Papers

The measurement of rheological properties from non-idealised flows is routinely used to characterise yield-stress materials. We extend the canonical slump test, which evaluates yield stress based on the spread of a large drop under gravity, by subjecting such a drop to vertical oscillation of its substrate. We test this flow configuration by direct comparison between experiments and numerical simulations of the time-dependent Cauchy equations coupled to the Saramito-Herschel-Bulkley (SHB) constitutive model. This provides a sensitive test of the SHB model near yield because the vibrated drop can releases stress exceeding the yield stress by adjusting its shape as the forcing acceleration is increased, and thus, remains close to the yield threshold for all forcing. We find that the SHB model systematically underpredicts the amplitude of the viscoelastic oscillatory response of the drop to forcing by a factor of five. However, spreading can be captured numerically by selecting a solvent viscosity that represents the appropriate post-yield rheology of the material at the expense of matching sub-yield properties. This highlights a fundamental challenge in simulating flows in which yielded and unyielded material coexist, such as those encountered in proto-rheological tests. We establish the vibrated drop as a powerful proto-rheological configuration for estimating the yield stress across drops of different rheology, size and shape, by establishing a proportional relationship between the threshold acceleration required to induce spreading relative to gravity and the yield number, the ratio of yield stress to gravitational stress acting at the centre of mass of the drop.

Analyzing flow fields on aerodynamic surfaces is critical to designing next-generation aircraft. Raw computational representations are high-dimensional and costly for complex three-dimensional bodies, while conventional low-dimensional representations apply only to the systems from which they derive. We introduce an approach that learns fluid flow representations from simple two-dimensional geometries and transfers them to complex real-world three-dimensional aircraft. Comparing the proposed Least Volume autoencoder (LVAE) to proper orthogonal decomposition (POD), we show both yield compact 28-41 dimensional representations of two-dimensional flow fields, with the nonlinear LVAE producing more accurate in-domain reconstructions at matched dimensionality. These models transfer zero-shot to three-dimensional systems, and counterintuitively the linear POD transfers more accurately than LVAE. Applied to extruded wings, POD-reconstructed lift and drag remain within 0.1% and 0.7% of true values, while transfer to complex blended wing body aircraft preserves lift and drag to within 0.3% and 0.7% without any three-dimensional training data. We further show that three-dimensional flow patterns missed by the pretrained model can be isolated to train a disentangled 3D latent space via a dual encoder-decoder transfer learning strategy, performing accurately in previously inaccessible data-scarce regimes. Using only five blended wing training cases, mean squared reconstruction error drops by 5x relative to the 2D pretrained models and 70x relative to models trained from scratch. These results establish that transfer learning from readily available two-dimensional datasets unlocks compact, interpretable representations of complex three-dimensional aircraft surface flows, enabling design insights in data-starved early phases where conventional approaches require hundreds to thousands of simulations.

An object releasing a chemical into a surrounding flow leaves behind a plume that encodes the rate of release, but for most solutes, that plume is invisible. Classical transport theory describes this configuration through a self-similar concentration boundary layer whose structure has never been resolved experimentally in forced flow at low Reynolds number: a century of measurements at these conditions has returned integrated transfer rates rather than the field itself. Here we show that both the field and the information it carries are experimentally accessible. Around hydrogel posts photopatterned inside a microfluidic channel, a released solute drives suspended colloidal particles away by diffusiophoresis, i.e., their drift along chemical gradients, carving a particle-free “shadow” downstream. Using a fluorescent solute, we resolve the concentration field around the post and recover the classical self-similar structure of convective mass transfer. For an invisible surfactant, the width of the shadow, benchmarked against a directly imaged solute on the same platform, then serves as a proxy for the dimensionless rate of mass transfer from the post. Finally, comparing two orientations of a triangular post tests a classical prediction by Brenner: the local concentration fields rearrange, yet no orientation dependence of the integrated transfer rate is resolved. For solute–tracer pairs whose diffusiophoretic response is known, colloidal shadows thus turn ordinary tracer particles into quantitative reporters of chemical exchange that cannot be observed directly.

