Papers

The propagation of narrowband wave packets is a classical problem with broad relevance across nonlinear wave physics. Within the framework of the nonlinear Schrödinger equation, solitons are known to propagate without changing shape, whereas Gaussian envelopes may undergo substantial reshaping depending on the balance between dispersion and nonlinearity. Here, we combine laboratory experiments with numerical simulations to systematically investigate the evolution of hydrodynamic Gaussian wave packets over a wide range of amplitudes and spectral bandwidths. We show that when the envelope amplitude and width match those of the stationary NLSE soliton solution, the wave packet propagates steadily in the wave flume. More generally, by varying the amplitude of the Gaussian envelope, the wave packet may undergo either dispersive broadening or nonlinear focusing, resembling the dynamics of Satsuma-Yajima breathers. These findings may facilitate the controlled generation and manipulation of localized wave packets in a variety of nonlinear dispersive systems, including optics, plasmas, and Bose-Einstein condensates.

Marine lakes offer a unique opportunity to study how physical processes, such as turbulent mixing, biomixing, and tidal exchanges, regulate the vertical transport of heat, oxygen, and nutrients in relatively isolated ecosystems. The effective diffusion coefficient characterizes the overall mixing and is critical in models of marine lakes, but it is difficult to measure directly. This paper addresses the problem of inferring the depth-dependent diffusion coefficient from synthetic and real measurements of vertical temperature and salinity profiles. To do so, an inverse problem governed by a marine lake model described by the screened-Poisson equation (similar to Helmholtz) is formulated. The inverse problem is formulated as a nonlinear least-squares optimization problem, where the cost functional quantifies the misfit between the observed and recovered profiles. A Tikhonov regularization term is added to improve the conditioning of the discretized problem, with a regularization parameter chosen using the L-curve method. We solve this problem using an adjoint-based inexact Gauss-Newton method. To leverage the complementary information in these profiles, the formulation optimizes the fit across both datasets simultaneously. The accuracy of the reconstructed diffusion coefficient and the method's robustness to noise are investigated through comprehensive synthetic studies. Additionally, we contrast this framework with physics-informed neural networks, highlighting the advantages and limitations of each. When applied to real marine lake data, the adjoint method reconstructed a smaller diffusion coefficient in regions of strong density stratification, in line with physical expectations. The results indicate that the proposed approach provides a foundation for accurate modeling of marine lake dynamics.

We formalize the gauge structure of the Navier–Stokes equation for incompressible fluids, interpreting $\nabla\cdot\mathbf{v}=0$ as a gauge fixing analogous to the Coulomb gauge in electromagnetism. We construct the Martin–Siggia–Rose action and its full BRST symmetry, introducing BRST doublets for the Gribov parameter $\gamma$ and the monodromy phase $\theta$. Through a Higgs mechanism, $\gamma$ acquires a vacuum expectation value $\gamma_{0}$, generating a mass scale for the vorticity and the ghosts; we compute the one-loop effective potential and analyze vacuum stability. Intermittency — measured by the exponents $\zeta_{n}$ — is described by fluctuations of the Higgs field $\sigma$ around the condensate, via a Gribov-inspired log-Poisson hierarchy that satisfies exactly $\zeta_{3}=1$ (Kolmogorov's four-fifths law). Fits to DNS data favor filamentary vorticity structures, with $D_{f}\approx1$ (one parameter) or $D_{f}\approx2.1$, $\Delta\approx0.44$ (two parameters). The one-loop anomalous dimension in $d=3$, $\Delta_{\sigma}\approx0.50$, supports the identification $D_{f}=2\Delta_{\sigma}$. The formalism unifies classical hydrodynamics with gauge theory and spontaneous symmetry breaking, opening the study of turbulence and intermittency to quantum field theory methods.

Physics-informed neural networks (PINNs) provide a mesh-free framework for solving governing equations, but their application to granular avalanche dynamics over curved terrain remains largely unexplored. This study extends a depth-averaged PINN formulation based on the Savage-Hutter equations to an exponentially curved chute with spatially varying inclination and a strain-rate-dependent Mohr-Coulomb earth-pressure closure. The model is validated against measured front- and rear-edge trajectories from a laboratory granular-avalanche experiment, with selected observations withheld from training. A staged temporal curriculum proved essential for accurate prediction, reducing the held-out trajectory error by approximately two orders of magnitude compared with training over the full time domain from the outset. Sparse-data experiments further showed that observation placement was more influential than observation number within the configurations tested. Four observations bracketing the transition from acceleration to deceleration achieved nearly the same accuracy as the eight-observation reference configuration, whereas observations clustered at early or late times performed poorly. The results demonstrate the importance of both training strategy and informative data placement when applying PINNs to granular flows over curved topography.

