Papers

Viscoelastic filament thinning is classically described by elastocapillary dynamics in extensional flows, yet in confined microchannels the combined effects of wall-induced shear, elasticity, and capillarity remain poorly understood. Here, we experimentally investigate the breakup of a shear-thinning viscoelastic liquid coflowing with an immiscible Newtonian fluid in a rectangular microchannel, focusing on the formation, stretching, instability, and breakup of the thin filament connecting the primary droplet to the upstream liquid. Four regimes: stable coflow, squeezing, dripping, and jetting are identified and mapped using the capillary numbers of the dispersed and continuous phases and an elastocapillary parameter. Although elasticity weakly affects the onset of primary droplet formation, it strongly alters later filament dynamics by delaying capillary breakup and stabilising long-lived filaments. Scaling analyses based on capillary, viscous, and elastic force balances predict the primary droplet size, critical filament thickness at instability onset, maximum filament length, and critical jet length. Particle tracking shows that confinement creates a non-uniform wall-induced shear field along the inclined filament, producing spatial variations in interfacial velocity and initiating the first bead-on-a-string instability at the location of maximum shear. A Rayleigh-Plateau analysis incorporating an effective viscosity derived from the Oldroyd-B model predicts the instability wavelength and growth rate to the correct order of magnitude. These results show that confined viscoelastic breakup is governed not solely by classical elastocapillary thinning, but by a coupled wall-shear-elasticity mechanism controlling filament stretching, instability, and secondary droplet formation, thereby providing a predictive framework for filament-mediated breakup in confined viscoelastic multiphase flows.

We investigate the exponential growth of uncertainty energy in 3D Navier-Stokes turbulence, emphasising the intermittent and highly localized amplification/production of uncertainty, a critical factor in understanding the predictability of turbulent systems. From the Navier-Stokes equations one can identify some key fields contributing to the growth/decay of uncertainty-production term $P_{\Delta}$: strain rate, vorticity, and vortex deformation. The dynamics of these fields are examined in the $Q-R$ plane, where $Q$ and $R$ are the second and third invariants of the velocity gradient tensor, to understand their role in the evolution of uncertainty-production term $P_{\Delta}$. We proceed by estimating committor functions across the entire spatiotemporal domain of direct numerical simulations (DNS) of turbulence in a periodic domain at different Reynolds numbers. Our estimates of the probability of rare extreme events of local uncertainty-production term as a function of uncertainty energy, strain rate, vorticity, and vortex deformation confirm the role of strain rate in driving uncertainty. Where strain rate and vorticity are too close to their space-average values, stable probabilistic forecasts appear impossible solely on the basis of the fields considered here.

Data assimilation (DA) uses Bayesian inference to update the state of a numerical forecast model with observed data. In this study, we propose a fundamentally different, unified approach to atmospheric data assimilation. We use latent video flow-matching to sample temporally consistent trajectories from a prior trained using ERA5 reanalysis (69 variables over an 8-day window). We also use posterior sampling to assimilate real observation sources, such as those from the NOAA Integrated Global Radiosonde Archive and the Integrated Surface Database. Because the prior generates a continuous trajectory, it naturally propagates information between observed and unobserved frames. Therefore, we can perform various DA tasks, such as filtering and smoothing, simply by changing the observed frames. Moreover, we generate full-state ensemble forecasts directly from sparse observations, achieving performance competitive with state-of-the-art observation-to-forecast models.

Transport in fluids is generally reduced to continuum laws parametrized by bulk coefficients and effective interfacial parameters, such as viscosities, diffusivities, slip lengths, and interfacial resistances. This description becomes incomplete at the nanoscale, where spatial heterogeneity, molecular structure, and finite relaxation times are inseparable from the transport process. Here we formulate coupled transport in nanoconfined fluids as a space–time-resolved Onsager response matrix and extract it from equilibrium molecular dynamics simulations. Applied to a confined charged fluid, the framework resolves the nonlocal and transient pathways coupling particle, solute, heat, and charge transport. Momentum transport appears as a long-lived, nonlocal hydrodynamic mode, whereas charge transport relaxes rapidly through localized ionic friction. Off-diagonal responses reveal distinct projected dynamics, providing a microscopic basis for nonlocal, history-dependent transport laws.

