Papers

Quantifying mitral regurgitation severity remains limited by the assumptions of clinical flow convergence methods, while high-fidelity simulation and volumetric velocimetry are too slow for routine use. We investigate whether a learned solution operator can reconstruct transient three-dimensional transvalvular hemodynamics from the sparse observation an in-vitro experiment actually provides: a single planar velocity slice and two boundary pressure traces. A Deep Operator Network is pretrained on an experimentally benchmarked URANS database spanning eleven mitral regurgitation orifice phantoms, learning a mapping from a masked two-component planar velocity snapshot to the surrounding volumetric field, and is subsequently adapted to unseen target cases by fine-tuning on their sparse measurements. Adaptation reliably corrects the flow topology within the supervised plane, reorienting a strongly eccentric jet that the pretrained operator predicts as straight, and yields full-field predictions in minutes rather than the days required by the underlying simulations. Its influence decays sharply with distance from that plane, however: measured against phase-resolved particle image velocimetry, the reconstruction error rises from 24.6% at 2mm to 52.6% at 6mm, and the resulting mismatch between corrected and uncorrected layers degrades physical consistency. Single-plane supervision thus constrains the observed plane far more effectively than the surrounding volume, which we identify as the principal obstacle to coherent 4D reconstruction from sparse planar data.

Human blood is a complex biological suspension whose macroscopic flow behaviour arises from the coupled microscopic dynamics of deformable blood cells, plasma proteins, and evolving cellular microstructures. As a result, blood exhibits a range of nonlinear rheological behaviours, including shear-thinning, viscoplasticity, viscoelasticity, and thixotropy, which strongly influence its physiological and clinical hemodynamics. This review provides a comprehensive assessment of the role of blood rheology in arterial and blood-contacting cardiovascular device flows, with particular emphasis on the extent to which different rheological characteristics alter clinically relevant flow quantities and on whether the conventional Newtonian approximation remains adequate for the analysis. The underlying physical mechanisms responsible for the major rheological behaviours of blood are first discussed, followed by a critical review of the constitutive models commonly employed in hemodynamic analysis, including generalised Newtonian, viscoelastic, and thixo-elasto-viscoplastic (TEVP) ones. The effects of blood rheology on arterial flows involving stenosis, bifurcation, and aneurysm under both steady and pulsatile flow conditions are subsequently reviewed and discussed in terms of several physiologically important parameters, such as pressure drop, flow resistance, wall shear stress, flow separation, and recirculation zone. The influence of blood rheology on cardiovascular devices, including prosthetic heart valves and stents, is also reviewed, particularly regarding flow stagnation, residence time, hemolysis, and thrombosis.

Undulatory propulsion is commonly interpreted through reactive added-mass loading associated with body kinematics and vortex-induced loading, but their relative contributions to the streamwise force have not been systematically quantified across swimming kinematics. Moreover, existing vortex-based descriptions do not resolve the signed spatial contribution of vortical flow to the streamwise force. We extend vortex force map (VFM) attribution to deforming bodies, demonstrated for prescribed two-dimensional undulating swimmers at $Re=5000$ across a range of Strouhal numbers and dimensionless wavelengths. The deforming-body VFM organises the streamwise force as a positive reactive added-mass scale with a signed vortex-pressure modification. Across the 80 cases, vortex pressure opposes the reactive contribution in 76 cases. Reference-configuration maps show that the near-body vortex-pressure contribution is consistently adverse, whereas the wake contribution changes sign across regimes and becomes favourable at high thrust. Net vortex-pressure assistance occurs only for the high-thrust anguilliform swimmer. A matched high-thrust pair further shows that the case with the higher peak downstream velocity has the smaller signed wake contribution, demonstrating that wake intensity alone does not determine its force effect.

