Papers

We investigate bottleneck formation in turbulence using the Voigt-regularised SABRA model and DNS of the corresponding Voigt-Navier-Stokes (NSV) equations. The Voigt regularisation introduces a scale-dependent slowdown of nonlinear interactions without enhancing dissipation, providing a natural setting to study the interplay between nonlinear transfer and thermalised behaviour. We find three distinct spectral regimes: an inertial range at $k<k_I$, an intermediate equilibrium-like range associated with partial thermalisation for $k_I<k<k_{II}$, and a high-$k$ thermal regime for $k>k_{II}$, where the Voigt contribution dominates the conserved invariant. The crossover to the high-$k$ regime occurs at $k_{II}\sim 1/\alpha$, while $k_I$ marks the onset of thermalised behaviour. Equal and multi-time statistics reveal a progressive suppression of intermittency and a tendency towards Gaussianity at small scales, together with a transition from dynamic multiscaling in the turbulent regime to simple scaling in the equilibrium ranges. The shell model resolves these three regimes over a broad range of scales, while DNS of the corresponding NSV equations reproduces the same qualitative trends, including bottleneck formation, delayed cascade completion, reduced intermittency, and a tendency towards Gaussianity at small scales. We find that bottleneck formation might be associated with scale-dependent dynamical slowdown and incipient thermalisation, rather than being purely dissipative in origin. We provide strong evidence that, in the regime where the regularization parameter $\alpha$ is much smaller than the dissipation length scale, the Voigt model reproduces the same inertial-range turbulent regime and turbulence statistics as the Navier-Stokes (NS) equations. This provides evidence that the Voigt model constitutes an excellent practical approximation to the NS equations for small $\alpha$.

This study identifies the scale-dependent processes that sustain turbulence in dense submerged canopy flows. Using a scale-resolved energy budget, we determine where in space and at which scales production, pressure-strain redistribution, and inter-scale transfer predominantly occur, and how they link the canopy layer to the overlying shear flow. We show that energy production is localised at the interfacial shear layer, over a narrow range of streamwise and spanwise scales, while fluctuations within the canopy are primarily maintained through inter-scale transfer and pressure-strain redistribution. The dynamically active scales in the canopy are largely imposed by outer-layer structures, with their organisation and coherence mediated by these inherited motions. Energy exchange across the canopy interface is asymmetric but not unidirectional: although the dominant transfer is from the outer layer towards the canopy, intermittent reverse interactions occur at all scales. The most intense cross-interface exchanges are associated with finer-scale motions rather than large-scale structures, indicating that extreme interfacial energy fluxes are governed predominantly by small-scale dynamics. The flexibility of the canopy weakens the coherence of outer-layer structures and reduces the efficiency of inter-layer energy transfer, thereby altering both the organisation and scale of the fluctuations within the canopy. These results clarify how turbulence in dense canopies is organised and sustained, providing a unified energetic interpretation that links coherent structures to scale-dependent mechanisms.

Building on the stochastic variational framework established in the companion paper, we investigate here the linearized stochastic water-wave system, consisting of a large-scale stochastic wave dynamics coupled to transport dynamics for the small-scale correlation modes. Within this framework, we develop, in the deep-water regime, a kinetic theory for surface gravity waves interacting with unresolved stochastic velocity fields. An energy analysis yields a wave-action kinetic equation exhibiting two distinct regimes: a diffusive scattering regime and a quartic interaction regime with structural similarities to Hasselmann–Zakharov theory. In the present framework, these effective quartic interactions arise through stochastic transport of unresolved fluctuations by the large-scale flow rather than through classical intrinsic resonant nonlinearity. Scaling laws are derived for the diffusion tensor and the effective growth rate, revealing a Miles-type production–dissipation mechanism. Using JONSWAP spectra, we then compare the strength of stochastic transport and classical Hasselmann interactions. For realistic oceanic values of unresolved velocity variance ($\sigma_u \approx 0.1\,\mathrm{m\,s^{-1}}$) and decorrelation time ($\tau_c \approx 10\,\mathrm{s}$), stochastic transport is found to compete with, and often exceed, classical four-wave interaction rates over broad spectral ranges. The transport intensity $S=\sigma_u^2\tau_c$ emerges as a key parameter controlling the transition between interaction regimes. These results suggest that unresolved stochastic transport may play a substantially larger role in spectral evolution than is commonly represented in operational wave models, and motivate the inclusion of transport-induced source terms alongside standard resonant interaction closures.