Extreme flows realize the largest possible growth, either instantaneously or in finite time, of certain quantities of interest which is achieved by a suitable choice of the initial condition or the applied forcing. The quantities of interest usually measure some small-scale properties and therefore provide information about the regularity of the flow. Extreme behavior is at the heart of several open problems in fluid mechanics including the dissipation anomaly in turbulence and formation of singularities in various models of fluid flow. In this essay we describe a framework making it possible to study such extreme behavior systematically by combining mathematical analysis, scientific computation and physics. As a first step, one aims to deduce rigorous upper bounds on the growth of the quantities of interest in the solutions of a given model. These inequalities express fundamental limitations on the most extreme behavior possible among all admissible solutions. However, given how they are obtained, these bounds may be conservative and overestimate the growth actually realizable in the system. In order to probe this possibility, as the next step, we set up variational optimization problems where the growth of the quantity of interest is maximized under suitable constraints. Solution of such problems is enabled by modern methods of numerical optimization. When properties of the thus obtained maximizers match the bounds, the bounds are declared sharp and therefore cannot be fundamentally improved. Finally, properties of the solutions saturating the bounds reveal insights about the physical mechanisms realizing the extreme behavior. We survey problems where this research program has produced sharp bounds together with extreme flows saturating these bounds. A collection of open problems is then presented and we close the essay with a discussion of possible methodological improvements.

Pipe flow at intermediate Reynolds numbers, between the laminar and fully turbulent regimes, takes the form of several spatially and temporally intermittent phases in which turbulent and laminar states coexist. In the lower range, $Re\in (1750,2300)$, turbulence appears in the form of localized traveling structures called "puffs", which form long-lived chaotic dynamical states, whose stochastic decays and splits control the steady state intermittency. At the other end, $Re\in (2300,3000)$, puffs are replaced by an extended turbulent state, with laminar pockets intermittently forming and disappearing within it. Using direct numerical simulations of pipe flow at $Re = 2400, 2450, 2500, 2550$, we provide evidence that these laminar gaps form a distinct dynamical state analogous to puffs: a traveling laminar pocket in a turbulent surrounding, stabilized by a shear-dependent self-tuning mechanism. We analyse the mean spatial profile of these gaps and show that their lifetimes are exponentially distributed, suggesting that gap closing corresponds to an escape from a chaotic saddle. Finally, we suggest these laminar gaps become unstable and disappear at a finite Reynolds number, $Re\sim 2900$, which can be interpreted as the onset point of spatially and temporally homogeneous turbulence.

Forecasting turbulent flow dynamics requires a balance between predictive fidelity and computational efficiency. Diffusion-based generative models can represent complex spatiotemporal dynamics, but their application to high-dimensional turbulent flows remains computationally expensive. In contrast, proper orthogonal decomposition (POD) provides compact, physically interpretable reduced-order representations, although aggressive modal truncation can remove relevant flow structures. This work introduces a hybrid reduced-order generative forecasting framework that combines POD with Generative Learning of Effective Dynamics (G-LED). The method performs temporal prediction in a physics-based modal space and uses diffusion-based reconstruction to recover physically meaningful flow-field representations. It is assessed using experimental measurements of the turbulent wake behind a circular cylinder. Three configurations are compared: full-field G-LED, global POD-G-LED, and localized POD-G-LED. Full-field G-LED provides the highest fidelity, preserving richer vorticity fluctuations and more consistent turbulent kinetic energy distributions, but requires approximately 17 h for diffusion-model training, 7 h for Transformer training, and 3 min to predict 100 future snapshots. By transferring prediction to a reduced POD space, global POD-G-LED reduces these costs to approximately 8 h, 2 h, and 50 s, respectively, while retaining dominant wake organization and coherent energetic structures. A localized POD-G-LED formulation assigns different modal resolutions to distinct wake regions and improves vorticity statistics and energetic distributions relative to the global reduced-order configuration. These results show that coupling physics-based modal representations with diffusion-based generative reconstruction offers an effective route to efficient turbulent-flow forecasting.

The free surface atop a turbulent liquid flow is deformed by the underlying fluid motion, with the turbulence imprinting its geometry on the surface. Here we develop a theoretical framework to model such deformations based on the Euler equation with gravity and surface tension, and evaluate it against simultaneous high-resolution measurements of surface topography and subsurface velocity fields in a zero-mean-flow turbulent water tank. We consider a range of Reynolds and Froude numbers, focusing on regimes in which the surface is unbroken. Over a range of spatial and temporal scales, we find close quantitative agreement between the measured surface curvature and that which is modeled based on the velocity field a few millimeters beneath the surface, both from the statistical and the local/instantaneous standpoints. Importantly, we verify a strong correlation between the magnitudes of the surface curvature and the divergence of the near-surface horizontal velocity, which in turn is directly related to gas and heat transfer at the air-water interface. We discuss how the sub-surface motion at increasing depths decorrelates from the surface shape, and does so more rapidly at smaller spatial scales. These findings demonstrate that measurements of surface deformations may be used to sense the state of the flow beneath the surface and provide a foundation to make optically-based inferences of processes controlled by near-surface turbulence.