Hair-covered appendages serve a variety of purposes in Nature, from chemical sensing and particle capture on the antennae of a crustacean to drag generation on bristled wings. At low to intermediate Reynolds numbers, these finite porous media experience three flow regimes. At low Reynolds numbers, the flow goes around the porous structure; this is the paddle or rake regime. As the Reynolds number increases, so does the relative flow rate through the array. If the fluid exits the structure mostly laterally, the flow is in the deflection regime. If the fluid exits downstream, the flow is in the sieve regime. Confining structures, such as the animal body or larger hairs, have been hypothesized to focus the flow on the hair-covered region. We investigate the influence of confinement on the flow through and around an array of cylinders, using a combination of experiments and numerical simulations. Experimentally, we vary the cylinder spacing, channel dimension, and flow rate and measure the velocity field using Particle Image Velocimetry. After comparing the results of finite element analysis with the experimental data, we numerically investigate a broader range of system geometries and flow parameters. Our results show that the confinement focuses the flow in the array and shifts the domains of existence of the three regimes. We present an analytical model that relies on the permeability of rectangular slits to predict the relative flow rate through and around the array. The model is in quantitative agreement with the numerical results, demonstrating that the flow through the array increases with increasing confinement, while the flow angle decreases. These results should provide insight into the morphology of hairy surfaces and have implications in the design of bio-inspired flow sensors and filters.

We present a meshfree numerical solver for the incompressible Navier-Stokes equations on oriented curved surfaces that are represented by surface point clouds. On curved surfaces, numerical challenges pertaining to stiffness and pressure-velocity coupling are exacerbated. Moreover, vector calculus on curved surfaces differs from its Euclidean counterpart. The presented method operates on surface point clouds in an Eulerian frame of reference without requiring a computational grid or mesh. It achieves consistent approximation in space and time with high order of accuracy; we demonstrate up to order six. The incompressibility constraint is locally imposed as a weak artificial compressibility approximation, avoiding global matrix inversion. We show that the method provides consistent and convergent approximations of surface vector fields and differential operators. We study the relationship between error, spatial resolution, and artificial Mach number and characterize the frequency spectrum of the artificial oscillations. We provide numerical solutions of the incompressible Navier-Stokes equations on symmetric surfaces, such as the sphere and torus, and on parametric and non-parametric asymmetric surfaces. Since the proposed method works directly on unstructured surface point clouds, it provides a promising approach for simulations on image-derived geometries, such as in biological morphogenesis from microscopy videos.

Prescribed tangential micro-jet injection can modify cloud-cavitation dynamics, but the chordwise location that improves mean hydrodynamic performance may differ from the location that minimizes unsteady loading. This study compares five injection locations (x/c = 0.15, 0.30, 0.45, 0.60, and 0.70) on a Clark-Y hydrofoil at Re = 7 x 10^5 and cavitation number 0.8. Transient large-eddy simulation with a Volume-of-Fluid formulation and the Schnerr-Sauer cavitation model is used in a two-dimensional parametric framework, with one representative three-dimensional case included to illustrate spanwise cavity deformation. The analysis considers vapor topology, turbulent kinetic energy, velocity and pressure fields, cycle-averaged surface pressure, hydrodynamic forces, force fluctuations, spectra, and cavity-thickness histories. Injection at x/c = 0.15 gives the highest cycle-averaged lift-to-drag ratio among the tested cases: drag decreases from 0.137 to 0.107 and the lift-to-drag ratio increases from 5.693 to 6.261, while lift decreases from 0.78 to 0.67. In contrast, x/c = 0.60 gives the lowest recorded force-fluctuation RMS, with lift- and drag-coefficient RMS values of about 0.112 and 0.0165. The preferred injection location is therefore objective-dependent: the location favored by mean hydrodynamic performance does not coincide with the location favored by unsteady-load reduction under the present conditions.

Modern explicit-time generative models, such as Flow Matching [Lipman et al., 2023] and Rectified Flow [Liu et al., 2023], are typically derived top-down via Optimal Transport and the continuity equation. This standard Eulerian approach focuses on the macroscopic transport of probability mass. In this paper, we present an alternative, bottom-up mechanical derivation grounded in a Lagrangian (particle-centric) perspective. By analyzing the local Taylor expansion of a continuous denoiser, we motivate a strict invariance condition required for optimal, singlestep generation: the conservation of target identity. Enforcing this condition yields a governing quasi-linear advection Partial Differential Equation (PDE). We demonstrate that solving this PDE via the Method of Characteristics analytically yields the straight-line trajectories of Flow Matching. This geometric perspective isolates the Jacobian of the denoiser as the primary source of trajectory curvature, providing a direct mathematical explanation for why straight-line flows enable massive step sizes, and why empirical models require distillation to flatten intersecting characteristics.