Hybrid Eulerian Lagrangian methods for multiscale cavitation represent grid resolved vapor structures in an Eulerian formulation and unresolved bubbles in a Lagrangian description, requiring transitions between the two representations as structures evolve. Existing approaches typically treat these transitions as local geometric operations, while resolved structures are identified independently at each time step, limiting the use of temporal history in representation changes. This work presents a conservative hybrid Eulerian Lagrangian framework with embedded, on the fly persistent structure tracking. Resolved vapor structures are detected using connected component labeling and reconciled across processor boundaries through a deterministic parallel procedure. Successive observations are associated using physics informed predictions of structure position and size, maintaining persistent identities and histories through birth, death, breakup, coalescence, and representation transitions. The retained history enables history aware Eulerian to Lagrangian transition criteria and initialization of Lagrangian bubbles with the radius and radius rate information required by the bubble dynamics model. Conservative bidirectional transfer operators preserve vapor mass and linear momentum while preventing simultaneous representation of the same vapor volume. Canonical tests verify persistent tracking through fragmentation, coalescence, and close crossings, repeated representation switching, conservation of mass and momentum, and deterministic parallel behavior.

We consider narrow-band deep-water surface gravity waves propagating above a background flow whose spatial scale is comparable to the wavelength. We focus on the regime where the background-flow speed is comparable to the Stokes drift of the waves to derive a two-way coupled model between the fast waves and the slow background flow. Nonlinear wave interactions arise at the same asymptotic order as the two-way coupling and must therefore be included in the derivation. The resulting model consists of a nonlinear version of the reduced wave equation obtained in part I, coupled to a Craik-Leibovich equation governing the evolution of the background flow. The model describes the evolution of the wave field and background flow over the slow turnover frequency of the background flow, thus saving the computational burden of temporally resolving the fast wave frequency. The inviscid model exactly conserves wave action, mechanical energy and horizontal momentum, while the viscous model exactly conserves horizontal momentum. The coupling terms are cast in compact form for ease of physical interpretation and numerical implementation.

We consider deep-water surface gravity waves propagating above a background flow whose spatial scale is comparable to the wavelength, focusing on the regime where the flow is slow compared to the group velocity of the waves. We introduce an "equivalent solvability condition" method to construct reduced equations, demanding that, upon multiple-timescale expansion, the reduced equations share the same leading-order solution and first solvability condition as the original system. This approach turns the full 3D problem into a 2D reduced equation for the wave field. We derive such reduced equations for broad-band waves above a depth-invariant background flow, and for narrow-band waves above a fully 3D background flow. In the latter case the reduced equation takes the form of a Schrodinger equation involving the near-surface vorticity of the background flow only, with the impact of the near-surface horizontal flow divergence shown to be subdominant. Beyond the reduction in spatial dimensionality, the latter reduced equation describes the evolution of the wave field over the slow advective timescale of the background flow, thereby eliminating the computational burden of time-resolving the fast wave period. We illustrate the capabilities of the reduced equations through an analytical solution for the weak scattering of a wave packet by a patch of organized flow, followed by numerical solutions for stronger scattering of a wave packet by a patch of disorganized flow.

Pipe and channel flows of viscoelastic fluids display chaotic dynamics at unusually low speeds, a phenomenon referred to as elasto-inertial turbulence, EIT. First reported in experiments a century ago, recent theoretical studies and model computations predict a variety of scenarios for the phenomenon's origin, ranging from hoop stress modes to center modes and to Tollmien-Schlichting waves. Lacking experimental confirmation, the relevant scenario in actual flows of polymer solutions remains unknown. We here determine the transition threshold of EIT in pipe experiments, covering three decades in elasticity number. Across this entire parameter range, the transition features center mode structures at onset. Eventually the instability diverges at a lower inertia (upper elasticity) limit, which is a robust signature of this center mode scenario. Finally, we report the first experimental observation of a traveling wave in viscoelastic pipe flow, and the sequences of localized structures found, are in excellent agreement with a center mode traveling wave, the "arrowhead" solution, discovered in model simulations.