The mechanism of turbulence modulation in particle-laden flow over erodible beds remains an open question. Using particle-resolved direct numerical simulations, this study realises a longitudinal-to-transverse bedform transition by varying the Shields number, revealing non-monotonic modulation of near-wall turbulence. At low Shields numbers, streamwise sediment ridges generate form-induced streaks that produce a distinct secondary peak in the premultiplied energy spectra, exceeding the conventional near-wall turbulent peak and enhancing the turbulent kinetic energy. As the Shields number increases, saltation intensifies and disrupts these structures, causing the secondary peak to vanish in the streamwise direction and weaken in the spanwise direction, thereby suppressing turbulence. Proper orthogonal decomposition of the bed surface reveals a redistribution of modal contribution from a single dominant mode to higher-order modes, with longitudinal features persisting as remnants, directly linking bedform evolution to turbulence modulation.

We extend the Carter-Govan multiple-scales analysis of weakly viscous, narrowband deep-water wave packets beyond Dysthe order within the potential-flow reduction of Dias, Dyachenko, and Zakharov (DDZ). We seek to determine whether this framework generates the complex multiplier $(1 + i\beta)$ used phenomenologically to modify the nonlocal Dysthe mean-flow interaction. Although order counting places a direct viscous carrier-mean interaction at sixth order, it does not exclude an indirect fifth-order contribution arising from viscosity dependent lower-order harmonics and nonlinear interactions. We therefore derive the first correction to the induced mean flow and the complete fifth-order first-harmonic solvability condition. The resulting nonlocal terms are derivative–dependent and contain no explicit viscosity, excluding the proposed indirect mechanism within the DDZ framework. At sixth order, a restricted calculation of the nonlinear viscous block isolates a direct carrier-mean contribution with the same operator structure as the imaginary component of the prescribed mean-flow correction. Independently, a finite-adjustment-time model yields an exact, frequency dependent mean-flow response. Its low-frequency expansion produces the multiplier $ 1 + i\beta_{\mathrm{eff}}(\Omega)$, with $\beta_{\mathrm{eff}}(\Omega) =\Omega\tau.$ When $\Omega\tau = \mathcal O(\epsilon)$, the resulting phase-lag correction enters at fifth order, one order beyond the leading Dysthe mean-flow interaction.

We investigate interfacial dynamics and multiscale energy transfer in immiscible Rayleigh-Taylor turbulence using numerical simulations with varying surface tension coefficients $\sigma$. Capillarity is shown to control characteristic length scales, interfacial area, and global energy and enstrophy budgets. The flow exhibits self-similar evolution with respect to surface tension, with the maximum kinetic energy scaling as $\sigma^{1/2}$ and the flow duration as $\sigma^{-1/4}$. A scale-by-scale budget shows that surface tension removes kinetic energy at large scales while injecting it at small scales, with the crossover occurring near the Hinze scale. We further recast and verify a local kinematic relationship between surface-tension power and interface stretching, up to conservative transport, $ \boldsymbol{f}^\sigma\cdot\boldsymbol{u} = - \sigma\mathcal{S}~|\nabla c| + \mathrm{Transport}$, where $\boldsymbol{f}^{\sigma}$ is the surface-tension force, $\boldsymbol{u}$ the velocity, $c$ the heavy-fluid volume fraction, and $\mathcal{S}$ the interface stretch rate. This relation links kinetic-energy transfer to the scalar-variance cascade and shows that energy transfer to the interface is governed by local strain. Statistics of individual bubbles and droplets reveal vertically elongated filaments with diameters of about three capillary scales, yielding a linear volume-area relation. Their vertical velocities scale with the square root of equivalent diameter, consistent with drag-buoyancy balance. These findings, particularly the direct link between surface tension power and resolved interface stretching, provide a rigorous physical framework for developing subgrid-scale closures for large eddy simulation of immiscible turbulent flows.