Understanding the coupling between transport, chemical kinetics, and structural response within solid fuel combustion requires in situ measurements at high spatial resolution. To examine the dynamics of biomass pyrolysis, we optimize synchrotron X-ray micro-computed tomography ($\mu$CT), and conduct 3D particle-resolved simulations. A micro-focused heating cell with controlled heating and flow rate is employed, achieving temperatures of up to 1240 K and 3D imaging at 3.24 $\mu$m spatial and sub-minute temporal resolutions. The pyrolysis of three biomass materials at sample heating rates of 10-14 K/min are examined. The $\mu$CT measurements capture pore deformation, cracking, anisotropic shrinkage, and provide simultaneous thermogravimetric and thermovolumetric analyses to examine specific secondary pyrolysis pathways. Complementary 3D simulations considering detailed kinetics and structural response reproduce the key trends observed, and identify deficiencies in capturing simultaneous mass and volume losses during pyrolysis.

Quantum-inspired algorithms are an emerging class of algorithms for computational fluid dynamics (CFD) with potentially favourable scaling for large problems compared to classical methods. However, their applications have been limited to incompressible flows due to arithmetic limitations, which are addressed in this work. This work introduces the first true end-to-end quantum-inspired computational fluid dynamics (QICFD) solver for direct numerical simulation of the compressible Navier-Stokes equations, that is, all arithmetic operations, as well as initialisation and post-processing, are undertaken in the tensor train (TT) format. Importantly, new division and square-root algorithms using TTs enable the use of Sutherland's law for viscosity, and leverages recent improvements in TT arithmetic algorithms for reduced runtime and memory cost. The new QICFD solver is validated by comparison with the classical CFD solver HiPSTAR and by way of a challenging fluid-flow test case, the low resolution Taylor-Green Vortex (TGV) at Mach numbers of 0.8 and 0.1. The TGV test case is a transient turbulent case that is very sensitive to accumulating errors, yet our QICFD solver achieves excellent agreement with the classical CFD reference. This work demonstrates the correctness of the new TT division and square-root algorithms, and that QICFD is capable of compressible flow simulations. The new QICFD solver is also able to perform simultaneous simulations, running multiple TGV-like cases initialised differently in parallel with reduced extra cost. Finally, the demonstrated TGV test case reveals additional challenges of QICFD as well as highlight the need for future advances to make TT methods viable for industrially-relevant conditions.

Predicting the transport of buoyant particles in a free-surface boundary layer is important to the study of many environmental systems, including microplastics in the upper ocean. Current transport models, adapted from sediment transport theory, typically rely on assumptions of a quiescent rise velocity and gradient diffusion with an uncertain turbulent Schmidt number $Sc_t$. Here, we test this type of model against experiments by studying the vertical mixing of near-neutrally buoyant, finite-size spheres, rods, and disks in a wind-driven, wavy free-surface flow. We measure particle diffusivity directly from Lagrangian trajectories and compare against Eulerian concentration-based estimates. Overall, we find that particle buoyancy is the main control on the diffusivity, and that the diffusivity decreases as particle rise velocity grows relative to the turbulent fluctuations. These observations we find to be consistent with the crossing-trajectories theory, even in the presence of waves. In addition, we find that inferring the diffusivity from concentration profiles with an assumed quiescent rise velocity overestimates the diffusivity by up to a factor of $5$, consistent with effective rise velocities up to $80\%$ lower than the corresponding quiescent values. We also directly measure $Sc_t \approx 1$ for the neutrally-buoyant particles and $Sc_t > 1$ for the buoyant particles. Together, these experimental results demonstrate how standard model closures may be biased in both their diffusivities and rise velocities when applied to buoyant particles at the ocean surface.

We clarify some mathematical features of the density of a dilute particle flow on a body surface in a two-fluid model, with a view toward its application to icing simulations. Inviscid solutions in the vicinity of a front stagnation point are obtained in exact and perturbed forms for small and large Stokes numbers, respectively, and the behavior of the density of the dispersed phase is clarified over the entire range of Stokes numbers. The viscous effect of the laminar boundary layer in the carrier phase on the particle-free thin layer appearing in the low-Stokes-number regime is also investigated based on the incompressible Navier-Stokes equations. An order-of-magnitude estimation of the velocity field of the dispersed phase reveals the cause of this layer and the criterion for its appearance. In particular, the latter result provides an improved form of Michael's criterion.

We use a large database of direct numerical simulations to investigate the transition of the Rayleigh–Taylor instability to turbulence and its evolution toward a late-time self-similar regime. In addition to tracking the growth of the mixing layer through the mean heavy-fluid concentration profile, we analyze one-dimensional profiles of turbulent kinetic energy and dissipation, two key quantities in classical turbulent-mixing models. We consider two reduced-order modeling strategies that differ in where nonlinearity is introduced: either in the construction of the latent space or in the description of its temporal evolution. The first method uses a linear encoder–decoder obtained using Proper Orthogonal Decomposition (POD), with nonlinear reduced dynamics learned by a physics-informed neural network (PINN). The second uses a nonlinear encoder–decoder learned by an autoencoder, while constraining the latent dynamics to remain linear and satisfy physical constraints. Both approaches achieve satisfactory performance in reconstructing, interpolating, and extrapolating the dynamics of the Rayleigh–Taylor instability.

