Papers

Martian dust particles are a few micrometers in diameter, comparable to the mean free path of the gas in the hypersonic shock layer. Their Knudsen number ranges from approximately 0.2 to 100, placing them in the transitional and free-molecular regimes, whereas the flow around the vehicle is a continuum. The two-way flow-particle coupling previously developed by the authors for a two-temperature thermochemical nonequilibrium flow is extended to a receding and pyrolyzing heat shield surface. The gas-surface interaction and the in-depth material response are solved on separate time scales. The surface balances are exchanged at every flow step, while the in-depth response is coupled implicitly over physical time windows. The flow-material coupling is assessed against graphite arc-jet measurements. The framework is applied to the Schiaparelli trajectory from 50 to 30 km. Three surface chemistry models (equilibrium, Park-5, and Zhluktov-Abe) are compared for fixed geometry, char-induced recession, and combined char ablation and particle erosion. At the final trajectory point, the stagnation point heat flux differs by 30-75% among the chemistry models. For the equilibrium model, surface recession changes this heat flux by less than 1% but lowers wall temperature and increases pyrolysis gas injection. Particle erosion contributes 1.73 mm of stagnation point recession, exceeding the char-induced recession, and more than doubles the total recession for all three models. To the authors' knowledge, this study provides the first quantitative comparison of particle erosion between rarefied and continuum drag correlations, and the continuum correlation underestimates the stagnation point erosion rate by 31-35%.

We show that a single Lagrangian trajectory encodes not only temporal but also spatial cascade structure–recoverable without access to a spatially resolved Eulerian velocity field. We report a Markov-Switching Multifractal (MSM) framework that infers hidden multi-scale cascade states directly from single-particle trajectories. Kolmogorov scaling fixes the model's switching rates, leaving a single calibrated intermittency parameter; exact Bayesian filtering then returns the posterior of the layer-resolved cascade state along the trajectory. When we apply the MSM framework independently to each trajectory of a particle pair, we find that the inferred states carry genuine spatial information: consistent with Richardson's locality picture, the Kolmogorov $r^{1/3}$ scaling is preserved when fine-scale layers are randomized, but collapses once the randomization crosses the layer set by the pair separation. Single trajectories thus encode the spatial organization of the cascade, opening a route to cascade diagnostics for turbulent flows accessible primarily through sparse or individual Lagrangian trajectories–from particle-tracking velocimetry to atmospheric and oceanographic tracking–where the instantaneous Eulerian field is out of reach.

We first prove a rigidity result for uniformly rotating vortex patch solutions to Euler equations in bounded simply-connected planar domains. Namely, if a bounded simply-connected domain with real-analytic boundary contains a nontrivial vortex patch that remains strictly inside the domain while undergoing a uniform rigid rotation, then the ambient domain must be a disc centered at the rotation center. The proof combines the rotating-frame formulation with harmonic unique continuation and the generalized Schwarz's reflection principle across analytic boundary arcs. These tools imply that, unless the outer domain is rotationally invariant, the velocity must vanish in an open region surrounding the patch, contradicting the nonzero circulation generated by the patch. In the same spirit, we show that only circular domains possess a circular point vortex orbit. As a second result, we construct quasi-periodic vortex patch solutions to the Euler equations in domains that are small perturbations of the unit disc $\mathbb{D}$. The amplitudes of the solutions are linked to the size of the domain deformation, allowing the classical Rankine vortices $b\cdot\mathbb{D}$, $b\in(0,1)$, to be regarded as equilibrium states. Our analysis is perturbative with respect to the construction developed in the undeformed case, and the resulting quasi-periodic solutions exist for most values of the inner radius $b$. This provides the first construction of quasi-periodic vortex patch solutions to the Euler equations in non-radial domains. Moreover, combined with the rigidity result established above, this shows that, in the periodic case, these solutions cannot arise from a purely rigid rotation.

We investigate how spatially uniform, time-modulated heating can be used to stabilize a thin liquid mirror in microgravity. Periodic heating generates oscillatory thermocapillary flows that suppress the instability associated with sustained heating, allowing the free surface to relax through the combined effects of thermal radiation, thermocapillary transport, and capillarity. Using multiple-scale analysis of a long-wave model, we derive the coupled surface-temperature evolution over many heating cycles. A subsequent linear stability analysis yields the stability criteria and decay times of individual surface modes. Numerical simulations validate the analytical predictions and demonstrate stabilization of meter-scale surface deformations over timescales of days.