Neural surrogates offer a promising route to accelerating computationally expensive simulations governed by partial differential equations across science and industry. Their practical deployment, however, is limited by unreliable predictions under out-of-distribution (OOD) conditions. We develop a solver-coupled surrogate-Newton framework that uses surrogate predictions as high-quality initial guesses for Newton-Krylov iterations, thereby combining rapid global flow-field prediction with high-accuracy numerical convergence at the terminal stage. On an OOD benchmark comprising geometries sampled from actual transonic airfoil optimization trajectories, the framework lowers the median residual L_2 ratio by over seven orders of magnitude while substantially reducing field and aerodynamic errors. In practical supercritical airfoil optimization, it improves online prediction reliability while achieving a 15.5-fold generation-level speedup over CFD. We further test the framework's extension to three dimensions using a flying-wing dataset. Together, these studies demonstrate the potential of surrogate-Newton coupling to deliver accurate, efficient and scalable steady CFD across industrial workflows.

Experiments on highly viscous polymeric films show that punctured holes expand exponentially in time, without sustained accumulation of liquid near the rim. This response departs from the Taylor–Culick description, in which displaced liquid accumulates in a growing rim that moves at constant speed. Although these differences were initially attributed to viscoelasticity, they were later rationalized using a purely viscous theory, leaving the role of viscoelastic stresses unresolved. We analyze the expansion of an axisymmetric hole in a freely suspended viscoelastic liquid sheet described by the Oldroyd-B model. Exploiting the separation of length scales between hole radius and film thickness, we derive extensional thin-film equations on the scale of the hole and an effective boundary condition from an asymptotic force balance in the tip region. Analytical solutions are obtained for weak viscoelasticity, $Wi\ll 1$, and the ultra-dilute limit, $\mu_p\ll\mu_s$, where $Wi$ is the Weissenberg number, while $\mu_s$ and $\mu_p$ are solvent and polymeric viscosities, respectively. For weak viscoelasticity, the dimensionless hole radius grows approximately as $e^{(0.5+\alpha Wi \beta_p)T}$, where $\alpha=(12 - 6\log 2-\pi)/21\approx 0.224$ and $\beta_p=\mu_p/(\mu_s+\mu_p)$. In the ultra-dilute limit, the radius grows approximately as $e^{(0.5+\alpha^{*}\beta_p )T}$, where $\alpha^{*}(Wi)>0$ is evaluated numerically. In both regimes, viscoelastic stresses increase the exponential growth rate relative to the Newtonian limit and induce film-thickness variations, with thickening near the retracting edge. This acceleration arises from azimuthal stretching and radial compression of the polymers, which redistribute stresses in the film and modify the stress balance at the tip, leading to a stronger outward radial extensional flow.

Fog harvesting efficiency with mesh collectors is governed by complex interactions between droplet inertia and geometry-induced flow structures. Although previous studies have primarily relied on mean-flow metrics, the present work introduces a spectral-dynamic framework to examine an important but often overlooked control on droplet capture. A two-way coupled Eulerian-Lagrangian model is used to simulate droplet-laden flow (2-40 microm) across five representative mesh geometries. The results show that capture efficiency correlates not only with the magnitude of velocity fluctuations, but also with their spectral distribution and persistence. Frequency-domain analysis indicates that mesh geometry redistributes fluctuation energy across pore and obstruction regions, thereby defining a characteristic flow timescale. By comparing this flow timescale with the droplet response time, a dynamic matching parameter, {\Pi}= droplet response time/flow time scale, is introduced. The highest capture efficiency occurs when {\Pi} is order unity, corresponding to sustained droplet-flow interaction in the near-mesh region. Geometries that generate broadband, moderately amplified spectral content (e.g., triangular mesh) increase droplet residence time and interception probability, whereas geometries with either weak or highly localized fluctuations reduce performance through insufficient forcing or premature bypass. A physics-inspired correlation for capture efficiency is proposed based on this condition. The study therefore provides mechanistic design guidance, rather than a definitive optimum, for geometry optimization in fog-harvesting meshes.