The propagation of sustained Boussinesq gravity-current fronts along a heated wall is examined through laboratory experiments. The gravity currents are generated by continuously supplying a mixture of air and carbon dioxide at the inlet of a rectangular channel, while uniform wall heating is provided by resistive fabrics. In addition to the Froude number, defined either at the source (Fr_s) or at the current front (Fr), we show that the front velocity is governed by \Lambda_s, the ratio of the two buoyancy fluxes per unit area driving the flow: that generated by wall heating and that supplied at the inlet. As wall heating increases (i.e., as \Lambda_s increases), the current front propagates more slowly. This slowdown results from the direct heating of the current, which reduces the buoyancy of its head, and from the interaction between the front and the thermal plumes generated by natural convection downstream. In the most strongly heated experiments, the front eventually stops at a distance from the source that is inversely proportional to \Lambda_s. In these cases, the buoyancy of the head changes sign, and the head evolves into a positively buoyant plume whose vertical extent continues to increase. The experimental results are compared with predictions from a lumped analytical model describing the propagation and eventual arrest of the current.

Reconstructing pressure and turbulence quantities from experimental velocity measurements is challenging, especially without time-resolved data. Furthermore, limitations such as low seeding density, finite resolution, and measurement noise severely hinder the reconstruction of accurate flow fields. We introduce SnapPINN, a two-stage physics-informed neural network (PINN) that successfully reconstructs 3D velocity, their spatial gradients, pressure fields and estimates turbulent kinetic energy dissipation from a single snapshot of sparse, noisy velocity data. Evaluated here on 3D DNS turbulent pipe flow data, SnapPINN uses a sine-activated architecture with sequentially trained, decoupled velocity and pressure sub-networks. In stage 1, the velocity network fits particle data while enforcing incompressibility, serving as a physically consistent smoothing operator that regularises velocity gradients against noise. In stage 2, the velocity network is frozen, and the pressure network is trained using the pressure Poisson equation and the pretrained velocity gradients. We systematically map reconstruction performance of SnapPINN across 100 test cases to mimic challenging experimental, such as adding significant position noise, linearization of velocity field and seeding sparsity as low as $0.07\%$ of the fully resolved DNS grid. Quantitatively, bulk velocity was reconstructed within $0.5\%$, while errors remained below $50\%$ for the gradient-sensitive energy dissipation rate and within $4$–$24\%$ for the a~posteriori inferred $\mathrm{Re}_{\tau}$, even under extremely sparse and noisy conditions. Finally, we establish a practical reliability map that shows which experimental conditions are likely to yield reliable SnapPINN reconstructions in the absence of ground truth.

Folding changes the linearized aeroelastic spectrum and can switch which mode becomes unstable first, with consequences for local postflutter interactions. This study formulates a three-component Z-fold wing by assigning every aerodynamic station to a structural component and a material coordinate. The same attachment map generates surface motion and returns pressure loads through virtual work. Geometrically exact component dynamics, an explicit-wake unsteady vortex-lattice model, and block-structured descriptor assembly preserve the physical paths of configuration actions. A two-parameter flutter analysis shows that a smooth flutter-speed envelope conceals a high-low-high sequence of controlling neutral branches, expressed as a critical-frequency valley and a redistribution of component deformation. Numerical continuation locates a near-1:2 double-Hopf point. Within a local model retaining quadratic and cubic structural restoring forces with aerodynamic and inertial operators fixed at the scheduling point, the cubic normal form captures selected 26-state observations and admits high-frequency-dominant and mixed phase-locked periodic solutions. The formulation links configuration-dependent flutter-mode identity to local resonant dynamics and supports blockwise sensitivity and design reasoning.

Viscoelastic compliant coatings offer a passive route to modify wall-bounded turbulence; however, their effectiveness for drag reduction remains unresolved. We perform resolvent analysis of turbulent boundary layers over linear viscoelastic continuum, and apply it to incompressible hydrodynamic and compressible aerodynamic zero-pressure-gradient turbulent boundary layers, using both standard and eddy viscosity resolvent formulations. Across a wide range of storage modulus E and coating thickness H, viscoelastic surfaces amplify near-wall-cycle-type modes while also attenuating the resolvent gain of very large scale motions (VLSMs) by up to 50%, which together result in a reduction of Reynolds stress. For density-matched coatings representative of aqueous incompressible flows, however, these favorable bands lie entirely within the regime where the effective coatings are linearly unstable to traveling wave flutter, rendering them practically unrealizable. Optimizing material damping does not eliminate this but provides a pathway to use weaker sub-optimal interactions. In supersonic flow, the large solid-to-fluid density ratio (O(1000)) shifts the favorable interaction to substantially higher moduli, weakening the achievable reduction in turbulence production to a few percent. However, the strongest interaction band occurs in the linearly stable regime. These results suggest that compliant wall drag reduction via coupling with high gain modes is fundamentally constrained by flow-induced structural instabilities in incompressible applications, whereas the high density ratios of supersonic flow offer a much narrower but stable window for practical coatings.