The conservative species weighting scheme enables the direct simulation Monte Carlo (DSMC) method to resolve trace species such as electrons and ions in weakly ionized flows. The present study extends this scheme to reacting flows, utilizing a split-merge concept for particles with species-dependent weights. Reactive collisions between differently weighted species are processed according to their respective weights, introducing the production of an integer number of product particles and a probabilistic approach applied to both reactant and product particles to satisfy mass conservation. The extended scheme was validated in single-cell dissociation and exchange reaction test cases, verifying mass and total energy conservation and the mole-fraction histories against conventional DSMC. This extension provides the electron number density required for predicting the onset of communication blackout at high altitudes during hypersonic reentry. The method was applied to the Orbital Re-entry Experiment (OREX) flight conditions from 105.0 km to 92.8 km altitude. Translational and internal temperatures showed good agreement with conventional DSMC results, validating the macroscopic flow-field computation. The scheme enabled continuous spatial distributions of trace electron number density, consistent with the communication blackout onset observed in the flight data. The computed ion current reproduced the overall trend of the in-flight electrostatic probe data. The influences of the ion recombination at the vehicle surface and of the uncertainty of the N + O associative-ionization rate were quantified, and the range of the computed currents encompassed the available measurements. The 105.0 km case extended the prediction beyond available measurements, consistent with the overall trend.

This series of papers studies the stability of accretion discs to the reflex motion of the central object under the gravitational pull of the disc itself. In this second paper, we use linear analysis to reproduce or discover seven distinct instabilities. We outline their defining characteristics and propose a classification. Of the four instabilities that had already been discovered, three are artificial: one does not survive the transition to modern surface density profiles such as power-laws, one is due to the location of the domain's boundaries, and one is due to the use of damping layers near the domain's boundaries. Only the SLING instability of Adams et al. (1989) and the three new 'cavity' instabilities seem capable of affecting accretion discs. All four can be described to a high degree of precision by WKB methods. They may drive eccentricity growth, affect planet migration, create spiral and crescent substructures in the absence of any planet, and boost accretion onto the central object. The issue is that the three artificial instabilities are extremely hard to avoid in simulations, and would bias the same observables. This suggests that our community may not have the tools to model the reflex motion of the central object yet.

If the mass distribution within an accretion disc is asymmetric, it will exert a gravitational pull on its central object. The central object must then move away from the origin of the reference frame, resulting in atypical gravitational pulls on the disc. The goal of the present series of papers is to investigate the stability of this feedback loop. In this first paper, we report a surprising finding: the choice of reference frame affects the number and nature of the waves and instabilities contained in the analytical equations. To show this, we use a simple example: the modes discovered by Sanchez et al. (2025, Appendix A.3). We provide the first analytical description of those modes, we explain their physical mechanism, and propose to call them 'bracket modes' because they arise from the bracket side of an integration by parts. We show that the same disc can be stable in the stellocentric reference frame but unstable in the barycentric reference frame. This is because the boundaries of the simulation domain are frame-dependent. To avoid this, one must model the entire disc all the way from the central cavity to the outer edge. But this is prohibitively expensive, and some discs do not have a central cavity anyway. Our results suggest that extreme caution is required when interpreting simulations of asymmetric discs, and that our community may not have the tools to model the reflex motion of the central object yet.

Using aerodynamic databases of progressively increasing complexity - from linear analytical theory to nonlinear separated RANS flows - we demonstrate that an autoencoder, trained solely by reconstruction, can spontaneously organize the latent representation according to physically meaningful variables and aerodynamic laws. Although the latent coordinates themselves vary under random initialization, the underlying physical organization is reproducible, even quantitatively. In addition, we present a three-dimensional latent space representation of the airfoil flow obtained by an unsupervised autoencoder with sequential training in which the inviscid field is decoupled from the boundary layer effects with the third latent variable strongly correlated with the Reynolds number and aerodynamic drag. Cross-validated regression and affine-alignment measures show that physical parameters and responses are strongly and linearly encoded in the learned coordinates, consistently across independent trainings.