The formation of a superlattice pattern in two-frequency-driven Faraday waves discovered and named SSS-I by Arbell & Fineberg (1998, 2002) is investigated by means of Direct Numerical Simulations (DNS) of the full three-dimensional Navier–Stokes equations with a free surface. Two simulations with distinct quasi-hexagonal initial conditions run at a forcing amplitude $25\%$ above the Faraday-wave onset followed quite different routes, but both led eventually to the same superlattice pattern after around 250 forcing periods. This regime is inaccessible to the approximations of weak nonlinearity or viscosity. The standing-wave pattern contain rows of patches, alternating in time between hills and lakes that are connected by a long skeleton resembing the backbone of DNA strands. The patches and skeleton of the pattern can be related to its spatial Fourier decomposition, which combines hexagonal modes with a spatially and temporally subharmonic mode. One of the transition routes passes through several fairly long-lived transients including different hexagonal patterns and another superlattice pattern; the other passes only through erratic and disordered states. After another 100 periods, the pattern became unstable and was succeeded by a dynamic version of SSS-I in which the superlattice is modulated and drifts in the direction of the backbone, while preserving its basic shape. Convergence to SSS-I states both experimentally in a large geometry and numerically from two different initial conditions and in a minimal geometry demonstrates the robustness of the SSS-I pattern.

Polluted white dwarfs provide a unique window into the composition of exoplanetary material, but interpreting their surface abundances requires a quantitative understanding of the mixing processes in their envelopes. Accretion of metal-rich debris onto hydrogen-rich white dwarfs drives thermohaline (fingering) convection in the underlying radiative zone. Previous studies have modeled this as enhanced diffusive transport, often inferring mass accretion rates, $\dot{M}_{\rm acc}$, that exceed constraints from X-ray observations. Here we develop a time-dependent model that treats thermohaline mixing as a propagating front whose evolution is coupled self-consistently to the surface abundance of heavy elements. We perform hydrodynamical simulations which demonstrate that thermohaline mixing drives the composition gradient towards marginal stability. Using this condition, we derive analytic solutions in shallow and deep stratification regimes, finding that the mixed layer depth, $h$, and surface abundance, $X_{\rm surf}$, both scale as $t^{1/2}$ at early times, transitioning to $h \propto t^{4/27}$ and $X_{\rm surf} \propto t^{10/27}$ at later times. The mixed layer reaches depths of only $\sim 100$ km over $10^5$ yr and, without gravitational settling, never reaches a steady state. Including settling leads to an equilibrium surface abundance scaling as $X_{\rm surf, eq} \propto \dot{M}_{\rm acc}^{30/43}$. Applied to G 29–38, the model matches the observed heavy-element abundance for $\dot{M}_{\rm acc} \sim 2\times 10^9$–$4\times 10^{9}~\mathrm{g~s^{-1}}$, in better agreement with X-ray constraints than prior estimates incorporating thermohaline mixing. We also present a general scaling relation for inferring accretion rates directly from observed surface abundances and stellar properties, giving a practical prescription for other polluted white dwarfs.

A multiple-scales asymptotic framework is employed to analyze the interaction between a field of small-scale convective circulations and the large-scale tropical circulation. Closed equations governing the large-scale flow are derived, providing a systematic closure for the influence of unresolved convection. The influence of unresolved convection enters through a non-local momentum diffusion operator that provides a first-principles representation of convective momentum transport and naturally couples the vertical baroclinic modes of the large-scale circulation. The classical Matsuno–Gill model is recovered as a limiting approximation in which the derived momentum transport operator reduces to the phenomenological damping introduced by Gill, thereby placing the classical theory on a systematic first-principles foundation. Two applications of the generalized theory are considered. First, steady-state circulations driven by localized equatorially symmetric heating are examined. Convectively induced vertical-mode coupling is shown to excite additional baroclinic modes beyond those directly forced, substantially modifying the vertical structure of the Walker circulation. Second, the equatorial wave spectrum is analyzed. The resulting eigenmodes comprise mixtures of the classical equatorial wave families, causing the dispersion relations to lose their distinct branch structure and exhibit systematic frequency shifts. These results demonstrate how convectively induced momentum transport systematically modifies both steady tropical circulations and equatorial wave dynamics.