Ultrasound is increasingly used to control biological cells, but its multiple physical effects, including radiation force, streaming, heating, and cavitation, require theoretical frameworks that can quantify their relative strengths. Here we develop a semi-analytical model to predict flow patterns and energy distributions of ultrasound-induced intracellular streaming. Cells are modeled as viscoelastic droplets immersed in a fluid with different viscoelastic properties. For this geometry, the momentum equation with an Oldroyd-B constitutive law is solved using a perturbation expansion commonly applied in acoustofluidics. The resulting equations for the different orders of the expansion are solved using partial wave expansion and explicit integration. We investigate our model for a range of parameters which is relevant both for synthetic polymer and for protein solutions. We find a series of flow reversals that we can connect to the distribution of energy into the different modes. We also consider density and compressibility contrasts, which shift these transitions and introduce new ones. Finally, we discuss the potential biological relevance of our mathematical results for cellular sensing and signaling.

A long-standing route to efficient surface-drag prediction in zero-pressure-gradient compressible turbulent boundary layers is to map the skin-friction coefficient $C_f$ and momentum-thickness Reynolds number $Re_\theta$ onto their `incompressible' counterparts. Reassessment against an extensive DNS database shows that existing formulations do not consistently recover the reference incompressible skin-friction behaviour, even when transformed data exhibit improved collapse. We define the mapped `incompressible' state as a constant-property counterpart of the physical compressible boundary layer and derive the transformation factors from prescribed mean-velocity and wall-normal-coordinate mappings. This definition-first approach links skin-friction scaling to the full-layer accuracy of the underlying velocity transformation and exposes inherited outer-layer errors. Van Driest's theory is recast in a finite-Re exact-integral form, with the classical vD I and II transformations recovered as leading-order asymptotic reductions. Their limitations at finite Reynolds numbers are quantified, and the historical success of vD II is traced to a fortuitous cancellation of truncation errors. The exact-integral formulation then yields modified transformations assessed through a priori scaling and standalone a posteriori prediction of $C_f$ from prescribed macroscopic and wall-thermal inputs. The VIPL-based modified transformation gives the best overall performance. Across $0.30 \leq M_\infty \leq 13.64$ and $-0.55 \leq \varTheta \leq 2.85$, its prediction errors remain below $11\%$, with a mean error of $3.07\%$. Overall, the analysis places skin-friction transformations on a mapping-based exact-integral footing, relating them directly to prescribed mean-flow mappings while avoiding the leading-order asymptotic truncations that limit classical van Driest theory at finite Reynolds numbers.

We use 3D direct numerical simulations to study the effects of vortex promoters in liquid metal duct flow to sustain Q2D states which are formed in the presence of strong magnetic fields, such as those present in cooling blankets of fusion reactors. Both for electrically insulating and conducting walls. In case of insulating walls, disturbances are found to be sustained. For conducting walls, the disturbances may be extinguished immediately and replaced by a Walker- or Hunt-type flow with its own jet-detachment instability. Furthermore, we add heat transfer by imposing constant heat flux at the Shercliff walls. We classify and compare possible configurations with respect to their turbulent transport properties. For conducting ducts, no additional effect is observed. For insulating ducts in horizontal position, we observe a small effect. For vertical ducts, the buoyancy forces have a significant impact due to buoyancy-driven instabilities, which produce intermittent fluctuations. The analysis of the turbulent kinetic energy (TKE) and the Nusselt number show that flows with the largest TKE may not have the best heat transfer performance. This is caused by side jets removing heat faster than mixing the bulk flow. The buoyancy force and wall conductance ratio are found to play a key role in determining the flow structure. Part of our work is a parametric study at fixed Reynolds, Hartmann and Prandtl numbers, which allows us eventually to compose a phase diagram showcasing the different flow regimes.

The initiation and propagation mechanisms of kerosene-fueled oblique detonation waves are key issues in the development of oblique detonation wave engines. In this study, numerical simulations of kerosene-fueled oblique detonation at a flight Mach number of 10 were conducted using the two-dimensional conservative Euler equations and a second-order two-step global chemical reaction model. The objective was to compare wedge-induced initiation with bump-forced initiation. The results show that, at different flight altitudes, the oblique detonation flow field follows the h̊o}L binary scaling law. Wedge-induced initiation requires highly precise matching of parameters such as the inlet-exit conditions, wedge angle and length, and equivalence ratio. In contrast, bump-forced initiation exploits the high total temperature and total pressure at the stagnation point and therefore does not require precise matching of these parameters. Therefore, the bump-forced initiation method provides reliable oblique detonation initiation and a stable oblique detonation flow field.

This work employs a new form of fixed structured uncertainty within the structured small-gain theorem approach proposed by Frank-Shapir & Gluzman (J. Fluid Mech., vol. 1030, 2026, pp A8) for the stability analysis of incompressible shear flows subject to finite-magnitude disturbances. Within this framework, the nonlinear advection term in the Navier-Stokes equations is replaced by a structured feedback uncertainty interconnection with the linearized dynamics to account for the impact of nonlinear feedback. Herein, a new uncertainty representation is derived via linear transformations of the input and output channels, transforming the feedback loop such that the resulting structured uncertainty has a repeated-diagonal structure. This structure aims to preserve the component-wise pathways of the nonlinear advection term while keeping the structured singular value computation tractable. We apply the method to two canonical base flows: Couette and plane Poiseuille flows. The resulting thresholds on disturbance magnitude to preserve stability are less conservative and more accurate. We compare the novel methodology presented here with previously proposed repeated and non-repeated block approximations of the uncertainty structure, where our stability threshold provided the closest agreement with previous numerical and experimental studies. We show that repeated and non-repeated block structures that were proposed in past studies result in an artificial energy-production term arising from using constant structured uncertainty in the structured input-output formulation, violating the divergencefree assumption. This energy-production term is smallest when using the methodology presented in this work, providing a more faithful representation of the impact of nonlinear feedback interconnection with the linearized dynamics of the Navier-Stokes system.