This document presents the theory, implementation, and verification of Motif, a two-dimensional incompressible flow solver developed as a teaching and research framework. The governing equations are discretized using the finite-volume method on staggered Cartesian grids. Convection is treated explicitly using the second-order Adams–Bashforth method, diffusion implicitly using the Crank–Nicolson method, and pressure–velocity coupling using projection methods. Both the Standard projection and the approximate second-order projection of Perot (1993) are considered. Particular attention is given to the discrete operators, boundary conditions, temporal treatment of pressure, conservation properties, and numerical dissipation and dispersion. The implementation is verified using a sequence of periodic, wall-bounded, and inlet–outlet flow problems on uniform and smoothly stretched grids. Spatial and temporal convergence, discrete mass conservation, kinetic-energy behavior, enstrophy, and energy spectra are examined. The results demonstrate the expected accuracy of the spatial discretization and distinguish the temporal behavior of the two projection approaches. The document is intended both to describe Motif in sufficient detail for independent implementation and to examine the numerical properties relevant to its continued development toward direct numerical simulation.

Adaptively Implicit-Explicit (AdImEx) time stepping provides stability for large time steps for mass-conservative transport, making it attractive for the numerical representation of advection in weather and climate prediction. Existing AdImEx transport schemes become first-order accurate in the large-time-step, implicit regime and may require multiple sparse matrix solutions per time step. This work introduces AdHImEx, a new AdImEx scheme that addresses both limitations simultaneously. AdHImEx provides second-order accuracy for large Courant numbers while requiring only a single matrix solution per time step. It is a Runge-Kutta scheme that blends third-order accurate explicit time stepping and Crank-Nicolson implicit time stepping to provide numerically verified stability for Courant numbers up to 100. AdHImEx is designed for flows that are predominantly explicit, activating implicit time stepping only where large Courant numbers occur. It retains the full efficiency and third-order accuracy of the explicit time stepping in regions with small Courant numbers. In this work, it is combined with a fifth-order accurate finite-volume discretisation in space for mass conservation. A second contribution of this work is a novel stage-dependent treatment of the divergence operator that preserves constancy despite different implicit and explicit Runge-Kutta stage time steps and spatially varying implicitness, removing spurious divergence. This innovation is applicable to other AdImEx time stepping schemes. Convergence, transport, and efficiency tests demonstrate substantial improvements over previous first-order AdImEx schemes, little phase and amplitude error, accurate transport on locally refined meshes with large Courant numbers, and promising efficiency characteristics for atmospheric transport.

Convective instabilities are studied from a Lagrangian perspective in order to gain new insights into how the resulting global, long-lived coherent flow structures organize themselves. We consider a 2D annular fluid layer uniformly heated from the inside and subject to radial gravity and propose several new Lagrangian diagnostics for characterizing its convective instabilities. In particular, we perform a comprehensive Lagrangian analysis of the flow field across a wide range of dimensionless parameters, establishing a heuristic correspondence between convective plumes and curves of local maxima of Finite-Time Lyapunov Exponent (FTLE) fields. Moreover, we characterize coherent swirling motions inside convective rolls, which are associated to the non-zero curvature of the flow. By introducing a sliding window method for our finite-time kinematic measures, we demonstrate a direct relationship with radial heat flux quantified by means of the Nusselt number and identify relevant dynamical transitions that leave a trace on both. Finally, we propose a formal criterion for determining viscous boundary layer (UBL) thickness by virtue of radial FTLE profiles and validated against a classical Eulerian method.

Navier-Stokes (NS) equations lose accuracy in the transition regime when the Knudsen number is large, while the Boltzmann equation provides an adequate kinetic description with a substantially higher computational cost. In this work, a data-driven generalized Navier-Stokes (GNS) model is proposed to extend the applicability of the NS equations to the transition regime. A new relationship between the non-equilibrium variables, such as the stress tensor and the heat flux, and the equilibrium variables, including the density, macroscopic velocity, and the temperature, together with the Knudsen number, is learned from the data formed by the numerical solution to the Boltzmann equation. The standard end-to-end learning is utilized to construct the loss function, based on which, a long-term end-to-end learning method is proposed for the loss function to reduce accumulated error and improve long-term predictive accuracy. Several numerical examples, including one-dimensional wave and Riemann problems as well as two-dimensional isentropic vortex and Taylor-Green vortex problems, are studied to validate the efficiency of this new GNS model.

