Papers

We develop a representation-independent symmetric-Fock formulation of the nonlinear Boltzmann collision operator for Maxwell molecules. Starting from the standard velocity-space operator, we give a short derivation of Bobylev's Fourier identity and isolate its characteristic structure: two linearly related Fourier arguments followed by multiplication. We then prove, independently of collision geometry and of any coordinate realization, a canonical lift–fusion intertwining theorem: one-particle linear maps lift to the two incoming Fock legs and symmetric-algebra multiplication fuses them into a single outgoing state. Bargmann coordinates make this intrinsic construction especially transparent, but do not define it; Bobylev's collision maps subsequently select the Maxwell vertex from the already graded lift–fusion class. The resulting bilinear map obeys the exact grading \[ \widehat{\mathcal Q}(\mathscr H_p,\mathscr H_q)\subseteq\mathscr H_{p+q}, \] which gives an intrinsic origin for the triangular structures of Maxwell kinetics. Its one-vacuum restriction yields the complete Wang Chang–Uhlenbeck spectrum, while moment adaptation makes the nonequilibrium hierarchy strictly triangular and every finite compatible Fock jet an exact autonomous factor with global exponential relaxation. For the inhomogeneous problem, we extend realization covariance to the nonlinear two-leg vertex and evaluate the moving-frame connection independently through Hermite-function and Fourier realizations. The two routes give the same abstract Fock propagation and the same first Chapman–Enskog source; its traceless level-$2$ and vector level-$3$ sectors are relaxed by the exact Maxwell rates, giving $\Pr=2/3$. This provides an explicit computational demonstration that coordinate realizations may be chosen for economy without entering the structural Fock formulation.

Droplet impacts rarely occur on horizontal smooth surfaces, yet the combined influence of surface inclination, microstructure, and fluid composition remains poorly understood for emulsions. Here, we experimentally investigate the impact of 20% (v/v) silicone oil-in-water emulsion droplets on smooth glass and micropillar arrays with two interpillar spacings (50 and 100 $\mu$m) inclined at 55$^\circ$. The role of surface wettability is further examined using a superhydrophobic coating. High-speed imaging is employed to characterise the impact dynamics over a wide range of Weber numbers ($18 \leq We \leq 565$), while optical microscopy is used to quantify the residual wetted area after impact. Five impact regimes are identified: deposition, sliding, partial rebound, complete rebound, and splashing. Surface inclination introduces asymmetry in spreading and recoil, whereas microstructured substrates reduce adhesion and promote rebound by decreasing the liquid-solid contact area. In contrast to water, the emulsion exhibit enhanced deposition on smooth surfaces, increased sliding on uncoated microstructures, and earlier ligament formation and secondary breakup at high Weber numbers. The dispersed oil phase locally modifies wetting and lubrication, producing liquid bridges, heterogeneous recoil, and larger residual wetted areas on smooth substrates. On microstructured surfaces, however, capillary confinement within the texture limits the projected wetted area despite increased liquid retention inside the microstructure. These results demonstrate that the impact behaviour of emulsions cannot be predicted solely from conventional dimensionless groups, as local phase redistribution fundamentally alters energy dissipation, wetting, and fragmentation. The findings provide new insight into spray deposition on inclined textured surfaces relevant to agricultural spraying and coating technologies.

Three-dimensional conjugate simulations were conducted to investigate saturated flow boiling in a rectangular mini-channel, with particular emphasis on the role of inlet Reynolds number on boiling mode selection and transition. A C++ based open-source numerical framework was employed, incorporating a physically informed multi-site nucleation model by coupling a nucleation site density correlation with a Halton-sequence based spatial allocation strategy. Two distinct Re-dependent transition pathways were identified. At low Re, boiling transition is mainly associated with localized dryout development associated with upstream active boiling and progressive downstream liquid starvation. At high Re, the transition is characterized by convective stretching and reorganization of vapor structures, through which elongated vapor slugs evolve into localized vapor films and eventually approach full surface vapor coverage. The global heat transfer characteristics and peak heat transfer capacity are further interpreted in conjunction with boiling mode transition, clarifying the respective roles of wall dryout and volumetric vapor fraction in heat transfer deterioration. Among all cases, Re=2000 provides the most favorable overall thermal response. Overall, within the rectangular mini-channel configuration and operating range considered in this study, Re is closely associated with vapor organization, boiling transition, wall dryout, and global heat transfer performance.