Modelling retinal haemodynamics is crucial for understanding retinal microcirculation but is computationally demanding because it involves coupling between the vasculature and surrounding tissue across multiple scales. This computational burden has been substantially alleviated by a recent analytic solution on the planar disc that enables lumping the capillary bed and surrounding tissue into an effective resistor. However, that formulation treats the retina as a flat surface, whereas the retina is a curved surface with a finite anterior aperture. In this work, we develop a nontrivial and physiologically necessary extension to spherical-cap tissue domains with varying apertures, where surface curvature and finite-aperture boundaries complicate solving coupled Darcy equations on a curved manifold. Using a stereographic projection and a decoupling transformation, we derive an analytic solution for the capillary-tissue system on the spherical cap that represents flow in both the capillary bed and interstitial tissue more realistically while retaining the efficient resistor formulation, a key advantage of the planar-disc formulation. This solution is coupled to one-dimensional (1D) arteriolar and venular flows to obtain a multiscale description of retinal haemodynamics. Using a vasculature model designed to capture retinal vascular features, we show that the multiscale model's predictions are consistent with experimental data. We further explore aperture effects using both a fixed hemispherical vasculature and aperture-dependent vasculature. The aperture affects retinal haemodynamics mainly through changes in the constructed vasculature itself, whereas the surface-averaged pressures and relative terminal flow distributions remain nearly unchanged. This framework provides a foundation for studying retinal pathophysiology on more anatomically realistic domains.

Solving inverse and optimisation problems with traditional shallow water equations (SWE) solvers can be computationally expensive, particularly when gradients with respect to model inputs or parameters must be estimated through repeated forward simulations. In this paper, we introduce DiffSWE2d, an open-source differentiable shallow water equations solver for end-to-end flood and tsunami modelling implemented in PyTorch. By leveraging automatic differentiation, DiffSWE2d represents the time-marching physics as a differentiable computational graph, enabling gradients to be propagated directly through the numerical solver. We validate the solver against two established benchmark cases and demonstrate its application to tsunami waveform inversion, showing its ability to infer model inputs through gradient-based optimisation. DiffSWE2d provides a flexible framework for integrating physics-based hydrodynamic modelling with modern optimisation and machine learning methods. The source code and reproducible examples are publicly available at: https://github.com/ZhonghouXu/DiffSWE2d

To solve the turbine design optimization problems efficiently, surrogate-based optimization (SBO) algorithms are frequently used. To further reduce the cost of turbine design, the multi-fidelity surrogate (MFS) based optimization is proposed by the researchers, who resort to augmenting the small number of expensive high-fidelity (HF) samples by a large portion of low-fidelity (LF) but cheap samples in surrogate modeling and optimization process. Nonetheless, according to our observations, the MFS based optimization sometimes can only have better convergence rate at the early stage of optimization process, but yielding worse final solution than the single-fidelity surrogate (SFS) based optimization that uses high-fidelity samples alone. The reason behind can be explained as follows. With the increase of HF samples in the optimization process, the LF samples can cause negative effect and therefore misleading the optimization search. To address the above issue, an ensemble weighted multi-fidelity surrogate (EMFS) is proposed. Specifically, the density-based spatial clustering of applications with noise (DBSCAN) is used to detect the region where the MFS cannot build a more accurate surrogate, and a local SFS is built there. Then, an EMFS is built by combining the MFS and SFS with adaptive weights, which is used to guide the optimization process. The related algorithm is named as multi- and single-fidelity surrogate fused optimization, i.e., MSFO. Through tests on GE-E3 blade optimization and the film cooling layout design of a turbine endwall, the effectiveness of proposed MSFO is well demonstrated.

Turbomachinery design optimization involves expensive black-box problems. Sample-efficient multi-fidelity optimization (MFO) offers an efficient solution. By utilizing multi-fidelity surrogates (MFS), the MFO algorithm can use fewer high-fidelity samples aided by low-fidelity samples to establish an accurate surrogate model. However, when MFS is used in sequential sampling optimization, it has been observed that the final optimal solution obtained by single-fidelity optimization (SFO) is better than that of MFO, even though MFO performs better at the early stages. This can be attributed to the assumption of an even and nested distribution of samples, which is incorrect when using a sequential adding strategy. To address these issues, we propose a novel algorithm called multi-single-fidelity optimization (MSFO) to overcome the limitations of the conventional MFO procedures. In the surrogate establishment of MSFO, we use the density-based spatial clustering of applications with noise (DBSCAN) method to detect local areas where low-fidelity samples are no longer effective. A combination of both global MFS and local single-fidelity surrogate model, built using high-fidelity samples alone, is used to establish an ensemble, which improves the anti-interference ability of the algorithm against misleading low-fidelity data. The effectiveness of the MSFO algorithm is verified first on numerical benchmark functions. Then, the algorithm is used to optimize the aerodynamic profile of a turbine and the film cooling layout design of a turbine endwall. Here, high-fidelity sample sources are obtained from fine-mesh CFD simulations, whereas low-fidelity sample sources are obtained from the same simulations run on a coarser mesh. The results demonstrate that our MSFO algorithm performs significantly better than the conventional SFO and MFO processes, with a higher level of robustness.