A physics-informed loss adds a discretised PDE residual to the data term, but is only strictly valid if the equations being enforced are closed on the fields being fitted. This fails on coarse-grained, stochastically forced data: nonlinear terms in the PDE generally do not commute with the filter, so the coarse-grained fields do not satisfy the original equations, and driving their residual to zero encodes an implicit closure into the learned operator. Under normalised, translation-invariant filtering on a periodic domain, constant-coefficient linear constraints remain valid on the filtered grid. For the 2D incompressible Navier-Stokes equations, two such constraints are continuity and global momentum balance. We enforce these exactly by applying a closed-form projection on the output of a Fourier neural operator (FNO) at $O(N \log N)$ cost. On two-dimensional isotropic turbulence, truncated so that its forcing lies entirely beyond the cutoff wavenumber, the projection achieves a continuity error of $5.0\times10^{-7}$ against 0.51 for a plain FNO and 0.17 for a physics-informed FNO, and a global momentum balance error of $8.6\times10^{-11}$ against $7.5\times10^{-4}$ and $8.3\times10^{-4}$. The projection only costs an extra 2% of training time, and takes the fraction of rollouts whose energy remains bounded at 448 steps from 0.18 to 0.87. On resolved Kolmogorov flow, test-time optimisation costs approximately 3,300$\times$ as much per trajectory as the projection, while leaving maximum divergence three orders of magnitude higher. Nonlinear constraints can also be enforced once their unclosed terms are modelled: closing the global energy balance with a constant subgrid flux, fitted from the coarse training data alone, removes the 20.9% energy deficit that enforcing the unclosed balance produces and keeps every free-running rollout bounded over 2,000 steps.

Direct numerical simulations of thermally stratified multi-layer Rayleigh-Taylor instability are performed to investigate the influence of interfacial Atwood number (At) on instability growth, interfacial coupling, turbulent mixing, and spectral characteristics. A fully compressible, three-dimensional, high-fidelity Navier-Stokes solver has been used to simulate ten cases spanning a broad range of interfacial $At$ to examine the evolution of coupled instability dynamics. The configuration consists of three superposed fluid layers with unstable density stratification across two interfaces generated through temperature variations. The temporal evolution of the flow is characterized using the maximum vorticity, mixing-layer growth, density fluctuations, turbulent kinetic energy, and energy partitioning between gravitational potential energy, TKE, and dissipation. The instability evolution is shown to proceed through distinct onset, quasi-exponential growth, and nonlinear saturation stages for all configurations. Increasing interfacial At leads to earlier instability onset, enhanced vorticity amplification, and accelerated development of turbulent mixing layers. The weakly stratified configurations exhibit dynamics resembling effectively single-interface RTI, whereas the strongly stratified cases develop two simultaneously active mixing layers that subsequently interact and merge into a coupled turbulent region. The wall-normal distributions of density fluctuations and TKE demonstrate progressive broadening of the mixing region and increasing redistribution of turbulent activity with increasing stratification strength. The late-stage spectra exhibit an approximate -11/5 scaling over an intermediate range of wavenumbers, consistent with buoyancy-dominated turbulent transport.

Liquid marbles (LMs), droplets encapsulated by hydrophobic particles, allow for non-wetting manipulation and containerless handling, making them well-suited for applications such as microreactors. When integrated with acoustic levitation, the LMs serve as contact-free reaction platforms. However, the complex behaviours associated with acoustic fields, including deformation, internal flow, and evaporation, remain insufficiently understood. This study investigates the evaporation dynamics of acoustically levitated LMs. Simultaneous visualisation of the droplet morphology and surrounding vapour concentration fields was achieved using backlighting and the Background-oriented Schlieren (BOS) method. At intermediate relative humidity (RH = 40%), the evaporation rates and vapour distributions of LMs closely resembled those of pure water droplets, indicating that the particle shell exerts minimal influence under these conditions. Conversely, significant differences were observed at high- and low-humidity, attributable to the evaporation resistance and interfacial properties introduced by the hydrophobic particle layers. Furthermore, although pure water droplets maintained a quasi-spherical shape, LMs demonstrated progressive flattening over time, suggesting mechanical constraints imposed by the particle shell. These findings provide new insights into the coupled evaporation and deformation behaviours of LMs in acoustic fields, informing the design of contamination-free microfluidic and microreactor systems.