The asymptotic properties, with vanishing viscosity, of inertial turbulence in Newtonian fluids have been of intense scrutiny over the years. Much less is known about elastic turbulence - a distinct spatio-temporally chaotic state exhibited by viscoelastic fluids. In this work, using direct numerical simulations of turbulence in a triperiodic box, we show that elastic turbulence achieves an ultimate state with increasing polymer relaxation time, i.e., the Deborah number, for two different constitutive models (Oldroyd-B and FENE-P). In the limiting state, various bulk quantities - the fluid dissipation, the polymeric energy transfer, as well as the elastic stresses - are shown to become independent of the polymer relaxation time scale, notwithstanding the microstructure deformation scales distinctly depending on the model.

Hydrodynamic ram (HRAM) loading remains a persistent challenge in impact mechanics, less due to exotic physics than to the difficulty of achieving convincing quantitative agreement in reduced-order representations. Prevailing studies typically employ a single mesh and boundary treatment validated against one experimental dataset, leaving unresolved whether agreement reflects genuine fidelity or compensating discretization errors. This work presents a planar 2D, GPU-accelerated WCSPH solver employing an Adami-type ghost-particle boundary condition, extended for the first time to a moving, decelerating disk penetrating a confined liquid channel at ballistic velocity. The boundary condition is examined against a purpose-derived potential-flow added-mass solution and the analytical acoustic reflection coefficient at the steel-water interface; this exploration reveals that the stiff equation of state and cavitation cutoff impose identifiable delineation of the solver's operating regime on quantitative agreement. A three-point resolution convergence study reveals a non-monotone near-probe pressure peak, attributed to a bounded ghost-fluid density inconsistency. A comprehensive coefficient sweep, conservation diagnostics, and O(N) GPU throughput scaling enable exhaustive characterization impractical in 3D. Qualitative comparison against literature evidence at 900 and 600m/s clarifies load bearing versus approximate elements. Notably, energy diagnostics reveal a modest total energy growth over the simulated window, with the fluid absorbing disproportionately more energy than the projectile relinquishes - an instructive signature of prescribed, non-back-reacting projectile kinematics that helps map the formulation's operating envelope. The resulting solver, while confined to planar geometry, delivers verified, convergence-checked performance well suited for rapid parametric design exploration.

Direct simulation Monte Carlo (DSMC) resolves rarefied-gas dynamics without a constitutive closure, but finite-sample estimates of macroscopic moments converge at markedly different rates. We develop a non-intrusive, geometry-native machine learning reconstruction of the retained two-dimensional moment hierarchy: number density, two velocity components, translational temperature, three pressure-tensor components, and two heat-flux components. From three sampling blocks, the estimator corrects a structured prior learned from development data with a bounded term computed from the current observation, while preserving additive-moment consistency and the measured zero-frequency content. In cavity development tests, the final observation-conditioned estimator, whose prior is a trained MambaIR restoration network, reduces transverse-heat-flux error to 0.658 and 0.672 times that of a ten-block direct average at two rarefied conditions. For a hypersonic cylinder, a cylinder-centred estimator is fixed before evaluation on six new observation/reference pairs. It improves both global transverse heat flux and near-wall normal heat flux in every pair; the ratios of arithmetic-mean normalised root-mean-square errors (NRMSEs) are 0.846 and 0.793, and the Holm-adjusted one-sided exact probabilities are 0.03125.