We investigate the dispersion of a reactive solute in a couple-stress fluid flowing between two parallel plates under the combined effects of pressure-driven flow, buoyancy, and an induced magnetic field. The model incorporates first-order heterogeneous reactions at both channel walls alongside a bulk reaction. Using Mei's multiscale homogenization technique accurate to third order, we develop a higher-order asymptotic formulation to determine the effective longitudinal dispersion coefficient and concentration field. Analytical predictions are complemented by Brownian dynamics simulations and finite-difference solutions, while the Aris method of moments quantifies transient mean displacement, spatial variance, and effective dispersivity. The hydrodynamic analysis reveals a singular branch in the velocity solution when the Hartmann number equals half the couple-stress parameter and identifies a characteristic quarter-power scaling between the Hartmann number and couple-stress parameter, separating couple-stress- and magnetically dominated regimes. The model recovers classical Taylor-dispersion behavior in the non-reactive Newtonian limit and agrees well with experimental measurements. Couple-stress rheology and magnetic damping suppress shear-induced dispersion, whereas buoyancy enhances dispersion through additional transverse velocity gradients. A distinct saturation regime of the dispersion coefficient emerges with an increasing couple-stress parameter, while unequal wall absorption induces persistent transverse asymmetry, and stronger absorption enhances solute removal near the source. Numerical and stochastic results validate the analytical framework while resolving higher-order concentration structures and particle-scale wall adsorption.

Reinforcement-learning quadrotor controllers are usually trained under simplified wind models, yet the impact of wind-field fidelity, as opposed to magnitude, on policy robustness remains unquantified. This paper compares five disturbance-fidelity levels, from wind-free flight and discrete 1-cosine gusts through statistical turbulence and synthetic coherent structures to large-eddy-simulation fields of the atmospheric boundary layer, in a full cross-fidelity train test evaluation of proximal policy optimization (PPO) agents, with cascaded PID and geometric SE(3) controllers as training-free references, over a 0-12 m/s wind sweep. Before any controller comparison is made, all disturbance data are validated: every synthetic generator is checked quantitatively against its analytical or certification-standard reference, and the large-eddy-simulation fields against the imposed log law. On a racing-class quadrotor in hover, the train test matrix is remarkably flat, and the cheapest structured training wind, which is discrete-gust domain randomization, ranks first in every test column, a ranking replicated on a wind-sensitive 27 g platform; a once-tuned geometric controller brackets the learned PPO policies at zero crash rate. Mechanism diagnostics show that control authority, not wind realism, bounds robustness, so wind-fidelity investment should scale with platform wind sensitivity.

We study the dynamics of collisions and near-collisions in the system of three point vortices in the plane. The dynamics is known to be completely integrable and can be reduced to the study of Hamiltonian systems on two-dimensional symplectic leaves. This still allows for interesting behavior of the solutions, various aspects of which have been investigated in a large body of work by many authors. Our focus will be on collisions and the possibility of their regularization through perturbations of suitable parameters of the system. We will use the reduced coordinate given by $\zeta=(z_2-z_1)/(z_3-z_1)$, where $z_1,z_2,z_3$ are the complex numbers representing the positions of the vortices. This choice seems very natural, although we have not come across it in the existing literature on the topic. Some of our results concerning the near-collision behavior appear to be new, and we also prove inequalities between critical energy values that we have not found in the literature. The calculations we do to analyze the collisions and near-collisions also reproduce various classical results that were previously obtained by other authors using different coordinates, and parts of the paper therefore have an expository character.

In this paper, the log-conformation reformulation of a Giesekus fluid near a planar stick-slip singularity is investigated analytically. In what is, to our knowledge, the first use of the log-conformation formulation beyond its numerical purpose, we present results that match the asymptotic stress analysis of Evans [JNNFM 222 (2015) 24-33] for the stick, slip, and core regions under the assumption of a given Newtonian velocity field. Furthermore, the logarithmic reformulation allows us to extend the existing asymptotic theory substantially, showing, e.g., that the determinant of the conformation tensor is asymptotically constant, as well as thoroughly characterizing the transition behavior between the boundary layers and the core region. Combining these results, we obtain a composite asymptotic solution of the log-conformation equation that is valid uniformly throughout a close neighborhood of the singularity.