A vectorial discrete unified gas kinetic scheme (V-DUGKS) is proposed for continuum compressible flows. In the vectorial kinetic framework, mass, momentum, and total energy are represented by coupled distribution functions with separate relaxation processes for momentum and energy transport, enabling an adjustable Prandtl number. All equilibrium distributions are truncated at the second-order Hermite level. Since only second-order velocity moments are required to recover the compressible Navier-Stokes equations, fourth-order Gauss-Hermite quadrature is sufficient for exact moment evaluation. Eliminating third-order Hermite terms allows compact discrete velocity sets to be used uniformly for all distribution functions, reducing sensitivity to the numerical reference temperature and improving stability and efficiency over the scalar DUGKS. The scheme employs a finite-volume formulation with characteristic-based flux evaluation and trapezoidal collision integration. Numerical tests, including shock-tube, Shu-Osher, two-dimensional Riemann, and three-dimensional Taylor-Green vortex problems, demonstrate its accuracy and robustness. For the three-dimensional Taylor-Green vortex, V-DUGKS achieves a speed-up of about 2.2-2.9 under the same CFL constraint due to a larger allowable time step and simplified equilibrium formulation. These results show that V-DUGKS provides a robust and efficient kinetic framework for continuum compressible flow simulations.

In this study, the lean extinction behaviors of CH4 and a 16% cracked ammonia surrogate fuel, CR16, in counterflow premixed flames were compared. Experiments were conducted along with one-dimensional simulations using OPPDIF; the GRI-Mech 3.0 and UCSD mechanisms were applied to CH4 and CR16, respectively. CR16 exhibited higher extinction strain rates and resilience to strain-induced blow-out (RSIB) than those of CH4 under lean conditions. At Phi = 0.66, although both flames had the same extinction strain rate, CR16 showed a higher RSIB because of its longer flame time. Near its extinction, CR16 sustained H2 consumption, radical reactions, and heat release through the interflame region toward the stagnation plane. Hydrogen oxidation coupled with nitrogen-related pathways, including NH2 + NO and HNO reactions, supported this behavior. These results clarify the chemical basis for the superior extinction resistance of economically favorable low-cracking-ratio ammonia fuel.

We solve the near-tip coupled hydromechanical problem of a hydraulic fracture propagating in a permeable poroelastic medium, represented locally as a semi-infinite crack moving at constant velocity. In the moving tip frame, all fracture fields are steady. The porous solid obeys linear poroelasticity, fracture propagation follows LEFM, fluid flow within the tensile fracture is governed by lubrication theory, and the fracturing and pore fluids are treated as identical Newtonian liquids. The primary unknowns are the fracture opening and the fluid displacement function along the fracture, determined from the resulting non-linear system of equations. In a viscosity–toughness scaling, the problem depends on four dimensionless parameters: a dimensionless permeability $\varrho$ (associated with the intensity of fluid leak-in), a dimensionless effective confining stress $\Sigma_0'$ (measuring the relative importance of fluid leak-off and leak-in), the drained–undrained Poisson's ratio contrast $\beta$, and the poroelastic stress coefficient $\eta$. The solution evolves from a drained, toughness-dominated near-tip asymptote with uniform net pressure to an undrained, storage-viscosity-dominated far-field asymptote. Numerical solutions are obtained over parameter ranges representative of various rock types. The fully coupled model is compared with simplified models, namely uncoupled and one-way coupled formulations, over distances from the fracture front spanning laboratory-to-field scales. The resulting relative difference maps in the $(\varrho,\Sigma_0')$ parameter space identify four characteristic regimes: negligible poroelastic effects, dominance of the direct mechanical poroelastic response, importance of the poroelastic backstress, and a fully coupled regime. The latter occurs mainly at large $\varrho$ and small $\Sigma_0'$, corresponding to strong leak-in relative to leak-off.

Which information tells a turbulent flow which way to cascade? We apply Haar-distributed Hermitian phases that retain prescribed same-mode quadratic information, including modal amplitudes, the energy spectrum, and same-mode two-time correlations. For the phase-Haar ensemble, the expectation of any integrable odd flux functional is zero. Finite ensembles strongly suppress mean transfer and forward-event bias in the primary block. An independent block retains sign separation but fails the scale-8 mean criterion. In matched evolution protocols, nonlinear Navier-Stokes dynamics restores the selected signed-flux scalar close to its natural reference, whereas linear evolution and an amplitude-matched frozen control do not. Flux and a local cubic geometry scalar recover together, yet high local correlation can survive erasure of the arrow. Signed transfer thus requires information beyond the retained quadratic record; the tested nonlinear dynamics rebuilds it.