Turbulence is a central testbed for machine learning on physical dynamics because its governing laws are known exactly. However, most existing studies remain in 2D, while 3D turbulence has fundamentally different physics and is far more costly to simulate. Existing 3D resources also typically provide only one realization per configuration, making it difficult to distinguish learning the dynamics from fitting the statistics of a single flow. In this paper, we introduce TIDE (Turbulent Incompressible DNS Ensembles), a 256^3 DNS corpus and benchmark for 3D incompressible turbulence, with 15 configurations on eight controlled axes, independent ensembles, pressure fields, and equation-level verification. The benchmark includes five tasks, standardized learned baselines, controlled generalization splits, and physical-fidelity metrics alongside pointwise error. Across the main forecasting configurations, current learned models barely outperform persistence and still make about twice the error of a spectral solver given the true equations. Moreover, lower pointwise error can coincide with severely distorted small-scale dynamics, showing that accuracy alone does not ensure physical fidelity. Generalization results further show that most regime shifts reflect limited training coverage, whereas forced-to-decay transfer exposes a missing conditioning variable: operators trained under forcing continue to predict driven evolution when the external drive is removed. Closing these accuracy, fidelity, and conditioning gaps is the central open problem made measurable by TIDE.

We study a physics-informed neural network (PINN) for the unsteady, two-dimensional incompressible Navier–Stokes equations in which the stiff divergence-free constraint is replaced by an artificial-compressibility (AC) relaxation governed by a single scalar parameter $\eps$. The relaxation reintroduces a pressure time derivative, converting a differential-algebraic constraint into an ordinary residual that a PINN can minimise directly. On the Taylor–Green vortex, which admits a closed-form unsteady solution, we quantify the effect of $\eps$: the residual divergence scales as $\eps\,|\partial_t p|$, so larger $\eps$ raises both the divergence and the velocity error, and both decrease monotonically and saturate as $\eps$ is reduced. On the $Re=100$ cylinder wake the plain forward AC-PINN collapses to the steady symmetric branch and does not reproduce von Kármán shedding; assimilating a few hundred sparse velocity sensors from a boundary-layer-resolved finite-element reference (whose Strouhal number, $0.176$, we bring close to the $0.164$–$0.172$ literature band by resolving the separating shear layer, though it remains just above it) recovers the unsteady vortex street to $7\%$ over the wake and its shedding frequency to within $3\%$ of that same reference — a bound set by the reference's own fidelity rather than an independent validation against the true flow.

We investigate the linear stability of particle-laden pulsatile channel flow using Floquet analysis within a two-phase dusty-gas framework. Uniformly distributed spherical particles are coupled to an incompressible Newtonian fluid through Stokes drag, and the governing equations are linearized about a time-periodic base flow driven by a sinusoidally varying pressure gradient. The effects of Reynolds number, Womersley number, pulsation amplitude, particle relaxation time, and particle mass fraction on temporal instability are examined. In the steady limit, particles with very short relaxation times destabilize the flow, whereas finite relaxation times introduce interphase slip and drag-mediated damping that stabilize disturbances. Under pulsatile forcing, increasing pulsation amplitude destabilizes the flow at low Womersley numbers but stabilizes it at sufficiently high Womersley numbers. This transition is governed by the penetration depth of oscillatory motion and is systematically shifted by particle relaxation time and mass loading through interphase momentum exchange. A critical corresponding value remains small throughout, indicating strong particle-fluid coupling and ruling out resonance-like particle dynamics. These findings provide a unified physical framework for the stability of pulsatile particle-laden flows relevant to physiological and periodically forced multiphase systems.

Effects of wind direction in realistic urban canopies remain difficult to characterize systematically because local flow patterns, building-height variability, and turbulent statistics within a realistic urban canopy may respond differently to changes in the approaching wind. To investigate these multi-scale directional impacts, we conducted high-resolution large-eddy simulations of the atmospheric boundary layer over the Zona Universitaria Pedralbes district in Barcelona. The computational meshes employ fourth-order spectral elements, yielding pedestrian-level resolutions below 1 m and resulting in approximately 5.0e8 degrees of freedom. Sixteen wind directions uniformly distributed over 360deg are simulated to capture the full directional response of the urban fabric.