Double-diffusive convection in the diffusive regime is often observed to be in a long-lived layered state, well-known in the Arctic ocean and in volcanic lakes, and thought to exist in the interiors of giant planets. The density profile resembles a `staircase', with stacks of convective layers of uniform density separated by strongly stratified interfaces. The governing parameters are the Prandtl number $\mathrm{Pr}$, diffusivity ratio $\tau$, density ratio $R_\rho$, and Rayleigh number $\mathrm{Ra}$. In this work, we perform direct numerical simulations in triply periodic domains to systematically investigate the properties of statistically stationary double-diffusive staircases with $\tau \le \mathrm{Pr} \ll 1$. We demonstrate that they can exist for significantly larger density ratios than previously reported, and propose a new criterion for the existence of long-lived layered states. Notably, this criterion depends weakly on $\mathrm{Ra}$. In all simulations, we measure the total fluxes of density $F^{\mathrm{tot}}_\rho$, temperature $F^{\mathrm{tot}}_T$ and composition $F^{\mathrm{tot}}_C$, and the flux ratio $\gamma =F^{\mathrm{tot}}_C/F^{\mathrm{tot}}_T$. We confirm that $\gamma$ is approximately constant for moderate to large $R_\rho$ but also depends weakly on $\mathrm{Ra}$. We show that the Nusselt numbers for composition and temperature scale as $\mathrm{Ra}^{1/3}$ in this limit, which notably differs from the $(\mathrm{RaPr})^{1/3}$ scaling previously found at lower $R_\rho$. We propose a new model for these findings that is based on the rise and turbulent mixing of density anomalies that form at the edges of the interfaces. The model explains the existing low $\mathrm{Pr}$ data with reasonable accuracy.

In this study, direct numerical simulations (DNS) are employed to investigate NOx formation in turbulent lean premixed hydrogen-air flames under engine-relevant conditions. Various turbulence intensities and molecular transport models are examined to isolate the individual impacts of turbulence intensity, Lewis number, and preferential diffusion on local and global NO production. Results show that global NO production is significantly enhanced in all of the turbulent cases, reaching approximately five times the value of the 1D steady flame at a mixture residence time of 0.1 ms. Increasing turbulence intensity is found to have three competing effects on NO formation: (1) it strengthens turbulence-instability interactions by inducing local super-adiabatic hot spots and elevating the concentrations of key flame radicals within the flame brush, thereby promoting the NO reaction rate locally; (2) it accelerates the turbulent flame speed, reducing the flame-brush residence time and thus suppressing NO production globally; and (3) it reduces post-flame temperature fluctuations, suppressing thermal NO enhancement in the post-flame zone. As a result, the global NO production is slightly lower at higher turbulence intensities among all the turbulent cases considered. Lewis number effects are identified as the primary mechanism driving thermodiffusive NO enhancement, with preferential diffusion playing a secondary role, as evidenced by the nearly identical mean profiles of the NO reaction rate between unity Lewis number turbulent flames and their 1D steady flame counterparts in both the progress variable space and the residence time space. Finally, an excellent correlation between the peak conditional mean NO reaction rate and the stretch factor is identified, and a conceptual model is proposed to improve the predictions of global NO production in practical engine simulations.

Phononic materials (PMs) with engineered resonances have been leveraged for fluid-structure interaction (FSI) with fluid flow instabilities, yielding beneficial outcomes such as transition delay, stabilized hypersonic boundary layers, and increased aerodynamic lift. Prior PM-FSI studies primarily identify spatio-temporal flow scales of interest and choose PM structural parameters producing structural dynamics conducive for FSI. However, a fully-coupled FSI system generally produces complex coupled dynamics that is not accurately captured by studying either physical system in isolation. In this context, our prior work established behavioral parameters that govern the coupled PM-FSI dynamics in a separated aerodynamic flow over a limited parameter range. Adopting this framework, this paper explores strongly-coupled high-fidelity PM-FSI simulations over a broader range of two behavioral parameters—truncation resonance frequency and displacement amplitude—to establish their quantitative (linear/cubic) relations to the coupled frequency, lift force, and circulation in the coupled system response. In addition, the results indicate the presence of distinct FSI regimes, depending on the proximity of the truncation resonance frequency or its sub-/super-harmonics to the vortex-shedding frequency. FSI dynamics ranging from multi-/single-frequency dynamics, downshifted coupling frequency due to fluid-added mass effects, generation of non-linear harmonics to convergence of FSI dynamics to the rigid plate case are observed. These results reiterate the importance of the PM frequency and amplitude in determining the coupled FSI dynamics, and the proposed quantitative relations provide a new pathway for designing PMs for aerodynamic flow control to achieve beneficial outcomes, e.g., lift force enhancement.

Many variational principles for acoustics have appeared in the literature, often introduced in an ad hoc manner by picking and choosing terms in a Lagrangian density to yield a desired governing partial differential equation. In this chapter, we show that such guesswork is unnecessary, as the governing equations of acoustics can be derived systematically from the primitive Lagrangians of classical continuum mechanics. Furthermore, we note that using Eulerian coordinates is not the only way to derive variational principles in acoustics. To this end, we review the construction of an action in the Lagrangian frame for compressible nondissipative fluids. We explore the consequences of material relabeling symmetry and the associated pseudomomentum balance, together with the boundary and jump conditions it implies. Via perturbation expansions, we show how to recover the equations of linear acoustics from each variational principle, the material frame yielding in addition the second-order acoustic energy balance. We show how weakly nonlinear approximations with variational structure emerge in each frame, in both cases for a general barotropic fluid, with the nonlinearity carried by the fluid's parameter $B/A$ and the perfect-gas results recovered as a special case.