We compare the predictions of the Euler-ensemble solution of freely decaying incompressible turbulence with simulations and experiments: the scaling function of the energy spectrum, the index of the second-order structure function and the decay laws. The predictions have a fixed shape; only their normalization and scale are fitted. In the final $4096^3$ direct numerical simulations of Rodhiya and Sreenivasan, the turbulent attractor is selected by a parabola law for the growth of the bulk length. Along it the collapsed spectrum depends only on the instantaneous Reynolds number, identically for Saffman and Loitsyansky initial spectra; extrapolated to infinite Reynolds number, it agrees with the theory to 1% in the bulk of the enstrophy range, below the dissipation range. The energy balance holds exactly. The energy integral of the theory diverges in the infrared, so energy and enstrophy depend on how a finite flow cuts off the spectrum: with a sharp cutoff $k_0$, the decay laws, energy $\propto t^{-5/4}$ and enstrophy $\propto t^{-9/4}$, are reached only when the cutoff enters the $k^{-7/2}$ tail of the spectrum. Such a cutoff is only an estimate; the reliable test is the bulk of the spectrum. Fitted to the simulations, the cutoff lies at the lower edge of the bulk, where the spectrum still carries the initial data, and the decay exponents depend on the initial infrared spectrum. In the Max Planck wind tunnel at $Re_\lambda$ up to 5779, the longitudinal index extrapolated to infinite Reynolds number matches the odd ensemble with one scale parameter at large separations, where standard crossover forms fail. The freely decaying turbulent blob of Matsuzawa et al. is too small, too inhomogeneous and too weak to display the attractor. The theory is derived in the first two papers of this series.

High-subsonic turbulent jets trap acoustic modes in their potential core. The modes lie in narrow frequency bands that are $O(0.1)$-wide in Strouhal number, $St$. By studying a Mach 0.9, Reynolds number $10^6$ jet, this work confirms an earlier hypothesis: each band is made up of $O(10)$ discrete frequencies, $\Delta St \sim O(0.01)$ apart. To resolve them, we collect $O(100\,000)$ snapshots from dedicated schlieren experiments and large-eddy simulations (LES), and apply spectral proper orthogonal decomposition (SPOD). Our SPOD algorithm uses sine tapers and enforces the jet's rotational and reflectional symmetries. For both the schlieren and the LES, the trapped SPOD modes are bounded in the $St$-$x$ and $St$-$k$ planes, where $x$ and $k$ are respectively the axial coordinate and wavenumber. The bounds quantise the modes in $St$, $x$, and $k$, such that the $n_x$th mode in $St$ has $n_x$ antinodes along $x$ and $k$. We then predict trapped modes with local, global, modal, and non-modal stability theories. We find evidence of a competition between modal and non-modal stability. From only the theoretical bounds, we build a simple in-phase standing-wave resonance model that predicts the quantised global-mode frequencies.

Preface for the English Translation: While checking out early USSR journal articles for our literature search, we recently had tremendous difficulty acquiring this 1934 Klyachko original publication through our library systems. After obtaining and reading a scanned copy of it supplied by the Russian library in Moscow, we realized that relatively scarce citations of this work in the Western literature are often accompanied by inaccurate descriptions and comments, indicating that most Western authors might have gotten only second-hand knowledge about it and never seemed to have read the original article. Compared with various correlation formulas in the modern literature, the Klyachko 1934 formula for sphere drag in fluid flow appears to be the most elegant and cleanest one thus far. Therefore, we decided to make an effort to translate this historical work and publish it in the open literature to facilitate its accessibility to English readers worldwide.

