision limit set by image noise, enabling accurate 3D particle tracking in a swirling flow through cylinder windows. This algorithm shows how to predict visibility and multiple images through curved windows, shedding light for 3D pipe flow measurements, accurate underwater reconstruction, and many real applications.

Periodic forcing is common in particle-laden jets, yet its influence on turbulence and inertial-particle clustering remains poorly understood. We investigate a turbulent planar jet at two Reynolds numbers, approximately 4950 and 9900 based on nozzle height, subjected to sinusoidal forcing at a frequency three orders of magnitude below the preferred jet instability. Hot-wire anemometry and high-speed particle imaging characterise the carrier turbulence, while Voronoi tessellations quantify preferential concentration of dilute inertial droplets. Despite its low frequency and moderate amplitude, forcing substantially modifies turbulence while leaving the mean-flow development nearly unchanged. The integral scale decreases by up to $40\%$, while forced and unforced jets retain the same time-averaged relationship between the dimensionless dissipation coefficient and Taylor-scale Reynolds number. Within the forcing cycle, velocity fluctuations and the Taylor microscale vary approximately in opposite phase, keeping the Taylor-scale Reynolds number within $\pm10\%$ of its cycle mean despite substantial variations in dissipation and Kolmogorov time scale. Particle clustering is even more sensitive, with forcing increasing mean preferential concentration and producing phase-dependent variations of $21$–$49\%$ of the cycle mean. Clustering peaks when the Kolmogorov time scale is largest, corresponding to the smallest particle Stokes number. Thus, markedly different clustering states occur at similar instantaneous Taylor-scale Reynolds numbers. These findings demonstrate that weak temporal modulation can control particle organisation without substantially altering the mean transporting flow.

The Boltzmann equation is the fundamental kinetic bridge between molecular mechanics and fluid behaviour. It converts binary encounters into the evolution of a velocity distribution, underlies rigorous routes from hard-sphere dynamics to Euler and Navier–Stokes–Fourier equations, and remains indispensable when continuum descriptions fail, from hypersonic shock layers and atmospheric re-entry to rarefied multiscale flows. Yet its nonlinear collision term is conventionally represented by an infinite three-index tensor of collisional brackets, with apparently new coefficients at every polynomial order. Here we prove that this entire hard-sphere tensor contains only one primitive collision law: the exact rank-two stress-production vertex $S$. Every polynomial collision vertex is obtained from $S$ by a finite sequence of universal differential and tensor operations, and every conventional bracket follows by differentiation. Thus the interaction physics and its representation separate exactly: all hard-sphere-specific information is concentrated in $S$, whereas the hierarchy above it is universal algebra. A blind eighth-order test in a Mach-5 shock agrees with independent collision sampling and strongly amplifies a weak kinetic precursor. The hard-sphere hierarchy is infinite in dimension, but its primitive collision content consists of a single scalar law.

We present DeboRheo v2.0, an unstructured, geometrically unsplit Volume-of-Fluid framework implemented in OpenFOAM for viscoelastic two-phase flows. Version 2.0 improves numerical robustness when large viscosity contrasts coincide with strongly deformed interfaces and thin viscoelastic lamellae or filaments. The revised interfacial viscosity treatment retains a sharp geometric interface while regularizing the viscous contribution to the momentum equation. The solver combines mass-momentum-consistent phase advection, optional SIMPLEC pressure-velocity coupling, and a modular rheological framework with conformation-tensor stabilization. We assess the method using two-dimensional, axisymmetric, and three-dimensional benchmarks governed by the Oldroyd-B and exponential Phan-Thien-Tanner models. The results agree well with published numerical and experimental data and demonstrate improved robustness for demanding viscoelastic free-surface configurations on unstructured meshes.

We generalize the second-order fluid constitutive model to accommodate a range of possible frame indifferent time derivatives. Using the Gordon–Schowalter derivative, which contains the upper-convected, lower-convected, and corotational (Jaumann-Zaremba) derivatives as subsets, we show how the subjective choice of derivative may change model predictions and we identify features that remain universal independent of this choice. Writing these models in terms of generic coefficients is non-universal and may lead to misinterpretations of flow predictions. However, writing the models in terms of zero-shear material functions or terminal relaxation time reveals universal and robust representations.

Three-dimensional conjugate heat-transfer simulations provide detailed predictions for microchannel heat sinks but can be computationally demanding when many geometries and operating conditions are evaluated. This study develops a versatile two-layer model (VTLM) that reduces the three-dimensional problem to two coupled two-dimensional fields while retaining the in-plane geometry of the flow passages and fins. Effects associated with the unresolved channel-height direction are incorporated through hydraulic and thermal closures that account for wall friction and the fluid- and fin-side contributions to interlayer heat transfer. The closures are evaluated from the representative channel geometry, flow-development condition, and fin configuration. The VTLM was assessed against three-dimensional reference models across broad ranges of channel aspect ratios and operating conditions, including uniform and nonuniform fin arrangements. Compared with the existing two-layer models, the VTLM showed improved overall agreement with the three-dimensional reference results. The results showed that prediction accuracy was governed mainly by the flow-development condition and channel aspect ratio, from which a conservative screening guideline was proposed for the examined straight-channel configurations. The assessment of finned expansion–contraction channels further supported the applicability of the VTLM to the investigated passages with abrupt width changes. Overall, the VTLM provides a reduced-dimensional framework for thermohydraulic analysis across the range of microchannel heat-sink configurations examined in this study without explicitly resolving the channel-height direction.

This study experimentally and theoretically investigates the electrically induced transition of a gas-focused liquid jet into a rim-emitting sheet. Ultra-high-speed imaging was used to examine the effects of applied voltage, gas and liquid flow rates, and liquid properties on sheet formation and breakup. Fully developed, quasi-stable sheets formed with ethanol, whereas isopropanol exhibited only initial sheet formation. Increasing voltage promoted sheet stretching, finer and more numerous rim jets, and a narrower spray. Higher gas flow rates shifted the transition towards the nozzle and produced finer structures, while higher liquid flow rates generated larger sheets with thicker rims. A first-order theoretical model assumes an equipotential interface and neglects finite charge relaxation, hydrodynamic perturbations, and nonlinear evolution. It balances destabilizing Maxwell-pressure perturbations against restoring capillary-pressure perturbations on a conducting cylindrical jet. The model identifies the elliptic azimuthal mode, m = 2, as the first unstable mode leading to sheet formation and predicts a critical electric Bond number of 3. Predicted onset voltages agree with measurements within 20%, and the threshold was consistent with published ramified-electrospray observations. The agreement with experiments supports electrocapillary symmetry breaking as the mechanism of onset and provides a compact, physically grounded criterion for predicting the transition from electrified jets to rim-emitting sheets.