A bubble bursting from a drop of finite size (a hollow droplet) is the generic bursting event in a breaking wave, yet it has been studied almost exclusively at unbounded baths. We follow it from the puncture of the film to the spectrum of a spray, in axisymmetric simulations over liquid-to-gas volume ratios $\Lambda$ from $1/16$ to $512$ and Ohnesorge numbers from $0.005$ to $0.11$. Ejection ceases at $\mathit{Oh}_1=\mathit{Oh}_c(1+2\beta/\lambda)$, with $\beta\simeq0.83$ and $\lambda=(1+\Lambda)^{1/3}$: confinement extends ejection to bubbles too small to eject at a flat surface, and the distance $\delta=1-\mathit{Oh}/\mathit{Oh}_1$ to that boundary organizes everything that follows. The collapse, driven by capillary waves, is that of a gas thread pinching next to its mouth, whether the liquid shell is punctured once or twice. The ejected volume is $M_e=C\,\delta\,V_{\rm red}$, with $C\simeq0.013$ and $V_{\rm red}=V_{\rm gas}V_{\rm liq}/(V_{\rm gas}+V_{\rm liq})$ a reduced volume. Whatever the confinement, the first droplet is smallest at $\delta\simeq0.2$ in units of the viscocapillary length $\ell_\mu=\mu^2/(\rho\sigma)$ and at $\delta\simeq0.3$ in units of the bubble radius $R_0$, where the unbounded bath also places its optimum. The largest reaches a tenth of $R_0$. Between them the census is exponential, with a scale set by $R_0$ and no lower cut-off: the smallest droplet a simulation records is set by its resolution, not by $\ell_\mu$, which belongs to the pinch singularity rather than to the droplets. Mixed over bubble populations, the census gives spray spectra in closed form, whose shape measures the population. The bursting also produces hollow droplets, each a potential new generator.

We predict a new viscochiral regime of electronic transport in which spatially varying Hall viscosity selects vortical flow patterns. Although uniform Hall viscosity cannot alter incompressible bulk flow, its spatial gradient redistributes vorticity, amplifying vortices in one chamber while suppressing the vortex in the other. We further determine the underlying mechanism to be generic to recirculating flows and insensitive to the details of the device geometry. The paper maps the resulting phase diagram and shows that the regime is experimentally accessible in valley-polarized bilayer graphene.

Highly resolved computational fluid dynamics (CFD) simulations are essential for design but too expensive for dense design-space sampling. This chapter presents an AI-driven CFD workflow that combines scalar-response modeling and reduced-order dynamics using jet-in-cross-flow examples. A reacting hydrogen jet-in-cross-flow study is first used to train a multilayer perceptron (MLP) mapping injector spacing to unburnt hydrogen throughput, wall heat transfer, and bulk temperature concentration, with shape-preserving interpolation as a baseline. The CFD samples show a non-monotonic spacing response, and the MLP identifies an intermediate-to-wide favorable region near eight jet diameters. Leave-one-sample-out validation shows strong dependence on the predicted quantity: the bulk temperature concentration is robust, while heat transfer and unburnt hydrogen throughput are substantially harder to predict. Sparse Identification of Nonlinear Dynamics (SINDy) is then used as a reduced-order modeling framework for field-derived Reynolds-stress statistics. The parametric SINDy model provides compact field-level predictions at simulated and out-of-sample spacings, though its aggregate spacing-mean Reynolds-stress error is $6.7\%$ higher than the POD-basis reconstruction because of degradation at selected cases. The broader conclusion is that AI-driven CFD is not a single-model prescription: MLPs are effective for fast scalar responses, while POD–SINDy is better suited when transient reduced dynamics and field-derived statistics are central to the question.

Hindered settling of non spherical particles remains significantly less understood than spherical particles due to the computational challenges in resolving the complex contact mechanics and hydrodynamic interactions. In this paper, we present a scaleable fluid structure interaction (FSI) framework coupling the open-source LBM software in OpenLB with the Discrete Element Method (DEM) implemented in LAMMPS to simulate arbitrary shaped rigid bodies in a fluid. Particle contacts are captured using a multi-sphere "clump" representation in DEM, while particle geometries are resolved on the fluid grid via voxelization. We validate our model against single and multi-particle benchmarks, and proceed to study the hindered setttling of cubes in systems containing upto 100,000 cubes. Our simulations show distinct differences between the settling of cubes and sphere, as cubes form pronounced coordination shells without face-parallel contact, in contrast to the contact-dominated clustering observed in spheres. Our results find that correlation length in velocity fluctuations scale with system size even for the largest system studied. These findings highlight the role of particle morphology in suspension dynamics and demonstrate a robust framework for simulating large-scale geotechnical and particulate flows.