Operator-learning surrogates have been benchmarked largely on single-field, single-interface problems, leaving unclear whether architectural choices validated in those settings transfer to constrained, multiphase flows. We introduce a three-phase interfacial-flow benchmark to examine whether the trunk coordinate representation matters for a multi-channel, interface-dominated target. The configuration consists of an air bubble rising through water, piercing a water-oil interface, and entraining a water plume into the oil within a bounded, wall-confined domain. Reference data are generated using a structure-preserving ternary Cahn-Hilliard-Navier-Stokes solver that algebraically preserves the simplex constraint. From 1,024 Sobol-sampled simulations spanning a nine-dimensional parameter space, we learn the mapping from physical parameters to five-channel space-time fields. We compare three parameter-matched DeepONet variants differing only in trunk representation: raw coordinates (DeepONet), random Fourier features (FEDONet), and a fixed tensor-product Chebyshev dictionary (SEDONet). SEDONet reduces the test relative L2 error by 16.8% compared with FEDONet and by 24.0% compared with DeepONet, while improving all five output channels. Spatial and temporal error analyses localize the principal gains near the diffuse interfaces and after bubble breakthrough. The results indicate that the Chebyshev representation is particularly effective for the strongly non-periodic wall-normal and temporal structure of this three-phase flow.

Predictive simulation of turbulent combustion remains challenging because stiff chemical kinetics, turbulent transport, molecular mixing, and heat release interact nonlinearly across unresolved scales. In the filtered or averaged formulations, reaction rate is unclosed, and the integration of detailed chemistry constitutes the dominant computational cost. Conventional closures such as mixing-limited models, flamelet and manifold methods, conditional moment closure, and transported probability/filtered density function (PDF/FDF) formulations, encode substantial physical insight, but rely on structural assumptions that may lose validity outside their calibrated regimes. Machine learning offers a complementary approach because of its ability to approximate complex nonlinear functions. In turbulent combustion, this capability can be used to relax restrictive closure assumptions, learn unresolved nonlinear mappings from data, and accelerate expensive computations such as detailed chemistry computation. However, purely data-driven models may violate conservation laws and thermochemical consistency. They may also extrapolate poorly outside the training domain and destabilize the CFD solvers in which they are embedded. Physics-guided machine learning (PGML) addresses these failure modes by incorporating prior knowledge throughout the modeling pipeline: in the training data and input features, the model architecture, the loss function, the hybrid closure structure, and the solver-aware validation protocol. This article reviews PGML for turbulence-chemistry interaction (TCI) modeling within this framework.

The self-starting behavior of vertical-axis wind turbines is strongly influenced by the development of vortical structures along the span. However, a fully coupled high-fidelity three-dimensional analysis of this process requires substantial computational resources. This study presents a computationally efficient, spanwise-periodic, three-dimensional large-eddy simulation framework in OpenFOAM. The motion of the rotor is prescribed using a combination of two logistic functions to reproduce the angular-velocity evolution of a vertical-axis wind turbine undergoing self-starting. The results show that boundary-layer separation and the subsequent roll-up of the separated shear layer generate detached vortical structures that convect into the wake as finite spanwise segments. The deformation of these structures along the span increases with increasing spanwise extent. The dead-band is characterized by sustained wake interference and weak net acceleration, whereas the rapid-acceleration stage exhibits greater attachment of the flow, with separation confined to smaller regions near the blade. During quasi-steady operation, the shedding of vortices into the wake becomes repeatable, and downstream blade–vortex interactions are reduced. The approach based on the prescribed motion of the rotor enables computationally efficient, spanwise-resolved studies of vortex evolution suitable for parametric investigations and the evaluation of flow-control devices.

Physics-informed neural networks (PINNs) provide a mesh-free approach for solving differential equations, but their performance can depend strongly on loss weighting, collocation placement, and optimization strategy. This study develops an adaptive PINN framework for the Blasius boundary-layer equation using gradient-norm-based adaptive loss weighting, nonuniform and residual-based collocation, and sequential Adam–L-BFGS optimization. In the representative run using the architecture $[1,100,100,1]$, the model predicts $f''(0)=0.3320762918$, compared with the high-accuracy benchmark $0.332057336215$, giving an absolute error of $1.896\times10^{-5}$. The final weighted loss is $6.789\times10^{-8}$, and the predicted stream-function, velocity, and shear profiles agree closely with an independent numerical boundary-value solution. A separate full-training architecture study shows that the two-hidden-layer model achieves the smallest wall-shear error among the four tested architectures, $1.629\times10^{-6}$, whereas the deepest network attains the smallest weighted objective but a substantially larger wall-shear error. Compared with the previously reported PINN value $f''(0)=0.33165$, the representative run reduces the wall-shear error by approximately a factor of $21.5$. The results show that the combined adaptive training framework can achieve high accuracy for the Blasius problem and that weighted loss alone is insufficient for identifying the most physically accurate PINN. Because the adaptive components are applied jointly, their individual contributions cannot be isolated from the present results and would require a controlled ablation study for separate assessment.