The mixing of two aqueous streams in small channels is usually modeled with constant density when the difference in density between the streams is only a few percent or less. In this paper, we investigate whether this holds in a confluence cell where calcium chloride and sodium sulfate meet and form gypsum. A constant density simulation of the reacting flow results in deposition on the floor along the channel centreline. However, in the experiment, gypsum instead forms bands on both side walls, and the deposition bands start further upstream as the flow rate decreases. Dye experiments with density differences between the streams of 0.14 to 2.1\,%, three channel heights, and 32 flow rates show that the distance at which the dyed stream reaches the opposite side wall is governed by the bulk Richardson number, $Ri=g'H/U^2$, and follows $L/H = 3.31\,Ri^{-0.66}$ over four decades of $Ri$ ($R^2=0.89$). When the two streams' densities match, the dyed stream no longer reaches the opposite wall under most conditions, and in a density-matched reacting experiment, gypsum deposits on the floor, as the constant-density simulation predicts. A small relative density difference is thus not a sufficient condition for neglecting buoyancy: the Richardson number must also be small. For the flow rates typical of centifluidic devices, it often is not.

Learning constitutive laws of complex fluids from velocity data (i.e. indirect observations) is a PDE-constrained inverse problem in which expressive neural parameterizations risk breaking the well-posedness of the forward physics model. We address this tension by learning, rather than the constitutive law itself, the dissipation potential: a scalar function whose convexity, frame-indifference, and dissipativity propagate into the underlying continuum mechanics and guarantee the structural properties needed for a well-posed and generalizable forward PDE. We introduce ICNNE, an input-convex neural architecture that exactly enforces convexity, frame-indifference, and evenness in the second strain-rate invariant via symmetrization, alleviating the numerical instabilities that occur at small strain rates in standard formulations. By weakly enforcing zero gradients in the origin of the potential via penalization, ICNNE also satisfies the dissipativity property. The loss objective and its gradient are computed using a combination of finite element and neural network methods, coupling the Firedrake and PyTorch libraries. We evaluate on four problems spanning compressible and incompressible regimes: compressible Navier-Stokes, Herschel-Bulkley yield-stress flow, Hibler's viscous-plastic sea-ice model, and discrete-element-method data with no known constitutive law. We show that the learned potentials (i) recover ground-truth physics where it is known, (ii) transfer accurately to geometries unseen during training, and (iii) succeed in regimes where unstructured methods diverge. These results suggest that embedding mathematical structure into the parameterization, rather than into the loss, is a robust path to learning physics from indirect data.

Starting from the robust foundation of the peculiar velocity based upwind (PVU) Boltzmann scheme, which fails to recognize contact discontinuities, this paper introduces new variants for the numerical solutions of equations of gas dynamics. A modified partial differential equation (MPDE) analysis of the original scheme reveals that the numerical diffusion coefficient corresponding to the peculiar velocity part does not vanish as the Mach number goes to zero. The numerical discretization of the peculiar velocity term is redesigned so that the numerical diffusion depends only on the bulk fluid velocity across the stationary contact discontinuities, enabling its exact capture in 1D and exact capture of slip surfaces in 2D. The resulting variants achieve low numerical diffusion while preserving the robustness of the original scheme, as demonstrated through several 1D and 2D benchmark compressible flow test cases.

A Direct Numerical Simulation (DNS) investigates transonic flow over a NACA0012 airfoil coupled with single-DOF structural dynamics. Analysis is performed for angle of attack ({\alpha}) 8{\deg} with varying reduced velocity (U*) from 2 to 8, reduced mass (m*) 5.0, Reynolds number (Re_\infty) of 3 \times 10^6, and Mach number (M_\infty) 0.8. The speed of sound in air is calculated as a = sqrt({\gamma}RT_\infty). It is noted that the magnitude of the aerodynamic loads and moments increased with higher reduced velocity. The Fast Fourier Transform (FFT) of the moment coefficient (C_M) in the fixed-airfoil condition is carried out to extract the non-dimensional dominant frequency, referred to as the Strouhal number (St), along with the coupled oscillation frequency of the airfoil (Stc). The FFT analysis for the stationary case at {\alpha} = 8{\deg} yields a value of St = 1.3161. The presence of high-frequency components indicates the onset of instability associated with shock-boundary layer interaction. The computed values of the coupled oscillation frequency (Stc ) are 0.0762 and 0.1716 for the cases with angle of attack (AoA) 8{\deg} and reduced velocities U* = 2.0 and 8.0, respectively. The corresponding natural aeroelastic frequencies (Stn) are taken as 1/U*, yielding values of 0.5 and 0.125. It is observed that for U* = 2, the coupled frequency (Stc) aligns with the subharmonic of shock-buffet frequency, indicating flow-dominated dynamics. In contrast, for U* = 8, Stc coincides with the natural pitching frequency, indicating a dominant influence of the structural mode. Pressure fluctuation contours are examined to analyze the characteristics of acoustic radiation. Vorticity and schlieren visualizations are employed to identify the nature of vortex structures, the strength of the shock, and its spatial location, respectively.