Internal waves often propagate in the presence of currents. Internal waves and currents are widespread in the world's oceans. The equatorial internal waves and the equatorial undercurrent (EUC) are perhaps the most representative illustration of this phenomenon. The current profile in this study is a quadratic function of depth, which is in agreement with the known results of the EUC. With this assumption the integrable nonlinear Gardner's equation is derived as a model for the wave motion of the thermocline, separating the two layers of slightly different densities. In addition, we derive the generalised Gardner's equation in the case of variable bottom. We demonstrate that the coefficients of the equation are very sensitive with respect to the parameters of the EUC.

We investigate laminar mixing of a passive dye in an infinite, two-dimensional domain filled with a Newtonian fluid by simulating a cylindrical stirrer that rotates at constant speed along a circular path, stirring an initially quiescent fluid. The fluid is marked by a passive dye in the lower half of the domain, enabling a systematic analysis of dye-interface evolution and mixing dynamics. By varying the stirring Reynolds number within the laminar regime, we identify how transitions in flow topology govern mixing and distinguish three mixing regimes spanning diffusion-dominated and advective mixing. In the diffusion-dominated regime, mixing is characterized by the formation of a well-mixed central region and the development of a spiral dye pattern that evolves in an approximately self-similar manner. Advective mixing is marked by substantial deformation of the dye interface beyond the central region. We provide a mechanistic interpretation of advective mixing by relating mixing events to specific flow features: (i) direct interaction between the stirrer and the dye interface, and (ii) vortex shedding near the stirrer and away from the central region. Enhanced mixing occurs when vortical structures are able to escape the central region and transport scalar gradients nonlocally. When vortical activity remains confined near the stirrer's path, mixing per stirrer period exhibits only weak dependence on stirring speed despite increasing stirring intensity. Significant enhancement of mixing per period occurs only when escaping vortices introduce a new transport mechanism that carries scalar gradients far beyond the stirrer's path. Overall, we present a mechanistic link between flow topology and mixing by identifying the transport mechanisms through which flow features govern scalar evolution, providing a bridge between the kinematics of mixing and the underlying fluid dynamics.

A robust finite-volume framework is presented for the simulation of compressible multiphase flows with surface tension across a wide range of Mach numbers. The method is based on a two-pressure, six-equation diffuse interface model incorporating viscous, gravitational, and capillary effects through the continuum surface force formulation. To consistently account for capillary-induced pressure jumps, an HLLC Riemann solver is developed using generalized Riemann invariant analysis, and the instantaneous pressure relaxation procedure is modified to preserve the Laplace pressure jump during phase equilibration. To overcome the excessive numerical diffusion of conventional approximate Riemann solvers in the low-Mach regime, a robust low-Mach correction is proposed by extending our previous formulation with a modified scaling strategy that remains stable in regions of strong pressure variation. The resulting method retains accuracy from nearly incompressible flows to compressible regimes while preserving the robustness of the six-equation formulation. The numerical framework is validated using a series of benchmark problems involving surface tension, viscosity, gravity, and compressibility. The results demonstrate accurate prediction of interface dynamics, capillary pressure, and low-Mach flow features, while significantly reducing numerical dissipation without compromising stability. The proposed methodology provides an efficient and reliable approach for the simulation of complex multiphase flows spanning a broad range of flow regimes.

This study evaluates viscosity-dependent limitations in refined potential flow theory (RPT) applied to incompressible flow over an impulsively started circular cylinder. RPT adapts classical potential flow theory to account for viscous effects, flow fluctuations, and three-dimensional variables. By utilizing a quasi-irrotational viscous stream function, the framework solves the continuity and Navier-Stokes equations while satisfying both free-stream and no-slip boundary conditions.

We develop a vectorial lattice Boltzmann model with a space-time adaptive relaxation coefficient, combined with adaptive time-stepping for compressible Euler dynamics with generic equation of state. The model, due to special form of the relaxation coefficient devised here is shown to converge to the Euler limit with second-order accuracy in the absence of shocks under acoustic scaling. The solver is robust and able to properly capture compressible gas dynamics for both ideal and non-ideal equations of state, including the Bethe–Zel'dovich–Thompson regime. This is verified and demonstrated through a variety of configurations of increasing complexity.