Space-based liquid mirror telescopes (LMTs) have been recently proposed to overcome the scaling limits of traditional rigid mirrors. In these new space architectures, capillary forces would shape a reflective liquid into a spherical optical surface in microgravity. However, the equilibrium, stability, and dynamic behavior of such liquid interfaces under orbital perturbations remain largely uncharacterized. This study investigates the feasibility of space LMTs by combining axisymmetric capillary with thin-film models. Solar radiation pressure and self-gravitation are found to be the dominant perturbations in Sun–Earth L2 orbits, causing equilibrium deformations that exceed the $\lambda/20$ optical threshold at apertures above 0.86 m for visible ($\lambda = 380$ nm) and 1.58 m for near-infrared observatories ($\lambda = 2.5$ $\mu$m). Micrometeoroid impacts self-heal within seconds to minutes, settling after filling requires years to decades at large apertures, and propulsive maneuvers breach optical limits within seconds to hours. These results highlight the need for interface control in large-scale systems such as NASA's 50 m Fluidic Telescope (FLUTE). Thermocapillary actuation supports apertures of 2.3/8.0 m (VIS/NIR) at 100 $\mu$K and 10.6/37.7 m at 10 $\mu$K. Simultaneously, parasitic Marangoni flows impose sub-mK uniformity for NIR and 1–100 $\mu$K for visible operation on any capillary LMT. Departing the capillary regime by imposing a surface-normal settling acceleration, ranging from 39 mm s$^{-2}$ (NIR,5 m) to 17 m s$^{-2}$ (VIS,50 m), is the most promising route to tens of meters in aperture. This approach enables a passive implementation effectively suppressing perturbation induced interface distortions and thermal Marangoni flows. Keywords: Liquid mirror telescope, Optics, Space

We present an analytical investigation of the global helicity budget associated with the salt-fingering instability within the two-dimensional, three-component framework. Our analysis shows that in the region of parameter space corresponding to salt-fingering, helicity amplification occurs when the Rayleigh ratio–quantifying the relative strength of salinity to temperature gradients–exceeds a critical threshold. This finding provides a possible theoretical explanation for the spontaneous emergence of helicity, observed in recent numerical simulations.

Numerical simulations of elastic turbulence in parallel shear flows of polymer solutions indicate that the phenomena is associated with the formation and instability of exact coherent states dominated by thin sheets of polymer stress. However, these “arrowhead” structures are yet to be seen directly in experiments, where simultaneous velocity and polymer conformation measurements are challenging to obtain. Motivated by these challenges, we introduce a method for the prediction of the polymer conformation field given a time series of vorticity measurements. Our approach consists of two components: the first is a convolutional neural network architecture which takes vorticity fields and outputs a positive definite conformation tensor. The second is the adaptation of an assimilation-based training algorithm (Zhu & Page, 2026) which does not require a pre-generated `offline' library of reference conformation fields, but is trained only using the vorticity measurements. This is particularly important in viscoelastic problems, where the appropriate model and parameters to compare to the experiments may need to be determined as part of the solution. In training, measurements made on a time-marched network prediction are required to match the saved time series, while the output of the solver and network predictions at later times are required to be self-consistent. We apply these ideas to two-dimensional Kolmogorov flow in a range of regimes, from simple traveling waves to a fully chaotic state. In all cases, our method produces robust predictions of the polymer stretch, while standard, unregularised variational assimilation is ineffective. In the chaotic case we show that our networks generalise to much larger domains – without further optimisation – than the `minimal' units in which they were trained.

A core inverse problem in the experimental sciences is the inference of a hidden dynamical state from sparse or indirect measurements. There is a natural opportunity for deep learning methods here, but machine-learnt reconstruction methods typically require full state data for training. We present Trajectory-Consistent Network Training (TraCTra), a label-free framework that trains reconstruction networks using only partial observation sequences and a differentiable forward model. TraCTra requires the network reconstruction and dynamical evolution to be mutually consistent: network-predicted states are marched forward in time to match subsequent observations and to agree in the full state space with independent reconstructions at later times. Across four fluid systems, the same objective reconstructs three-dimensional turbulence from coarse-grained fields, velocity from observations of density fluctuations, and three-dimensional density and velocity from sequences of projected two-dimensional shadowgraphs, while also recovering global vorticity from observations confined to a small spatial window. TraCTra outperforms assimilation-only and physics-informed neural approaches, preserves dynamically important multiscale structure, and remains accurate beyond the optimisation window. It transfers to held-out times in the three-dimensional shadowgraph problem and, when trained across trajectories, generalises to unseen flows in the two-dimensional problem. The results establish trajectory consistency as a general supervision principle for reconstructing hidden dynamical states without full state training targets.