Implicit Large Eddy Simulation (ILES) is a well established approach for modeling high-Reynolds-number turbulent flows by numerical solution of the inviscid Euler equations in 3D. These turbulent flows cover a wide range of Mach numbers, including within individual simulations. For example, Richtmyer-Meshkov instability simulations transition from a high-Mach compressible regime to a low-Mach quasi-incompressible regime during the late-time evolution. These flows motivate the development of a semi-implicit all-Mach numerical method, which is subject to a CFL stability constraint corresponding to the fluid velocity, but independent of the speed of sound, and can be applied efficiently and accurately across the whole spectrum of Mach numbers. Furthermore, finite-volume discretization is chosen to maintain strict conservation and ensure robust and accurate capturing of strong shocks. The method is validated in both high- and low-Mach regimes. Validation is also presented for stratified atmospheres in the presence of gravity, and the method is thus shown to be applicable to buoyancy driven flows. We present favorable comparison against previously published ILES simulations of multimode Richtmyer-Meshkov instability from the $\Theta$-group collaboration, Thornber et al., (arXiv:1706.09991).

This study combines a stochastic renormalization group (RG) in space with a path-integral description of the time evolution, giving a spatial hierarchy of coarse-grained dynamics together with the distribution over spatiotemporal paths. The RG is defined as a diffusion process that applies scale-dependent Laplacian damping together with additive Gaussian noise. The time evolution at each spatial scale is formulated as an Onsager–Machlup action, with a drift (i.e., the predictor) and white noise whose amplitude is fixed by the RG. The predictor of these dynamics is optimized by minimizing the Kullback–Leibler divergence between the path distributions from the RG and from the path-integral description. The optimal predictor contains the score function that connects the spatial scales, so the predictor and the score are two aspects of the same multiscale path formulation. The formulation unifies simulation using the predictor, unconditional generation using the score, and super-resolution using both. The predictor has no closed form, so it is computed by a neural network in two realizations that differ only in how the score is computed. The first realization obtains the score by automatic differentiation of the path distribution, remaining faithful to that formulation. The second obtains the score as an additional network output trained by denoising, at a lower computational cost. These two realizations are validated through numerical experiments on two representative multiscale systems, the Kolmogorov flow and the two-timescale Lorenz-96 model.

Inspired by a recent gauge field description of shallow water equations [SciPost Phys. 14 (2023) 102], in this work we build a simple Lagrangian formulation for the case of constant potential vorticity. An attractive feature of the construction is that it does not appeal to a Clebsch-like parametrization or the use of auxiliary fields. It is also emphasized that on the equator, where the Coriolis parameter vanishes, the shallow water equations exhibit extra SO(2,1) conformal invariance. Using the group-theoretic method, a new exact solution is found, which is associated with the scaling symmetry transformation entering the conformal group.

Body-body interactions have long been investigated to leverage the performance of various fluid-based machines. This study analyzes the flow interaction between a cylinder and a NACA0012 airfoil using direct numerical simulation and machine learning. We consider a two-dimensional incompressible flow at Reynolds number 100, where the airfoil is positioned in the wake of a cylinder. By sweeping the parameter space, composed of the distance between the cylinder and the airfoil $\Delta x$, the relative height $\Delta y$, and the angle of attack of the airfoil $\alpha$, four characteristic vortex-shedding regimes are observed. This study particularly focuses on suppressed vortex shedding at a certain arrangement as oscillation death in coupled oscillators, with the theoretical prediction of flow stability on a machine-learned low-order coordinate. Independent flows around each body are regarded as a system that exhibits isolated periodic vortex shedding at infinite distance, and interactions appear at smaller distances. We employ a synchronization-theoretic autoencoder to derive models for two coupled oscillators from an aerodynamic coefficient. The proposed approach, which enables the assessment of system stability and the prediction of vortical interaction behavior, may pave the way for the analysis of unsteady body-body interactions from the data-driven and synchronization perspectives.