We present a novel reduced-order data assimilation framework, termed Reduced-Order Dynamical Assimilation (RODAS), for reconstructing high-resolution, time-resolved flow fields from sparse velocity measurements. The method combines low-dimensional experimental observations with a physics-based parametric reduced-order model, enabling both spatial extrapolation beyond the measurement region and temporal super-resolution. The approach first identifies the dominant dynamics from sparse measurements through Dynamic Mode Decomposition (DMD), and subsequently reconstructs the corresponding full-order flow evolution by projecting the identified dynamics onto a parametric Proper Orthogonal Decomposition (POD) manifold generated from high-fidelity numerical simulations. Unlike conventional reduced-order data assimilation methods that estimate independent snapshots or treat time as an additional parameter, RODAS reconstructs an entire dynamical trajectory in a single inference step while naturally incorporating parametric variability. We assess the proposed methodology on vortex shedding behind a circular cylinder for both Newtonian and non-Newtonian (Carreau-Yasuda) fluids. Numerical experiments demonstrate accurate reconstruction of high-resolution velocity fields from localized, low-resolution measurements, achieving sub-percent reconstruction errors with sufficiently rich reduced bases, robust performance under severe temporal undersampling, and accurate prediction of engineering quantities of interest such as the drag coefficient. These results demonstrate that RODAS provides an efficient framework for real-time, physics-informed reconstruction of unsteady flows from sparse experimental data.

Surface active agents (surfactants) are common contaminants found on most air-liquid interfaces. Surfactants lower the surface tension, and hence surfactant concentration gradients generate surface tension gradients, which leads to flow. A canonical surfactant-induced flow is the outward spreading due to the localised deposition of surfactants onto an otherwise clean liquid interface. Eshima et al. (Phys. Rev. Lett., accepted, 2026) demonstrated experimentally and theoretically, through a late-time similarity solution, that surfactant solubility enhances surfactant-induced flows of air-liquid-air sheets and that soluble surfactant solutions can be mapped onto equivalent insoluble surfactant solutions. Here we extend the work theoretically and numerically, developing a systematic framework for the derivation and analysis of such solutions. The relevant nondimensional parameters are quantitatively defined, and the physically accessible parameter space is wide, which our theory and numerical simulations are able to span. We link the solutions for finitely soluble surfactants to the solutions for the limiting regimes of insoluble and infinitely soluble surfactants, where the latter link only holds transiently: the solution of the infinitely soluble limit appears as an intermediate solution that persists ever longer as solubility increases, before the ultimate late-time solution, which maps onto insoluble surfactants, is obtained.

Atmospheric surface layer flows are computationally challenging, predominantly due to surface roughness and the high Reynolds number, both of which demand exceptionally high spatial resolution in the near-surface region. We have developed a 2-D stochastic-based model for the generation and the streamwise concatenation of instantaneous, step-like velocity profiles featuring key elements of wall turbulent flows, i.e., uniform momentum zones (UMZ) and shear layers (Ehsani et al. 2024a,b), and vortices (Ehsani et al. 2026). The model is extended herein to the top of the logarithmic layer to reproduce the high-Reynolds-number, rough-wall, turbulent boundary layer measured by Saddoughi and Veeravalli(2000), without the support of a UMZ dataset, using only a handful of critical flow parameters: the Taylor microscale {\lambda}T, the boundary layer height {\delta}, the friction velocity u{\tau}, and the aerodynamic roughness length z0. The primary challenge lies in the integration of the stochastic model with the scaled distributions of the UMZ and vortex characteristics. The resulting statistical moments, energy spectra, and structure functions are compared against the experimental results. The validated code is made available in a GitHub repository.