The downwash wake of a hovering quadrotor governs both the vehicle's own performance and the safe spacing of multi-rotor formations. Prior measurements have largely characterized the mean flow, using single-point anemometry, volumetric tracking, or planar cuts through part of the rotor system. Higher-order turbulent statistics of the merged wake, and how they relate to canonical jet scaling, have remained unresolved, particularly for small quadrotors at the low-Reynolds-number end of the size range. Here, we present a detailed particle image velocimetry (PIV) study of the downwash of a hovering Crazyflie 2.1 quadrotor (arm length, $l = 46$ mm), sampled along a diagonal cut, passing through rotors along the symmetry axis of the quadrotor, and a front-rotor cut, passing through adjacent rotors. The four rotor jets merge into a single column by $z/l \approx 5$, beyond which the mean velocity profiles progressively approach the canonical round-jet self-similar form, collapsing by $z/l \approx 13$ when scaled by the local centerline velocity and half-width. Centerline decay and half-width growth follow canonical scaling laws with an effective source diameter $D_\text{eff} = 2.29\,l$, effective Reynolds number $Re_{D_\text{eff}} = 3 \times 10^4$, at the low end of the range over which canonical jet scaling has been established, and spreading and decay constants nonetheless within the canonical round-jet range. Resolving both cuts shows that the turbulent normal stresses retain a bimodal, cut-dependent signature of the four-rotor source throughout the measurement domain.

The statistical description and acoustic diagnostics of anisotropic turbulence remain challenging. Real Schur flows (RSFs), prototype models of component-wise dimensionally reduced flows (CWDRFs), provide effective platforms for studying such problems. We combine absolute statistical equilibrium with the acoustic analogy to investigate helicity effects on the far-field directivity of sound radiated from three types of CWDRFs: two different RSFs, and a further reduction of them (liberated Schur flow). We evaluate the directivity from the vortex-sound source spectrum which is calculated with the Wick theorem from the absolute equilibirum Gaussian ensemble. Helicity amplifies the dimensional reduction induced anisotropy of the directivity functions across all CWDRFs, with distinct patterns.

Navigation in turbulence is challenging because local flow measurements provide limited information about favorable paths beyond the flow correlation scales. We investigate vertical navigation by swimmers in homogeneous isotropic turbulence and compare strategies using local flow information with strategies guided by high-performing trajectories. Compared with naive upward swimming, local strategies enhance the mean vertical velocity by about 10% of the root-mean-square flow velocity, while guidance by precalculated trajectories reaches enhancements of about 40%. This gain is limited by the time required to intercept favorable trajectories, particularly for slow swimmers. We then show that precalculated trajectories are unnecessary: swimmers can dynamically identify high-performing members of a swarm and use them as targets. For sufficiently fast swimmers, this collective strategy keeps much of the benefit of precalculated guidance using only the instantaneous swarm state. Our results demonstrate how distributed trajectory information can be used to overcome limitations of local sensing for navigation in turbulence.

In this contribution, Part I, we present a coupled thermo-hydro-mechanical formulation for modeling and analyzing water-to-ice phase change in a deformable fully-saturated porous medium. It is implemented in the multi-physics computational platform OpenGeoSys-6. We compute a series of carefully designed benchmark problems which critically examine the corresponding formulation components and the overall implementation. Several ingredients that have a qualitative and quantitative impact on the numerical results are identified, particularly dissected and commented on. Simulations also account for soil deformation induced by freezing (as a result of 9% volumetric expansion caused by water-to-ice phase transition). The forthcoming Part II will complete the code verification and validation campaign by considering a real full-scale three-dimensional case study of shallow subsurface ice storage. More specifically, we simulate the ice growth process in a fully saturated soil specimen surrounding a group of borehole heat exchangers (BHEs) that contain subzero temperature coolant fluid. A snapshot of the numerical results of this task is already depicted here in Part I as a teaser.