Flows in random networks are known to exhibit heavy-tailed statistics, giving rise to anomalous transport in a range of biological, environmental and engineered systems. Yet, how structure determines flow remains an open question. Here we derive a dual network approach that relates flow statistics and network properties. Conditional statistics in a range of networks reveal the existence of two interlaced subnetworks with distinct hydraulic behaviors. Based on this hidden structure, we derive a universal analytical approach that predicts heavy-tailed flow statistics based on network topology and disorder distribution across a range of random networks.

Numerous experimental and computational studies have been conducted in the past few decades to understand the swimming performance of fish, and to identify the optimal kinematic strategies for a swimming fish or fish-like robot. Many of these studies model the swimmer in a `tethered' condition, in which the swimmer is held fixed while it is subjected to a free stream. Its performance is then quantified using power expenditure, thrust generation, and efficiency. However, the dynamics of a tethered swimmer are different from those of a self-propelled swimmer, whose performance is best measured using its steady-state swimming speed in still fluid and its efficiency. It is an open question whether the conclusions drawn from studies of tethered swimmers can be directly applied to free swimmers. In this study, we use an unsteady panel method to systematically compare the swimming performance of a tethered fin and that of a self-propelled fin attached to a virtual drag-producing body to investigate how their performance varies over a set of prescribed kinematics. After validating the numerical model against previous experimental results, we show how the pitch amplitude, heave amplitude and the phase offset between them affect the efficiency and thrust generation in the tethered case, and how they affect the speed and efficiency in the self-propelled case. We find that the kinematic strategies that optimize the performance of a tethered swimmer do not necessarily optimize the performance of a self-propelled swimmer.

Nonlinear dynamical systems often evolve on low-dimensional manifolds with intricate geometry, making them difficult to approximate with a single global reduced-order model (ROM). To address this, we previously introduced quantized local reduced-order models (ql-ROMs), which partition the solution manifold into $K$ clusters and construct local ROMs around the corresponding centroids. In the sharp formulation, discontinuous switching between clusters can induce discontinuities, spurious oscillations, and loss of accuracy near cluster boundaries. Here, we propose a fuzzy extension of ql-ROMs based on fuzzy c-means clustering. The resulting fuzzy local ROM (fl-ROM) advances all local reduced states in parallel and combines their predictions through continuous membership weights, yielding a smooth partition-of-unity coupling of the local dynamics. We also introduce a pseudo-Bayesian information criterion to guide the selection of the number of clusters in the fuzzy setting. The methodology is assessed on the two-dimensional Kuramoto-Sivashinsky equation in periodic, travelling-wave-like, quasi-periodic, and chaotic regimes. In all cases, the local ROMs outperform the global ROM, while the fl-ROM provides smoother and generally more accurate predictions than the sharp formulation. In the chaotic regime, where long-time trajectory tracking is inherently limited, the fl-ROM achieves the best compromise between short-time predictive accuracy and long-term statistics. These results show that fl-ROM provides an effective, robust, and interpretable framework for reduced-order modeling of nonlinear dynamical systems with regime transitions and complex attractor geometry.

Physics-informed neural networks (PINNs) have emerged as a compelling pathway toward trustworthy artificial-intelligence-based computational fluid dynamics (CFD) by embedding governing equations directly into the learning process. Many existing AI flow models require large simulation or experimental datasets and often remain problem-specific, limiting their generalization and physical reliability. Data-free PINN frameworks offer an alternative by learning flow solutions from the Navier-Stokes equations and prescribed boundary conditions, potentially reducing dependence on expensive CFD datasets while retaining physical consistency. However, traditional PINN frameworks have struggled at high Reynolds numbers, limiting their application in CFD. In this work, we present NeuralFlowNet, a data-free, physics-informed proof-of-concept framework designed to solve steady Navier-Stokes problems across low- to high-Reynolds-number conditions. We describe the proposed methodological framework and demonstrate its applicability using benchmark problems with increasing physical and geometric complexity. The results demonstrate that NeuralFlowNet can accurately recover steady flow fields across a broad Reynolds-number range, including cases with strong pressure gradients, without training on external flow-field data and while maintaining good agreement with reference numerical solutions. These findings establish NeuralFlowNet as a reliable framework for future testing of unsteady and more complex simulations and could provide a basis for developing trustworthy and efficient AI solvers for high-Reynolds-number fluid dynamics.