Long-term instabilities in astrophysical fluids are inherently nonlinear, where even small-amplitude perturbations can trigger dramatic instability. However, owing to the complex interactions among non-normal modes, the perturbation structures responsible for the greatest growth remain poorly understood. In this paper, we employ the nonlinear optimization method known as the conditional nonlinear optimal perturbation (CNOP) to identify the most dangerous initial velocity perturbation, i.e., the perturbation that maximizes the kinetic energy growth in the two-dimensional compressible Rayleigh-Taylor instability in astrophysical hydrodynamics. Compared with random perturbations, the optimal perturbation forms a coherent wave-packet structure localized around the density interface. We investigate its dependence on spatial resolution and optimization time horizon through two sets of numerical experiments. For a fixed optimization time, increasing the spatial resolution produces a more sharply localized wave packet, whereas for a fixed spatial resolution, increasing the optimization time causes the wave packet to become progressively more dispersed. Furthermore, we analyze the optimal perturbations in Fourier space using the fast Fourier transform (FFT), which provides a clearer characterization of the spectral distribution. Higher-resolution simulations concentrate most of the perturbation energy into only a few dominant modes, while longer optimization times distribute the energy over a broader range of modes. These results indicate that short optimization time horizons involve relatively weak modal interactions and remain closer to the linear regime, whereas longer optimization times enhance nonlinear modal interactions, broaden the spectral distribution, and reduce the predictive capability of linear stability theory.

The centre-mode elastic instability, prevalent in rectilinear flows of dilute polymer solutions, allows dynamic states to emerge even in the absence of inertia. Here, we show that this instability can be significantly enhanced when the base flow has a nonuniform spatial-distribution of polymers. In such a flow, the polymeric stress not only depends on the conformation tensor (determined here by the Oldroyd-B equation) but also varies proportionally with the polymer concentration field, which satisfies a scalar transport equation. Focusing on the inertialess Stokes limit, we first consider the simple setting of periodic Kolmogorov flow. A linear stability analysis shows that a nonuniform polymer concentration either promotes or suppresses the centre-mode instability, depending on whether the polymers are localised near or away from the maximum of the base-velocity profile. We then focus on a base flow with a distinct polymer-laden stream overlying the base-velocity maximum, and sandwiched between polymer-free streams. We find that the critical Weissenberg number (product of the elastic relaxation time and the typical strain-rate) at the onset of instability undergoes a sudden decrease as the total polymer loading is increased. An energy analysis attributes this destabilisation to elastic feedback forces that arise from concentration gradients near the interfaces between the polymer-laden and polymer-free streams. The insights from Kolmogorov flow are shown to carry over to channel flow, where localising polymers about the centreline strongly promotes the centre-mode instability.

Predicting the transition of wind-forced, gravito-capillary surface waves from smooth to corrugated states remains a longstanding problem in nonlinear surface wave mechanics. Solving driven-dissipative, nonlinear potential flow equations we map these waves ($4-13$ cm) onto a Reynolds number – wave energy phase-space. We identify a transition band separating smooth from corrugated wave states - the wave steepness exhibits a non-monotonic dependence on Reynolds number within this. Subharmonic (in)stability analysis reveals that the fastest-growing mode intensifies corrugations on alternate faces of the carrier wave. Our results offer insights into parasitic capillary wave formation on steep carrier waves and are of interest to ocean remote-sensing.

This work introduces a robust deterministic framework for approximating solutions of the Boltzmann equation with binary collisions by discretizing their dependence on time, position, and velocity using Galerkin methods. By employing a family of parametric Galerkin closures based on $\varphi$-divergences in velocity space, we derive rigorous hierarchies of moment equations that govern fluid dynamic variables. Addressing the limitation that these closures alone do not guarantee dissipation of a $\varphi$-divergence entropy for the true binary collision operator, we restore this property by formulating a compatible approximate collision operator tailored to each closure. This constructed operator intrinsically retains fundamental physical properties essential for high-fidelity flow simulations, including Galilean invariance, exact conservation of mass, momentum, and energy, and strict dissipation of a $\varphi$-divergence entropy. Furthermore, we show that the resulting closed moment systems are symmetric-dissipative, yielding Cauchy problems that are well-posed locally in time. To translate this mathematical foundation into an efficient computational tool, we discretize the position and time variables with an entropy-stable discontinuous Galerkin (DG) finite element method. The fully implicit, entropy-stable space-time approach enables time steps far beyond typical CFL-limited step sizes and the direct computation of steady states. The robustness and accuracy of the methodology are verified and validated through numerical simulations on the supersonic nozzle flow of argon, mass flow through a channel, and heat transfer between parallel walls, demonstrating agreement with analytical benchmarks, experimental measurements, and stochastic particle simulations.