Inertial particle dynamics in turbulence are commonly interpreted in terms of the instantaneous particle Stokes number, as supported by studies in statistically stationary homogeneous isotropic turbulence. But in freely decaying turbulence the Kolmogorov time scale evolves continuously, causing the effective Stokes number, St, to vary even though particle properties remain unchanged. Whether preferential concentration remains uniquely determined by this instantaneous St or depends on the flow's previous evolution has remained largely unexplored. We investigate inertial-particle clustering during the decay of homogeneous isotropic turbulence using direct numerical simulations of heavy point particles in the one-way coupling limit. Clustering is quantified through 3D Voronoï tessellations for populations evolving either from statistically stationary clustered states or initially random distributions. We consider both conventionally forced homogeneous isotropic turbulence and velocity fields reconstructed using physics-informed neural networks. We show that preferential concentration cannot be described solely by the instantaneous St. While particle slip velocity follows the classical steady-state dependence on the instantaneous St, clustering statistics retain a measurable history dependence throughout decay. Existing stationary scaling laws remain applicable to cluster-size evolution, but only through history-dependent prefactors. Particle distributions evolving from different initial conditions rapidly converge towards similar large-scale spatial organisation, indicating that the carrier flow determines the geometry of preferential concentration while finer clustering statistics preserve imprints of the previous evolution. These results demonstrate that preferential concentration in non-stationary turbulence is governed jointly by the instantaneous flow state and its initial state.

Pipe flow controlled by streamwise-travelling waves of azimuthal wall velocity is studied using direct numerical simulations at a bulk Reynolds number $Re_b=4900$. A comprehensive analysis of drag reduction shows that the flow response differs fundamentally from that of channel flow. Under suitable forcing, pipe flow relaminarizes, whereas channel flow does not. Depending on the control parameters, the flow exhibits the spatially localized turbulent state characteristic of transitional pipe flow, with turbulent puffs persisting at bulk Reynolds numbers up to three times higher than in the uncontrolled case. The bulk Reynolds number alone does not determine the onset of localization. Moreover, drag reduction, which alters the natural relation between bulk and friction velocities, is insufficient to identify a universal onset criterion. An intermittency indicator based on the spatial variance of the cross-sectional turbulent kinetic energy relates the emergence of localized turbulence to the low wall friction produced by the control, although the correspondence is not one-to-one. Despite their qualitative resemblance to canonical turbulent puffs, the controlled puffs exhibit distinct properties; for example, their fronts may propagate faster than the bulk flow. Overall, this work provides a comprehensive characterization of the subcritical turbulent state and its turbulent puffs in controlled pipe flow, and offers a new perspective on control strategies that aim at flow relaminarization.

A physics-informed method for PIV-based surface pressure reconstruction that combines least-squares optimization with both local and global physical constraints is proposed. The standard deviation of the surface–normal pressure gradient is introduced as a physically meaningful weighting function in the optimization process. Moreover, a physical global constraint is also introduced to reconstruct surface pressure outside the suction region. The results show very good agreement with data obtained from pressure taps. Near the leading edge, the surface pressure reconstruction error has been reduced by one-third.

Viscoelastic fluid flows over micro-textured surfaces - densely covered by slender protrusions like cilia lining the body airways or villi covering the intestinal epithelium - underpin essential biological processes including transport, mixing, and absorption. Despite their ubiquity, the dynamics generated by the interplay between fluid elasticity and these complex geometries remain largely unexplored. Here we combine fully resolved numerical simulations with microfluidic experiments to reveal the flow dynamics established above dense arrays of microscopic pillars (canopies) immersed in the low-Reynolds-number flow of a viscoelastic liquid. We observe that the flow above the canopy tips spontaneously develops elastic turbulence. Remarkably, the chaotic state coexists with elastic waves emerging from the coupling between fluid elasticity and the heterogeneous shear induced by the canopy geometry. These ordered fluid motions persist across a broad range of flow conditions and canopy configurations. Our results demonstrate that coherent wave propagation and elastic turbulence are complementary manifestations of viscoelastic fluid flow. Beyond their fundamental significance, these mechanisms have broad implications for transport in biological and engineered environments, and reveal how structured geometries can harness the spontaneous dynamics of viscoelastic liquids to manipulate complex flows.

The coefficients of the transport equations, describing the propagation features, are particularly important in astrophysics, interplanetary physics, and experimental plasma physics. In this paper, the variable-dependent diffusion coefficients are investigated. For the momentum transport equations, we find that the coefficients are related to statistical quantities, some of which are new. In addition, these coefficients take logarithmic forms, which are different from the results derived in previous papers. For isotropic pitch-angle scattering, we also obtain a formula that takes a logarithmic form. For fractional transport equations, the coefficients expressed in terms of the moments are obtained from the governing equations.