Tensor networks (TNs), originally developed for simulating many-body quantum systems, provide a systematic framework for approximating high-dimensional fields. This is achieved by factorizing the field into interconnected tensors with small bond dimensions, thereby restricting the correlations captured across field bipartitions. Belonging to the family of TNs, the matrix product state (MPS) ansatz is utilized here as a reduced-order modeling framework to construct truncated representations of isotropic turbulent flow data. Two direct numerical simulation (DNS) datasets are considered: the hydrodynamic field of an incompressible three-dimensional flow, and a conserved Fickian scalar in a similar flow. Each field is encoded as an MPS through a sequence of singular value decompositions (SVDs) in which small singular values are discarded. The truncated representation is contracted back to the full grid, and the resulting reconstructed field is compared against DNS. An interleaved ordering of the spatial tensor indices of the transport variables is applied prior to decomposition in order to localize the dominant inter-tensor correlations. Velocity reconstructions achieve $99.8\%$ fidelity using only $5\%$ of the original DNS memory, while the scalar field reaches the same fidelity at $15\%$ memory usage. A wide range of lower- and higher-order statistics, including velocity gradients, dissipation, and structure functions, are systematically examined. At these compression levels, the total kinetic energy and the scalar energy are both recovered within $0.2\%$ relative error, while the mean dissipation and mean scalar dissipation remain within approximately $10\%$ of the DNS generated values. These findings support the suitability of MPS for scalable reduced-order analysis of complex turbulent datasets and motivate further exploration of TN-based methods in computational turbulence.

A collapsing cavity throws up a ligament, which fragments into a train of droplets whose sizes are commonly given a lower bound at a fixed multiple of the viscocapillary length $\ell_\mu=\mu^2/\rho\sigma$. We show that no such bound exists, for a reason more general than the fate of one parameter: an impulsive jet possesses no length of its own. The similarity solutions that govern each pinch contain none, the cascade of stretching and iterated satellites introduces none, and $\ell_\mu$ belongs to the singularity rather than to the droplets. A size distribution built on such a process can inherit a scale from one place only, the cavity that launched the jet. Computations of bubble bursting, confined and unconfined, bear this out. The floor they display is the one the mesh imposes, not a property of the fluid, and wherever the mesh looks below $\ell_\mu$ it finds droplets. The census of unique emitted droplets is exponential, with a single scale set by the cavity radius, indifferent both to how vigorous the event is and to how much liquid surrounds it. An exponential is the least structured census compatible with a prescribed mean, so the fragmentation keeps the size of the cavity and no other memory of its parent. Sustained stretching does keep such a memory, imprinting the corrugation of the parent thread and yielding the peaked, gamma-like distributions reported for ligament-mediated fragmentation. The manner of loading, and not the fluid alone, selects the shape of a spray.

Convective turbulence in planets and stars is often driven by internal heating. This forcing mechanism has also been proposed as a means of accessing the diffusion-free scalings of the geostrophic turbulence (GT) regime at modest forcing. We test this with the asymptotically reduced quasi-geostrophic model, which is formally valid in the limit of vanishing Ekman number, $Ek \rightarrow 0$, and retains the Prandtl number as an independent parameter. We find no such shortcut: the Nusselt and Reynolds numbers are no closer to their diffusion-free predictions than in the boundary-heated case, and at $Pr = 7$ they are further from them; the predicted $Pr^{-1/2}$ collapse fails; and the prefactor depends on the form of the heating. Our no-slip/stress-free cases track the radiatively driven simulations of Hadjerci et al. (2024) case by case, yet a $25\%$ variation in $Nu$ persists between sweeps that share the same reduced Rayleigh and Prandtl numbers but differ in Ekman number. Those data span only the narrow range of forcing over which the compensated Nusselt number is stationary; across the wider range accessible to the reduced model it rises to a maximum and then falls. We argue that bulk transport scalings are incomplete diagnostics of GT, whereas the saturation of the interior mean temperature gradient and of the vertical velocity kurtosis remain reliable indicators.

We derive necessary conditions for instantaneous dynamo action for rotating convection. A magnetohydrodynamic model is considered in two settings: the rapidly rotating plane layer where inertia and viscosity are absent, and at an arbitrary rotation rate where viscosity is finite. In contrast to kinematic dynamo bounds, the evolution of the magnetic field is coupled via an inertialess force balance. The buoyancy-driven part of the flow $\mathbf{u}^{\mathrm{A}}$ in the event of dynamo action must in fact satisfy, for $3\leq p \leq \infty$ $$ Rm\, A_p\| \mathbf{u}^{\mathrm{A}}\|_{L^p} \geq 1 $$ where $A_p$ is an explicit constant, and $Rm$ is the magnetic Reynolds number. In the inviscid model, $\mathbf{u}^{\mathrm{A}}$ depends only on the horizontal gradients of the vertical primitive of temperature. A refinement via the poloidal-toroidal decomposition allows us to replace $L^p$ in our constraint with an anisotropic norm for $L^{\infty}_z \dot{H}^1_{x,y}$. For the viscous model, we also derive necessary conditions for the growth of magnetic enstrophy and a combined thermo-magnetic energy. One branch of our constraints implies that the scaling $Ra_\nu \gtrsim Ek^{-3/2}$ is necessary for dynamo action, where $Ra_\nu$ is the classical Rayleigh number and $Ek$ is the Ekman number.