Stochastic Differential Equations (SDEs) have become a cornerstone of scientific machine learning, though they are predominantly utilized as algorithmic tools for uncertainty quantification or distribution matching. In contrast, leveraging SDEs fundamentally to model macroscopic, nonlinear physics as stochastic processes remains largely unexplored. This work introduces a probabilistic, non-intrusive reduced-order model (ROM) for chaotic dynamical systems. We argue that projecting high-dimensional nonlinear dynamics onto a low-dimensional manifold introduces irreducible uncertainty, compounded by the chaotic attractors and multi-admissible futures inherent to turbulent flows. Consequently, a chaotic system governed by a partial differential equation can be effectively modeled by an SDE in a suitable latent space. To this end, a nonlinear autoencoder is employed to map the flow field into a low-dimensional representation, within which the temporal evolution is explicitly governed by an SDE. The predictable component of the dynamics is captured by a learned drift term, while state-dependent stochasticity is absorbed by a diffusion term. We demonstrate that this probabilistic framework successfully propagates highly nonlinear states, offering a robust alternative to traditional deterministic methodologies for chaotic regimes. Ultimately, our model generates new chaotic flow trajectories that remain locally and globally consistent with the true transition kernel learned from Direct Numerical Simulation (DNS) data. Even though these generated trajectories are unique and distinct from the training set, they preserve the underlying statistics and manifolds, validating the strong generative performance and robustness of our methodology.

High-dimensional sensitivity analysis and uncertainty quantification for multiscale gas dynamics, spanning the continuum to rarefied regimes, require computationally efficient and mathematically consistent gradient evaluation. This paper develops a discrete adjoint method for the unified gas-kinetic scheme (UGKS) based on a dual-consistent formulation. The adjoint system is derived directly from the discrete microscopic velocity-distribution equation coupled with the macroscopic-moment compatibility conditions. To resolve the stiff cross-scale coupling, we propose an asymptotic-preserving (AP) adjoint formulation constructed via macroscopic-moment projection and microscopic lifting. Under this framework, the AP adjoint formulation eliminates the stiff collision coupling and removes the collision-time step restriction in the continuum regime. Numerically, a memory-efficient residual-evaluation algorithm that mirrors the forward UGKS cell-vertex data structure is implemented to bypass the memory bottleneck in velocity space. Furthermore, a macroscopic–microscopic predictor–corrector implicit marching scheme is designed to accelerate convergence without solving a globally coupled system. The accuracy, consistency, and robustness of the proposed AP-adjoint scheme are rigorously verified against an independent linearized UGKS solver across a wide range of Knudsen numbers, including lid-driven cavity heat conduction, microchannel thermal creep flow, and hypersonic flow past a circular cylinder.

This study presents a systematic manufacturing approach that combines metal additive manufacturing and subtractive machining to construct flexible wing models for transonic wind tunnel testing. Two wing designs were fabricated and evaluated in terms of geometric accuracy, structural characteristics, and aeroelastic behavior. Three-dimensional scanning, static load tests, ground vibration tests, finite element analyses, and transonic wind tunnel tests were conducted. The fabricated models reproduced the designed geometries and structural properties with good accuracy. The average surface roughness was below 1.0 micrometer, and the average surface deviation was below 0.3 mm, improving geometric precision over previous skill-dependent polishing methods. Independently manufactured models also exhibited highly consistent flutter behavior, with measured flutter frequencies of 157.0 and 158.0 Hz. The results demonstrate that the combined additive and subtractive manufacturing approach enables efficient and reproducible production of flexible wing models for reliable aeroelastic wind tunnel experiments.

This study investigates the droplet size distribution (DSD) and atomization characteristics of a liquid jet injected into a crossflow (LJICF) under varied momentum flux ratios, Weber numbers, and flow conditions. Numerical simulations are performed using the validated compressible Volume of Fluid-Lagrangian Particle Tracking (VOF-LPT) coupled framework to capture both the primary and secondary atomization processes. Key parameters, including momentum flux ratio, Weber number, crossflow pressure, and velocity, were analyzed to assess their impact on droplet size characteristics, including Sauter mean diameter (SMD) and standard deviation (STD) in the downstream region. The discrete size distribution of droplets comprising probability density and cumulative distribution reveals a shift toward finer, more uniform droplets under enhanced breakup conditions. The findings emphasize the critical role of aerodynamic forces and instabilities in driving efficient atomization, with higher momentum flux ratios and Weber numbers leading to finer and more uniform droplets. Increased crossflow pressure promotes finer droplet formation but is found to reduce droplet density in the downstream domain due to a confined spray plume, delayed particle conversion, and reduced droplet residence time. The log-normal and Rosin-Rammler distributions effectively capture droplet size trends, with the former closely representing the skewness and tail behavior and the latter accurately representing intermediate and larger droplets. However, both have limitations in replicating sharp peaks and the smallest droplet sizes, respectively.