A direct, analytical, non-iterative ghost-cell reconstruction framework is developed for Cartesian-grid embedded-boundary methods. Analytical expressions impose Dirichlet and Neumann boundary conditions directly at the embedded boundary, eliminating intermediate image-point reconstruction, matrix inversion, and precomputation or storage of geometry-dependent reconstruction weights. For the Cartesian stencil considered, dependencies among neighboring ghost cells form a directed acyclic graph. A topological ordering partitions ghost cells into dependency levels, permitting level-by-level reconstruction without iterative updates. The formulation is combined with hybrid ghost cells (HGC), whose centers may lie on either side of the embedded boundary. This placement satisfies the linear reconstruction-stability criterion previously derived for scalar advection while retaining a compact nearest-neighbour Cartesian stencil. An extended-stencil classical ghost-cell formulation (CGC_ES) serves as a stability-preserving reference, distinguishing the effects of reconstruction stability and stencil compactness. The same analytical relations provide solution values and spatial gradients directly on the embedded boundary, enabling evaluation of pressure forces, wall stresses, drag, and lift without separate surface reconstruction or filtering. Simulations of flow past a circular cylinder and an airfoil show that the linear criterion remains a useful indicator of reconstruction stability for the nonlinear incompressible Navier-Stokes cases considered. Classical ghost-cell reconstruction develops spurious oscillations when the criterion is violated, whereas CGC_ES and HGC remain stable. HGC additionally satisfies the stability requirement with a compact nearest-neighbour stencil.

In this study, we use a constrained Schrödinger–induction system to investigate kinetic-energy fluctuations induced by a fluid singularity. Assuming the cited Navier–Stokes construction with zero initial velocity and its exact exterior profile, we construct a periodic trajectory from a constant normalized wave function and zero connection. The prescribed body force admits a smooth space–time extension across the normalized singular time $t=1$. In this construction, the probability density remains constant and the mean matter kinetic energy stays bounded, whereas the gauge-invariant kinetic-energy variance diverges. We prove a lower growth bound of order $(1-t)^{-1/2-5h}$, with $h$ fixed by the source construction, by integrating the fourth power of the complete velocity's magnitude over an exact exterior region where all oscillatory corrections vanish. After fixing a gauge with constant wave function, we identify a unique weak $L^2$ connection limit outside $L^4$ and construct its positive self-adjoint kinetic operator through the associated magnetic form. We further show that the normalized endpoint state belongs to the form domain but not the operator domain: its first kinetic spectral moment is finite, whereas its second is infinite. These results connect fluid concentration to a loss of kinetic-domain regularity and provide a dynamical benchmark for assessing the limits of mean-energy control in hydrodynamic wave formulations.

This study investigates the nonlinear kinematics of a premixed slit flame using a two-dimensional $G$-equation level-set framework. Results show that combined forcing induces nonlinear saturation in the FDF, characterized by early gain flattening and premature phase drops, which intensify with the transverse forcing amplitude. Kinematic analysis reveals that this geometric nonlinearity manifests as a reduction in the time-averaged flame height, defined as the mean shift. In the quasi-steady limit, this mean shift is analytically quantified via a multivariate asymptotic expansion, where fourth-order terms successfully capture the saturation mechanism at elevated amplitudes. By introducing a scaling parameter to account for transverse dominance, the frequency-dependent decay of the mean shift in the compact limit collapses onto a single master curve, enabling the derivation of a unified theoretical model that integrates this asymptotic response with a second-order low-pass filter. Furthermore, because the mean shift reduces the physical extent of the flame, it alters the wrinkle propagation time. Correcting the Strouhal number using the measured mean shift collapses the dispersed nonlinear FDF curves onto the linear theory prediction. The analysis is further extended to disturbances convected at a finite speed, for which the linear transfer function is derived analytically and the correction with the measured mean shift continues to collapse the nonlinear FDF. These findings establish that the nonlinear FDF behavior under multidimensional forcing is fundamentally governed by the kinematic mean shift, providing a theoretical baseline for decoupling geometric nonlinearities from other thermo-diffusive or hydrodynamic instabilities in turbulent flames.