Stable prediction of unsteady flows requires accurate multiscale spatial representation and robust temporal propagation. We introduce the Compensated Koopman U-shaped Neural Operator (CoKo-UNO), which combines a U-shaped spectral backbone with Koopman-dominated latent propagation. Finite-dimensional Koopman truncation produces a state-dependent residual that is repeatedly reinjected during autoregressive rollout. CoKo-UNO models this residual with a selective state-space model (SSM), a principled input-dependent compensation mechanism, together with resolution-adaptive compensatory skip connections and an overlapping-warmup rollout strategy. \NEW{Across four benchmark problems, CoKo-UNO achieves the lowest mean rollout error among all compared methods. Its largest gain is a $76.76\%$ reduction relative to the strongest baseline, while requiring about $41.40\%$ of RNO's training time.} These results show that explicit residual compensation improves stable autoregressive prediction of unsteady flows.

We develop an exact Fock-space representation of the Lebowitz–Frisch–Helfand kinetic equation. The familiar square-root Maxwellian transformation is used only as a convenient starting point: it maps the local Ornstein–Uhlenbeck relaxation sector to the bosonic number operator and thereby exposes an elementary grading. The main issue is the representation of the complete kinetic dynamics when the velocity realization depends on local macroscopic parameters. We formulate the pull-back through an arbitrary admissible realization map, show that external space–time derivatives acquire a differential connection, and prove an intertwining theorem for first-order propagation operators. The physical velocity moments are represented by dual Fock-space functionals; a transport–moment intertwining theorem then evaluates the complete propagation contribution without requiring the explicit differential connection. Compatibility between realization parameters and kinetic moments may be imposed algebraically or propagated dynamically by exact balance laws. In the hydrodynamic limit, the number grading selects the second and third Fock levels responsible for viscous stress and heat flux, leading directly to the Navier–Stokes–Fourier constitutive terms. Finally, we prove covariance under local changes of coordinate realization and illustrate it explicitly for Hermite-polynomial and Hermite-function coordinates. Thus the Hermite realization is computationally privileged, while the intertwined Fock dynamics, physical moments, and compatibility structure are representation-independent within the admissible similarity class.

The motion of a slender vortex in ideal incompressible fluid is a classic problem in hydrodynamics. Formulae for the velocity of a vortex ring go back to work of Kelvin, Helmholtz, Hicks and Dyson in the nineteenth century, while more recently a number of models have been created for simulating the motion of slender tubes of vorticity of general shape. For a vortex tube or filament localised near to a curve C(t), the relevant small parameter to measure slenderness is the tube radius divided by the radius of curvature of C. The present paper revisits this range of classic problems by introducing a coordinate system closely linked to the geometry of vortex surfaces in a slender vortex. The motion of fluid elements in this coordinate system has an action–angle form, and with this the vorticity equation simplifies radically. At the same time, however, most aspects of the shape or evolution of a vortex are thrown into the description of the coordinates, and in particular the corresponding metric and volume form. As the coordinate system is non-orthogonal and time-dependent, tools of differential geometry are most easily used to describe the structure of both vorticity and coordinate system, and a general mathematical framework is set out. This resulting system of equations is taken as far as possible with only the assumption of vortex slenderness in place, but allowing arbitrary motions and distortions of the vortex core and of the curve C(t). The modelling is applied to calculate the motion of a slender vortex ring with arbitrary axial flow, solving directly for the shape of perturbed vorticity surfaces and giving results in agreement with earlier studies. The general framework set up in this paper is suitable for the development of simplified equations for vortex motion and interaction in future studies.

Hypersonic flows in the near space often couple continuum-rarefied multiscale effect with finite-rate chemistry. This paper extends the UGKWP method to multiscale gas mixture flows with a single elementary reaction. In the UGKWP method, hydrodynamic waves are employed to describe near-equilibrium distribution functions, and numerical particles are used for the evolution of nonequilibrium ones. The adaptive conversion between waves and particles, guided by the characteristic integral solution, together with the introduction of dt into the flux as an observation scale, has enabled the UGKWP method to succeed in many multiscale problems involving complex physics. In this work, rather than relying on a comprehensive reactive kinetic model for the entire distribution function, chemical source terms are first evaluated at the macroscopic level and then incorporated into the wave-particle update, while free-transport particles are kept chemically inactive in the monatomic setting considered here. This approach leverages the modeling advantages of wave-particle decoupling, facilitating extension to more complex chemical reactions. Moreover, an approximate extension of an advanced multispecies kinetic model is developed in this work for multispecies effect with species number larger than two. The present UGKWP method is assessed for the Zeldovich-type reaction O2+N=NO+O through hypersonic cylinder flows over a wide Knudsen number range, covering chemically inert, forward exothermic, forward endothermic and dE=0 conditions, and through shock structures with hot upstream/downstream equilibrium states. Agreement with DSMC is obtained for gas mixture flow fields, species mole fractions and wall quantities. A three-dimensional side jet flow over a blunt cone is further simulated to demonstrate the three-dimensional capability of the present code.