Liutex core lines are systematically applied to Hurricane Dorian to investigate the three-dimensional vortical organization of an intense tropical cyclone. Unlike conventional analysis based on wind speed or vorticity, Liutex core lines identify the local vortex axes and provide a compact geometrical representation of rotational structures. The results show that Dorian is not characterized by a single vortex core, but by a large population of vortices embedded within a coherent hurricane-scale circulation. Stronger and more vertically organized vortices are concentrated in the inner-core region, whereas numerous weaker, inclined, and curved vortical structures extend outward and collectively retain the spiral organization of the storm. The complete core line field therefore reveals a three-dimensional, multiscale vortical skeleton of the hurricane. These results suggest that a tropical cyclone can be viewed as an organized multiscale vortex system rather than a single monolithic vortex. Beyond visualization, Liutex core lines provide a potential framework for quantifying vortex geometry, spatial organization, and temporal evolution, offering a new approach for studying structural changes and vortex dynamics in tropical cyclones.

This study presents a theoretical investigation of generalized solute dispersion in magnetohydrodynamic multiphase tube flow with porous layers. A two-fluid analytical model is developed for applications in biofluid and environmental fluid dynamics. The model comprises a micropolar (non-Newtonian) fluid core representing the rotational behaviour of red blood cells and a Newtonian plasma periphery embedded with Brinkman and Darcy porous structures, corresponding to the glycocalyx and endothelial layers with distinct permeability characteristics. A transverse magnetic field is incorporated to investigate how magnetic-field-induced modifications of the carrier flow influence solute localisation, with potential relevance to magnetic nanoparticle-mediated drug delivery. Using the generalised dispersion framework of Sankarasubramanian & Gill, analytical solutions are derived to investigate how the coupled axial velocity field and associated microrotational dynamics influence solute transport. The analytical predictions are independently validated through Brownian dynamics simulations, demonstrating excellent agreement for the temporal evolution of the zeroth and first transport moments. The results reveal the previously unexplored influence of microrotational dynamics on solute concentration, convection coefficients and effective dispersion, providing new insights into the coupled roles of translational and rotational fluid motion in biofluid transport. This work bridges an important gap in the literature and establishes a generalized theoretical framework linking magnetic fields, micropolar fluids and porous arterial structures for biofluid transport, targeted drug delivery and clinical engineering applications.

Streaming-potential-mediated transport of viscoelastic fluids has attracted research attention owing to its applications in electrokinetic energy conversion and microfluidic transport. Existing analytical and semi-analytical models in published literature provide valuable physical insights, but require repeated numerical evaluations for exploring large design spaces and identifying the optimal operating conditions. In this work, a surrogate-assisted framework is developed for rapid design optimization of pressure-driven electrokinetic transport of simplified Phan-Thien-Tanner fluids in a slit microchannel. A high-fidelity numerical database is generated over a broad range of governing dimensionless parameters, which includes the zeta potential, the Debye parameter, the Dukhin number, and the viscoelastic parameter. A Machine Learning surrogate model is subsequently trained to accurately approximate the nonlinear relationship between the governing parameters and the streaming potential, while the volumetric flow rate and hydroelectric energy conversion efficiency were calculated from closed form equation by using the streaming potential predicted by the surrogate. This is coupled with a multi-objective optimization strategy to identify operating conditions that simultaneously maximize energy conversion efficiency and volumetric flow rate. The proposed methodology can significantly accelerate parametric exploration compared with repeated numerical simulations across different parameters and provides practical design guidelines for electrokinetic microfluidic devices. The study demonstrates the potential of combining computational fluid mechanics with data-driven surrogate modeling for efficient engineering design and optimization.

Kolmogorov-Arnold Networks (KANs), inspired by the Kolmogorov Arnold representation theorem, provide an interpretable alternative to multilayer perceptrons (MLPs) by using learnable activation functions on edges rather than fixed node activations. We propose a Physics-Informed Kolmogorov-Arnold Network (PI-KAN) framework for solving forward problem of viscoelastic fluid equations, which arise in many complex fluid dynamics applications and are characterized by strong nonlinear coupling between fluid fields. For viscoelastic fluid equations, we adopt the generalized hydrodynamic model, which is well established in the field of dusty plasma. To evaluate the performance of the proposed framework for viscoelastic fluid, we consider benchmark problem based on the Taylor-Green (TG) flow and a modified Taylor-Green flow. We systematically investigate the effects of different network architectures, hyperparameters, and collocation point distributions on the accuracy and convergence behavior of PI-KANs for the range of viscoelastic parameter ($\tau_m = 1$–$20$). We also study the impact of random seed initialization on training outcomes. The obtained results provide useful guidance for the design and implementation of physics-informed Kolmogorov-Arnold networks (PI-KANs) in solving viscoelastic fluid equations