Externally generated wakes can impinge on porous layers in several practical heat transfer applications. However, the transport of these macroscale vortices and their resulting influence on heat transfer in the porous layer remain unknown. In this paper, two-dimensional pore-resolved simulations are used to examine a square-bluff-body wake impinging on a porous layer composed of an in-line array of heated square obstacles at Re = 500-4000, Pr = 0.7 and 7.0, and porosities $\phi$ = 0.75, 0.85, and 0.95. The incident macroscale vortices break down starting immediately at the porous-fluid interface. Following macroscale turbulent thermal transport in this entrance region, fluctuations farther downstream are aligned with the pore geometry and are generated at the microscale level by pore-throat shear, separation, and repeated obstacle wakes. Direct impact locally improves heat transfer at the porous-fluid interface by increasing the local Nusselt number relative to a non-impingement region. The interfacial heat-transfer enhancement varies with porosity, Reynolds number, and Prandtl number, with a peak enhancement of 18.2% observed for $\phi$ = 0.85, Pr = 7.0, and Re = 1000. The wake-associated macroscale turbulent heat-flux contribution decays within a consistence entrance region extending approximately 3-4 unit cells into the porous layer across all investigated porosities, Reynolds numbers, and Prandtl numbers. For Re$\ge$1000, the persistent wake momentum deficit subsequently causes the heat-transfer contrast to become negative, resulting in lower heat transfer in the impingement region than in the non-impingement region.

This study performs a scale analysis for the dynamics of equatorial flow systems like the Madden$-$Julian oscillation (MJO). This analysis makes three assumptions about the geometry of the flow and focuses on the leading order terms of the mass continuity and momentum equation system. First, the flow is meridionally narrow. Second, the zonal structure is planetary wavenumber 1. Last, the flow is vertically shallow. When constrained by these geometric assumptions, the system shows a time scale much longer than a day depending on the meridional narrowness. Specifically, for equatorial Kelvin waves, the oscillation period ranges from 36 to 64 days given a ratio of the planetary radius to the meridional width scale from 6 to 8 (i.e., an e-folding latitude from 9.59$^\circ$ to 7.18$^\circ$ either side of the equator). Given the long, narrow, and shallow geometry, the dynamics can sustain Kelvin waves only at low frequencies. This result suggests that the intraseasonal time scale of the MJO arises from the Kelvin wave frequency limit due to the planetary wave geometry. This planetary intraseasonal scale relation is independent from thermodynamics, and an open question remains on what physical processes coordinate the thermodynamics in the same length or time scale.

Dense granular flows are a common occurrence throughout nature and industry, but still exhibit phenomena that are not fully understood. One of these phenomena is the segregation of particles that constitute a dense granular flow, where particles separate due to differences in properties such as size and density. This work approaches segregation from a new perspective by developing a force model for a single particle based on the observation that there are two opposing drag forces acting on the particle. Validation of the model in mono-disperse flows reveals a family of velocity profiles, including a Bagnold profile. Further validation is done by comparing with known particle scaling laws in literature. The force model shows that the mechanism of segregation is always present in dense granular flows and that mono-disperse flows are a unique case where it is not distinctly visible. The insights in this paper prove a fundamental new way of thinking about dense granular flows and its individual particles, opening the field for new research directions.

We investigate turbulent boundary layers at Mach 2.5 over sinusoidal roughness at matched $Re_\tau=784$. We considered three wall temperatures, $T_w/T_r=$ 1.0, 0.7, and 0.4. Each wall temperature was repeated with a smooth and rough surface, the latter following a three-dimensional sinusoidal profile with effective slope 0.5 and matched $k^+=79.1$. In total six direct numerical simulations were completed. Analysis of mean wall shear and heat transfer detailed the augmentation in skin friction and heat transfer coefficient between smooth and rough cases; resulting in the classical failure of the Reynolds analogy for rough walls. We also show that differences in shear stress across wall temperatures are driven by the viscous component even though the pressure component dominates. The roughness sublayer was found to be $R_{RSL}=3k-6k$, consistent with the literature. Moreover, the wall offset $d=d_\Theta\approx0.5k$ for both momentum and thermal boundary layers, signifying the offset represents the half peak-to-valley height rather than the "mean roughness height." For the mean momentum boundary layer, we find the present conditions recover the incompressible roughness function $\Delta u_1^+$ when matched via the semi-local roughness Reynolds number $k^*$. For this reason, an equivalent sand-grain roughness of $k_s^*\approx3.7k^*$ is proposed. The existing compressible transformations hold regardless of wall temperature or roughness - contradicting recent claims otherwise. The generalized Reynolds analogy works for smooth walls but fails for rough walls; a roughness correction term is proposed and validated. Compressible mean temperature transformations fail for cold walls, especially when $(T_w-T_e)/(T_r-T_e)<0$. The thermal roughness function, $\Delta\Theta^+$, is reported with caution given transformation singularities.