This study employs swirling hot coflow to ensure improved fuel-air mixture and stable flame, which are essential for designing low-emission, swirl-stabilized combustors. The present study introduces a swirling confined hot coflow around an air-diluted methanol spray. We have used the Eulerian-Lagrangian approach for multiphase simulation, resolving the dispersed liquid phase via the Lagrangian framework while addressing the continuous gas phase through the Eulerian framework. The Modified Flamelet Generated Manifold (FGM) model facilitates accurate and computationally efficient simulation of gas-phase reactions. The swirl numbers (SN), which are 0.2, 0.6, 1.0, 1.4, 2.0, and 3.0, are employed in this study to evaluate their impact on flame stability and auto-ignition. A higher lift-off height is observed as the swirl number rises from lower to moderate (SN = 0.2, 0.6, and 1.0). It decreases after the lift-off height reaches the critical swirl number (SN=1.0). These large swirl numbers also cause the time-averaged flame structure to change from a sharp columnar flame to an evenly spread combustion region. It also produces a more compact and widely dispersed flame for higher swirl numbers. Particle statistics, Flame Index, proper orthogonal decomposition (POD), and the mean gas-phase flow field distribution are used to study these impacts on flame dynamics in detail.

We study the motion of inertial particles in two-dimensional inviscid and viscous vortex crystals, where vortices are placed at the tips of a regular polygon, and determine the conditions under which long-term trapping of particles can occur. In crystals with a central vortex, we find that trapping points in addition to those found in a previous analysis may exist finding, furthermore, that particle trajectories may approach a limit-cycle which can be described by means of asymptotic methods. We show that these newly discovered fixed points persist temporarily in the presence of viscosity, and study the different transitions following viscous vortex mergers. We find that for moderate Reynolds numbers, the annular merger of the vortex crystal form an annular vortex layer that can keep particles trapped within a disk centered at the origin. For larger Reynolds numbers, pairwise vortex merger leads to crystals with a smaller number of vortices, with particles clustering at the fixed points of the newly formed vortex crystal.

Airborne pollen transport is a key concern for urban air-quality assessment, allergy-risk forecasting, and smart-city planning. However, conventional dispersion models generally assume smooth spherical particles, neglecting how pollen dehydration alters particle morphology and impacts aerodynamic and thermal behavior. To address this gap, this study presents, for the first time, advanced CFD simulations evaluating the aerodynamic drag forces and convective heat transfer of realistically dehydrated (dry) pollen particles. Investigations are conducted at Reynolds numbers ($0.1 \leq Re_p \leq 15$) at the particle's scale corresponding to realistic atmospheric wind speeds ranging from 0.27 to 30 km/h. The findings reveal that dry pollen particles exhibit drag coefficients 8% to 15% higher than those predicted for hydrated pollen spherical particles. Conversely, their Nusselt numbers are 5% to 15% lower than those for hydrated pollen particles. These considerable deviations confirm that conventional spherical correlations are inadequate for simulating dry pollen Lagrangian transport and evaporation. These findings highlight the need to account for realistic dehydrated shapes when modeling airborne allergen transport in urban environments.

This book has one primary goal: To get you moving quickly from learning basic principles of colloid science, to designing colloidal systems for function or motion in the lab. It is not intended to provide encyclopedic knowledge about all aspects of colloid and surface science; rather, I have chosen not to include many topics of genuine importance. In reaching the intended goal, I use two parallel strategies. First, I give practical results that can be used immediately. If there is a cumbersome calculation, I have worked to reframe it into a table or figure. This is the case for Hamaker constants and hydrodynamics of spheroids, for instance. Second, I describe the physics of various colloidal phenomena, so that you as a researcher can think about alternative strategies. In balancing algorithms with explanations, I provide plug-and-chug example problems to familiarize you with units, constants, and typical values. The practice problems provide extensions to the most basic theory that open new possibilities, while also giving results that are useful in practical and research studies. Throughout the book, I provide data we commonly use for viscosities, zeta potentials, ionic phenomena, and other parameters. Rather than providing every reference and every technique, I have provided those references and techniques that we most often use in our lab. In the end, this book aims not to be an exhaustive study of colloids, but rather to be a doorway to producing desired colloidal systems as quickly as possible.