We present a novel computational framework that couples smoothed particle hydrodynamics~(SPH) with a triangulated membrane mesh to simulate the dynamics of vesicles suspended in fluids. A novel interface-tracking approach enforces membrane impermeability naturally, without resorting to non-physical constraints such as particle reflection or bounce-back boundary conditions. The membrane model incorporates four distinct bending energy formulations, namely the minimal model, the spontaneous curvature (SC) model, the bilayer couple (BC) model, and the area difference elasticity (ADE) model, providing a versatile tool for diverse biophysical scenarios. The framework is rigorously validated against equilibrium shapes and tank-treading motion of a vesicle, demonstrating excellent agreement with previous theoretical and numerical studies. A systematic investigation into the effects of each bending model on the vesicle's inclination angle, revolution frequency, and morphology in shear flow reveals key physical insights. Notably, spontaneous curvature has a negligible effect on steady-state orientation but profoundly alters rotational dynamics at low reduced volumes through the emergence of dumbbell-like shapes with deep constrictions. In contrast, the BC and ADE models induce characteristic asymmetric and stomatocyte morphologies. Our results establish the proposed SPH–mesh coupling as an accurate and robust tool for exploring the complex, shape-dependent dynamics of vesicles in fluid flows.

We present a conditional latent generative framework for parametric rarefied flows that separates neural-field representation, latent transport, and frozen physics adaptation. Neural-field auto-decoders compress discrete-velocity cavity solutions and direct simulation Monte Carlo cylinder solutions into shared coordinate decoders. Train-only principal-component charts support conditional flow matching (FM) and diffusion without a deterministic condition-to-latent backbone, and structured low-rank adapters correct selected decoder outputs while the upstream pipeline remains frozen. On two steady benchmarks, the frozen pipelines interpolate out-of-sample conditions with cavity kinetic relative $L_1$ errors at the $10^{-5}$ level and cylinder per-field area-weighted RMSEs of 0.038 (density), 0.041 (temperature), and below 0.01 (velocities). For the cavity, physics adaptation reduces the matched-grid Bhatnagar–Gross–Krook diagnostic by 28.65% while preserving field accuracy; for the cylinder, the analytic wall map enforces no-penetration exactly and, jointly with the learned FM adapter, reduces the inlet violation to 0.277 and the global mass-balance ratio to 0.963 of the frozen values with negligible field-error change. A five-seed controlled comparison with deterministic condition-to-chart multilayer perceptrons shows that, although the generative pipelines do not surpass the compact MLP in point accuracy on these single-valued steady problems, the results validate sampling-based conditional transport on the shared representation as an effective steady surrogate, with a natural route to multivalued or stochastic solution families.

Pressure anisotropy and off-diagonal pressure stresses are ubiquitous and play important roles in collisionless/weakly collisional plasmas. The Chew-Goldberger-Low (CGL) MHD model is often used; however, it can lose hyperbolicity when the pressure anisotropy or plasma beta becomes large, making it hard to develop approximate Riemann solvers. An alternative approach is to use the 10-moment MHD equations, but their eigenmode analysis is also difficult, which similarly hinders the development of less-diffusive Riemann solvers. This paper presents a new energy-consistent finite difference scheme for 10-moment MHD designed to operate over a broad range of plasma beta. The proposed scheme extends the 10-moment MHD model using the energy-consistent finite-difference approach developed for conventional MHD. Nonlinear filtering is applied to all six independent components of the pressure tensor, and the kinetic and magnetic energies dissipated by the filtering are explicitly transferred to the diagonal pressure components under an equipartition assumption to maintain consistency with the total energy balance. The proposed scheme is validated against seven test problems in the isotropic limit, the gyrotropic limit, and without isotropization/gyrotropization. The results demonstrate the expected spatial convergence and total energy behavior, reproduce the linear growth rate, and yield pressure tensor structures qualitatively consistent with theoretical expectations and previous simulations, spanning plasma beta values from $10^{-10}$ to $10^{10}$. The proposed scheme provides a promising framework for large-scale simulations of collisionless plasmas across widely separated plasma beta regimes and opens a path toward applications such as solar wind turbulence and plasmoid-mediated reconnection.