Perfusion of soft materials such as biological tissue or hydrogels is essential for the functioning of organ and laboratory systems such as chromatographic columns and bioreactors. Inspired by these applications, we model fluid-driven compaction in a long, thin cylindrical porous medium bounded by an impermeable elastic membrane and study how flow regimes relate to elastic parameters. Using a Lagrangian formulation of Darcy flow coupled to small-strain linear elasticity with porosity dependent permeability and elastic moduli, we perform an asymptotic reduction in the small aspect ratio limit and obtain a leading-order nonlinear diffusion equation for the porosity, which we solve numerically. Whereas rigid boundaries produce a compaction plateau, compliant walls exhibit, at most, an intermediate plateau beyond which the flow increases once the imposed pressure becomes comparable to the product of membrane stiffness and initial porosity. When the membrane is less stiff than the porous medium, flow rate can exceed that expected for a rigid medium. A parameter space map distinguishes regimes where plateau and breakthrough occur, where the steady flow rate is below (sub-Darcy) or above (super-Darcy) the undeformable-medium prediction, and delineates the small-strain domain in which the theory applies. An asymptotic solution for negligible gravity captures the departure from the plateau and yields compact expressions for effective permeability and flow rate.

A physics-embedded training framework is used to close the sub-grid-scale dynamics of turbulent premixed flames. The trained model augments the resolved flow equations and is trained to match its predicted flow field to trusted data. An end-to-end optimization of the coupled resolved equations and embedded model leads to a model that is robust and effective for a freely propagating premixed flame in turbulence, modeled by a single-species, single-step, and irreversible chemical reaction. Important constraints are built into the training formulation for conservation, scalar boundedness, and equivariance. The model is scaled based on the residual of the resolved flow equations to focus its influence where the closure is needed. It outperforms other cases considered — no-model, dynamic closure, and the same machine learning model trained directly to fit the residual data — for a long-time simulation, correcting the turbulence dissipation and flame kinematics. Finally, it is shown how the prediction-based training better informs the model than the precise residual data.

Computational models of blood flow are caught between fully resolved cell-based methods, which faithfully reproduce the dynamics of individual cells but are computationally prohibitive at vessel scale, and continuum models, scalable yet blind to particle motion. We present an unresolved, mesoscale computational fluid dynamics-discrete element method (CFD-DEM) model of platelet dynamics that bridges this gap and, coupled with an existing unresolved description of deformable red blood cells, moves closer to a scalable model of whole blood. Within this framework, implemented on the open source OpenFOAM-LIGGGHTS coupling, platelets are represented as rigid oblate particles advanced by orientation dependent drag, lift and hydrodynamic torque closures. The model is first validated against resolved simulations and experiments in cylindrical microvessels of diameter $100-200\,\mu m$, across wall shear rates $\dot{\gamma}=150-1650\,s^{-1}$ and hematocrit Ht $=10-20\%$ then used to characterize platelet margination. The model quantifies diffusion coefficient, CFL formation and their dependence on shear rate, Ht and channel size. In particular, platelet diffusivity grows with vessel size and shear rate, while remaining insensitive to Ht, whereas CFL thickens with shear rate and thins with Ht. We further show that even at this mesoscale level, the model remains sensitive to platelet shape: oblate platelets marginate faster and diffuse nearly an order of magnitude more than their spherical surrogates, reaching a comparable steady state distribution but along markedly different temporal paths. Together these results demonstrate that shape driven platelet dynamics can be recovered at a fraction of the cost of fully resolved methods.

State estimation in magnetohydrodynamic flows is critical for real-time monitoring of liquid metal blankets in tokamak fusion reactors. Due to the multiphysics nature of these phenomena, high-fidelity simulations are computationally prohibitive for real-time applications. This work investigates a data- driven Reduced Order Model framework: the Shallow Recurrent Decoder (SHRED) coupled with Principal Component Analysis, to map sparse temperature measurements to the full thermo-hydraulic system's state. The major contribution of this work lies in the two-parameter analysis of a fully three-dimensional domain representative of the DEMO breeding blanket configuration. Here, the flow is subjected to an external magnetic field varying in direction and intensity and is hindered by two cylinders acting as a water-cooling system, which impose a temperature boundary condition on their surfaces. This double-parametric magnetic variation induces nonlinear transitions in the flow dynamics, ranging from chaotic behavior at low magnetic field intensities to laminarized regimes at high intensities, characterized by the formation of asymmetric side layers at an inclination angle of 30 degrees. SHRED reconstruction maintains a mean relative error of approximately 5% for the temperature, pressure, and velocity fields. This accuracy is maintained across both weak and strong magnetic fields, ranging from 0.075 T to 0.300 T, and for inclination angles from 5 to 30 degrees, reflecting its dominant toroidal component. These errors are only slightly larger than the lower error bound dictated by low-rank truncation. The results establish SHRED as a reliable state estimator for complex and realistic engineering applications involving completely unseen parametric scenarios and validate it as an accurate real-time state estimation technique suitable for online monitoring and control of real facilities.