Oblique drop impact onto a deep liquid pool produces asymmetric crowns, directional jetting, and splashing transitions that cannot be characterized by the total impact inertia alone. We numerically investigate water drops impacting a quiescent deep pool over $41\leq We\leq1790$ and $10^\circ\leq\theta\leq90^\circ$. The simulations reproduce the principal features observed experimentally and identify five post-impact regimes in the $We$–$\theta$ plane: deposition, front splashing, side splashing, side-front splashing, and crown splashing. The deposition–front-splashing transition is described by the tangential-inertial parameter $K_s=We\cos\theta$, with $K_s^c\approx120$. This criterion follows from the competition between downstream crown-rim inertia and capillary retraction at the Taylor–Culick velocity. The transition from front to side-front splashing is instead governed primarily by normal impact inertia, with a critical normal Weber number $We_N^c\approx318$. Beyond these regime transitions, the secondary-droplet statistics reveal fragmentation behavior common to the different splashing regimes. The droplet-size distributions are positively skewed, and the median diameter follows $d_{s,\mathrm{med}}/D\sim We^{-3/5}$. Second-order velocity structure functions support a scale-dependent capillary–inertial description of rim and ligament breakup. Combined with mass conservation, this scaling gives $N_s\sim We^{9/5}$, providing a numerical explanation for the secondary-droplet-number scaling observed experimentally. Thus, directional impact inertia governs the macroscopic selection of splashing regimes, whereas the secondary-droplet populations across these regimes exhibit a common capillary–inertial fragmentation scaling.

We perform Lagrangian particle-tracking experiments in turbulent Rayleigh-Bénard convection at aspect ratio Gamma = 10, Rayleigh number Ra = 9.3 x 10^7, and Prandtl number Pr = 4.8. Approximately 50,000 neutrally buoyant particles are tracked for durations of up to 150 Kolmogorov times. The resulting trajectories are sufficiently long to capture the mean-square displacement of single particles from the short-time ballistic regime to the long-time diffusive regime. We further analyse Lagrangian velocity structure functions and particle-pair dispersion, both of which exhibit scaling behavior consistent with theoretical expectations in their respective temporal regimes. In the Richardson-like regime, the pair-dispersion exponent exceeds 3, most clearly in the lateral direction. Multi-particle statistics are investigated by analysing particle clouds with initial radii of approximately 8 and 20 Kolmogorov lengths using principal component analysis. The clouds spread more strongly in the lateral directions than in the vertical direction and deform from initially spherical shapes into oblate ellipsoids within approximately 10 Kolmogorov times, revealing pronounced anisotropic dispersion. The dynamics is identified from the particle-connectivity network through a spectral analysis of the graph Laplacian followed by k-means clustering. Furthermore, we examine the probability density functions of all three acceleration components and assess the statistical convergence of their second and fourth moments. The lateral acceleration components are more intermittent than the vertical component, as indicated by their heavier tails. Acceleration statistics conditioned on the bulk region are slightly less intermittent than those obtained over the full measurement volume, which we attribute to the highly intermittent plume-ejection and plume-aggregation events occurring near the walls.

This paper presents a numerical study of the stability of a polymer solution flow between concentric cylinders with a rotating inner cylinder. The case of a small-radius inner cylinder is considered. The fluid motion is described using a specific case of the Kelvin-Voigt model, often referred to as the Oskolkov model. This model is applicable to very dilute polymer solutions, where the retardation time is much smaller than the characteristic time of the problem and elastic forces are much smaller than viscous forces. The stability of the steady-state motion is investigated using a fully nonlinear approach by means of direct numerical simulation of a perturbation introduced as finite-duration white noise. Depending on the Reynolds number, the perturbation either decays or grows. The critical Reynolds numbers obtained for both Newtonian and non-Newtonian fluids are found to be in agreement with the predictions of the linear theory. It is also shown that an increase in the elastic forces makes helical perturbations more dangerous than their axisymmetric counterparts.