Micron-sized iron powders are a rapidly advancing novel energy storage technology. In order to improve the design of real-world iron-powder combustors, adequate understanding of the ignition behavior in such settings is necessary. In this work, a jet-in-hot-coflow (JHC) burner designed by Hameete et al. (2024) to test ignition of iron particles in lab-scale turbulent flames is modeled numerically using LES and Lagrangian point-particles. The JHC burner is simulated in two different modes–an open flame and an enclosed flame–similar to the experimental reference. Two iron-oxidation-rate models–the first-order model and oxide-layer model–are used to examine the effect on capturing the ignition behavior. For the radiative heat transfer between the two phases, a simplified Stefan-Boltzmann approximation model and the P1 model are considered, similar to Ramaekers et al. (2025). Analysis of flame structure indicates ignition in the circumference of the jet, aided by the break-up of the coflow. At higher $T_\mathrm{coflow}$, ignition onset and oxidation completion is earlier prior to jet break-up. Minimum coflow temperature for particle ignition with the oxide layer model is $1125\mathrm{K}$ with complete oxidation at $1250\mathrm{K}$, and for the first-order model at $800\mathrm{K}$ and $900\mathrm{K}$, respectively. Both of these results do not match the experimental results of Hameete. Oxidation degree is predictably higher for enclosed flames. For the chosen particle distribution, the P1 model exhibits higher radiative heat loss and results in a slightly lower oxidation degree. Analysis on particle ensembles with partial oxidation shows that the overall oxidation degree at a sufficient height above the nozzle reflects particle ignition probability. Further analysis in regards to particle size shows ignition failure is more prevalent in larger particles.

Attached-flow unsteady aerodynamics underpin the dynamic stall models used in wind turbine aerodynamic and aeroelastic codes, particularly over the outboard blade region that dominates power production and loading. Here, angle of attack and relative velocity vary while the flow remains predominantly attached. A complete engineering model combines airfoil polar lookup, shed-wake memory, non-circulatory loads, consistent force definitions, and separated-flow dynamics. Although the underlying theory is classical, existing descriptions do not provide a complete and internally consistent implementation route for these attached-flow contributions in wind turbine solvers. This work formulates the attached-flow contributions as lift, drag, and moment coefficients for blade-element momentum (BEM), lifting-line (LL), and actuator-line (AL) methods, for use with 2-D airfoil polars from measurements or CFD. Starting from classical unsteady thin-airfoil theory, circulatory and non-circulatory loads are derived in coefficient form and key modeling choices are clarified. Shed-wake memory is formulated using downwash velocity rather than angle of attack as the aerodynamic state variable. Rotor-level implementation is verified using two cases. A coned straight-blade case provides a cross-method benchmark and quantifies thrust and power errors caused by omitting three required contributions. Lift-direction projection has the largest influence on power, while omitting the mid-chord heaving-acceleration term removes the non-circulatory normal-force cancellation and produces a thrust error. A zero-onset-flow vertical-axis wind turbine (VAWT) case verifies that, in the ideal thin-airfoil limit, all circulatory and non-circulatory contributions cancel, yielding zero total rotor torque.

We experimentally investigate the creeping motion of water droplets sliding along an inclined surface immersed in a viscous oil. The droplet velocity, width, and height are measured over a broad range of droplet sizes and inclination angles. The velocity increases with droplet radius according to a power law, but the corresponding exponent depends strongly on the inclination angle. At small inclinations, the exponent is close to 3/2, whereas at larger inclinations it progressively approaches 9/4. The results therefore reveal a continuous inclination-induced crossover in the velocity-size scaling of lubrication-mediated droplet motion. A scaling analysis based on Landau-Levich-Derjaguin film formation and viscous dissipation in the dynamic meniscus reproduces these limiting behaviors, which correspond to the quasi-spherical and pancake scaling regimes, respectively. Remarkably, the evolution of the velocity scaling is substantially more pronounced than the corresponding evolution of the macroscopic droplet shape. While the velocity data progressively approach the pancake scaling law at large inclinations, the global droplet dimensions evolve in a more complex manner than expected from a simple pancake-shape picture. In particular, the approach to pancake-like velocity scaling occurs even when the measured droplet dimensions remain far from the corresponding pancake-limit geometry. These observations suggest a crossover in the dominant lubrication-dissipation mechanism beneath the droplet that is not directly reflected in the global droplet morphology. The results identify inclination angle as a key control parameter governing lubrication-mediated droplet motion and highlight the distinction between global shape evolution and local dissipation dynamics in liquid-liquid systems.

We present a novel unfitted computational framework for simulating fully nonlinear potential flow-based water waves. Focusing on wave propagation, we describe the core methodology, which involves a high-order polynomial-corrected shifted-boundary approximation on unfitted spectral elements. This approach allows for the simulation of a curved, highly time-dependent (moving and deforming) free surface affected by bathymetric changes. All that on a simple Cartesian background mesh without re-meshing or further approximations of non-affine geometric features. In addition, we highlight the importance of proper gradient recovery using a polynomial-preserving technique to accurately capture the vertical free-surface velocity. Ultimately, the goal is to develop a high-order convergent numerical scheme capable of simulating highly nonlinear waves over long periods. This is achieved through an arbitrary-order finite-difference approximation of the free surface combined with added hyperviscosity for numerical stability. We present verification and validation test cases for wave propagation in both periodic and finite domains. Emphasis is placed on convergence studies, the justification for using high-order approximations, the importance of optimal gradient recovery, long-time simulation of highly nonlinear waves, and nonlinear wave interactions with both affine and curved bathymetry changes, as well as with vertical walls, for highly nonlinear stream function waves and high-amplitude solitons. The novel computational model offers a comprehensive, all-in-one framework for simulating ocean waves and their interactions with offshore structures. It provides significant geometric flexibility, enabling boundaries such as the free surface to move and deform over time without the need to re-mesh a boundary-fitted mesh.

Satellite drops form widely during the breakup of liquid threads and constitute deleterious byproducts across a broad range of industrial technologies, yet their complete suppression has remained a longstanding challenge. Here, we experimentally report that surface viscoelasticity introduced by a small amount of bovine serum albumin can fully eliminate satellite drops, via modulating the localized spatiotemporal topology near pinch-off singularity. During the late thinning stage, surface shear viscosity counterbalances the capillary and stably anchors the thinning neck at the midpoint between the two primary beads, fundamentally precluding satellite droplet formation. We further propose a scaling law to describe the unique self-similar thinning behaviors dictated by surface viscosity. These results shed light on the thinning dynamics of liquid threads with surface rheology and offer a promising strategy to eliminate satellite drops in practical applications.

In this study we examine applicability of the quasi-two-dimensional (Q2D) model of natural convection in a laterally heated rectangular box subject to a transverse magnetic field. For this purpose, results obtained using the Q2D model are compared with fully three-dimensional calculations for rectangular boxes with a square cross-section and horizontally elongated ones with the length to height ratio 8. The width to height ratio is varied from 1 to 10. It is argued that the Q2D model is valid under certain conditions, which include perfect thermal and electrical insulation of the spanwise boundaries and reflection symmetry with respect to the spanwise midplane. It is shown that under these conditions, the Q2D model yields quantitatively correct results for boxes with square cross-section, as well as for horizontally elongated cavities, independently on the width to height ratio. Three-dimensional results obtained for boxes with perfectly conducting walls exhibit asymptotics at gradually increasing width ratio, which, however, does not agree with the predictions of an amended Q2D model. It is shown also that when is applicable, the Q2D model can correctly predict steady-oscillatory transition of three-dimensional flows. It is proposed to seek for extensions of the Q2D model for cavities with perfectly conducting spanwise boundaries.

High-order computational fluid dynamics (CFD) methods combined with actuator-based blade representations provide an attractive approach for simulating rotating energy systems. In this work, we develop a high-order computational framework that couples the flux reconstruction/correction procedure via reconstruction (FR/CPR) formulation with a rotating actuator line model (ALM). Blade rotation and unsteady aerodynamic forces are implemented through time-dependent source terms applied on a fixed cartesian grid. This approach allows simulations of a fully rotating turbine without using explicit blade geometry. Aerodynamic loads are computed using quasi-steady airfoil data and distributed into the flow field with Gaussian smoothing to maintain numerical stability in the high-order scheme. The framework is tested using a two-bladed vertical-axis wind turbine (VAWT) operating at a low tip speed ratio (TSR). The phase-averaged blade motion and overall load are analyzed to study variations with azimuthal angle. In addition, instantaneous and mean flow fields are examined to describe wake structure and unsteady vortex shedding. Normalized mean wake velocity profiles are used for validation through comparison with experimental measurements and blade-resolved large-eddy simulations (LES) reported in the literature. The results show that the proposed high-order virtual-body framework can reliably capture major blade-loading trends, flow organization, and wake features under strongly unsteady conditions, while maintaining geometric simplicity.

Direct numerical simulation (DNS) of compressible transitional and turbulent flows requires numerical methods that combine high-order accuracy, robustness, and computational efficiency to resolve a broad range of spatial and temporal scales. This paper presents a massively parallel hybridizable discontinuous Galerkin (HDG) solver for DNS of the compressible Navier-Stokes equations on GPU-accelerated high-performance computing systems. The proposed solver combines high-order HDG discretization with robust shock capturing, diagonally implicit Runge-Kutta (DIRK) time integration, and an efficient Newton-GMRES solution strategy accelerated by additive Schwarz preconditioning and reduced-basis approximation. A distributed implementation of these methods based on GPU-aware MPI, Kokkos, and CUDA/HIP libraries enables scalable execution on heterogeneous computing platforms. The solver is demonstrated on three canonical benchmark problems covering a wide range of Mach-number flow regimes: subsonic transitional flow over the Eppler 387 airfoil, the supersonic Taylor-Green vortex, and hypersonic boundary-layer transition. Numerical results are compared with available experimental measurements and published DNS data, showing good agreement across distinct flow regimes. The results demonstrate the ability of the proposed solver to resolve laminar-turbulent transition, strong compressibility effects, shock-associated flow structures, and fully three-dimensional turbulent dynamics.

We develop a moisture vorticity theory for the boreal summer quasi-biweekly oscillation (QBWO) in the tropics and analyze it with the aid of GPT-5.5. The model is formulated on a weak-temperature-gradient slow manifold, in which moisture anomalies diagnose the divergent circulation while the rotational circulation evolves through Rossby wave dynamics and vortex stretching. The key coupling is controlled by eddy advection of the background moisture gradient, with the projection $(\mathbf{k}\cdot\nabla\bar q)$ modifying propagation and the cross-gradient factor $(\mathbf{k}\times\nabla\bar q)_z$ controlling moisture extraction and growth. In the weak-coupling regime, which is relevant for the real-world situation, the QBWO is a Doppler-shifted Rossby mode whose growth or decay is determined by phase-coherent moisture extraction and subsequent vortex stretching; moisture damping weakens this feedback but does not introduce a sharp threshold in the minimal linear model. In terms of subtropical geographical locations, this renders the QBWO unstable over the Bay of Bengal with an intraseasonal growth rate and co-located vorticity and moisture anomalies, and it decays over relatively drier regions such as Central and West Africa with a quadrature relation between vorticity and moisture anomalies. The equations also admit a strong-coupling regime where the system approaches a moist-vortex limit. The theory interprets the QBWO as a Rossby-moisture-vorticity instability whose regional behavior depends on background moisture-gradient geometry, coupling strength, damping, and mean-flow advection.

We present a finite element framework to simulate rotating mixing devices using the Mortar Element Method as a domain decomposition strategy. The model is implemented within a matrix-free Navier-Stokes framework which uses a high-order Continuous Galerkin method. The discretized domain is subdivided into rotor and stator parts. An Arbitrary Lagrangian-Eulerian approach accounts for the relative rotor-stator motion, and stabilization is ensured through the Streamline-Upwind/Petrov-Galerkin and Pressure-Stabilizing Petrov-Galerkin methods. The rotor-stator domains are connected by an interface composed of mortar cells, and continuity is weakly enforced in a Discontinuous Galerkin fashion by accounting for boundary integrals at the rotor-stator interface. Verifications of the convergence order in two-dimensional steady and transient examples report optimal rates. The geometric non-conformity created at the mortar interface due to rotor rotation does not introduce significant error in the solution. A three-dimensional example is used to investigate the model's scalability, which yields ideal strong scaling for large problems. A two-dimensional Rushton impeller example uses a torque analysis to showcase the mesh convergence, and the corresponding velocity profile is in agreement with existing numerical results. In a three-dimensional pitched blade turbine case, the power number curve (Np vs Re) shows good agreement with experimental data for Reynolds number values from 1 to 2000. An energy balance analysis reports a numerical dissipation of 1% for Re=200 and of 10% for Re=2000. By exploiting modern hardware capabilities through matrix-free methods, the proposed model is a robust, accurate, and efficient framework suitable for simulating flows with rotating geometries.

Recent advances in generative artificial intelligence have led to significant potential applications in conventional fluid flows, including those that are turbulent. Can these methods be carried over to studies of novel types of turbulence, such as turbulence induced by non-reciprocity in binary-fluid systems? To answer this question, we analyze the statistics of Lagrangian-tracer particles in non-reciprocal binary-fluid turbulence, which has been studied recently in the non-reciprocal Cahn-Hilliard-Navier-Stokes (NRCHNS). We obtain our ground-truth data via extensive pseudospectral direct numerical simulations (DNSs) of the two-dimensionsl (2D) NRCHNS model. Our study yields a variety of intriguing results for probability distribution functions (PDFs) for particle accelerations and velocity-component PDFs; the latter turn out to be bimodal, completely unlike their 2D-fluid-turbulence counterparts. We relate this bimodality to lane-type structures in Eulerian-velocity components. Furthermore, we characterize Lagrangian multiscaling via Lagrangian velocity increments, their structure functions and flatnesses, and multiscaling exponent ratios, for the first time in non-reciprocal hydrodynamics. Finally, we use generative diffusion models to obtain synthetic Lagrangian trajectories for the NRCHNS system, assess how effectively they can emulate the Lagrangian statistics that we obtain from our DNSs, and highlight open challenges in the application of generative artificial intelligence in non-reciprocal systems.