Immersed-boundary lattice Boltzmann (IB-LBM) simulations of cylinder and particle flows are usually compared by ranking boundary-enforcement schemes, kernels, and collision models. Such comparisons can obscure the mechanism that controls each response. Here, canonical fixed-cylinder, oscillating-cylinder, and sedimenting-particle cases are used as controlled probes of Eulerian-Lagrangian interface momentum transfer. For prescribed bodies, differences among direct forcing (DF), multi-direct forcing (MDF), and distribution-function correction (DFC) are most clearly discriminated by local no-slip fidelity rather than by a universal drag ranking. For DFC, the kernel-dependent drag-coefficient ranking reversal between the hat and Peskin 4-point kernels is associated with the spatial redistribution of the marker-resolved correction and the resulting near-boundary slip and pressure deviation, rather than the total correction magnitude alone. For sedimenting particles, single-particle settling provides a moving-body baseline, whereas two-particle differential-density wake-interaction sedimentation shows the wake-exposed light particle to be comparatively more sensitive to the explicit internal-mass correction in the force evaluation, a configuration-dependent, finite-window moving-boundary closure response. Targeted two-relaxation-time (TRT) and central-moment multiple-relaxation-time (CM-MRT) collision controls remain secondary to the boundary and closure mechanisms within the tested regimes (prescribed-body comparisons at Re <= 200, two-dimensional, and the reported moving-particle cases). The resulting picture replaces a universal scheme ranking with a mechanism-resolved interpretation of IB-LBM interface momentum transfer.

We perform DNS of ventilated cavitation over a sphere at subcritical (Re=10,000). The flow is modeled as a homogeneous mixture of water and air, with the interface tracked using the volume-of-fluid method. Unlike previous numerical investigations, surface tension is explicitly included. Air is injected through a circular strip on the sphere at three locations selected based on the bulk flow dynamics: front (FR025, (18^\circ\leq\theta\leq63^\circ)), mid (MD025, MD050, (75^\circ\leq\theta\leq104^\circ)), and back (BK025, (120^\circ\leq\theta\leq180^\circ)), with (C_q=0.2) and (0.4). The injection location strongly governs cavity inception and stability and alters flow separation in the front- and mid-injection cases. Front injection produces an unsteady bubbly cavity due to vigorous puffing, which fragments the injected air and increases drag by (\sim56%) relative to the single-phase case. In contrast, mid- and back-injection produce stable cavities with distinct leading-edge dynamics. In the mid-injection cases, puffing dominates and, despite delayed flow separation, the cavity detaches from the leading edge of the injection patch. For back injection, the cavity detaches upstream of the injection patch owing to the adverse pressure gradient induced by cavity formation. Kelvin–Helmholtz instabilities and divot formation characterize the back-injection cavity. Stable cavities exhibit strong air entrainment and close through a re-entrant jet. The mid-injection cases achieve (35%) and (25%) drag reduction at (C_q=0.2) and (0.4), respectively, while back injection yields a maximum drag reduction of (46%) relative to the single-phase case.

Heat transfer in a dense gas between two parallel plates is studied for assessing the quantitative difference of two variants of the Enskog equation, i.e., the original Enskog equation and the Enskog equation with a modified Enskog factor recently proposed in Phys. Rev. E 111, 065108 (2025). The main advantage of the latter is that the H theorem, which the former lacks, has been established. The influence of the modification is assessed by comparing the macroscopic quantities in detail. It is found that the impact of this modification is quite limited and the two variants reasonably agree as a whole.

The minimalist approach for linear stability analysis is applied to fluids and magnetized ideal plasmas in cylindrical geometry. In this approach, the dispersion relation is obtained by integrating a single first-order differential equation - referred to as the principal equation - subject to appropriate boundary conditions. We first derive the principal equation for a general unperturbed state with radially varying density and pressure, axial and azimuthal components of both the velocity and magnetic field, and a radially directed gravitational field. We then use this formulation to analyze rotating flows with axial magnetic fields, addressing both wall-bounded and interface-driven axisymmetric instabilities. In addition to exact results for selected unperturbed states, we obtain approximate dispersion relations using the WKBJ method in the incompressible and compressible limits. The analysis encompasses centrifugal, magnetorotational, and buoyancy-driven instabilities as special cases, and it clarifies how compressibility modifies their stability properties.

Accurate prediction of the macroscopic width of Rayleigh–Taylor (RT) and Richtmyer–Meshkov (RM) turbulent mixing layers is central to inertial confinement fusion and supernova dynamics. However, bubble–spike asymmetry, density-ratio dependence and unsteady forcing pose a persistent closure challenge: existing low-order buoyancy–drag models struggle to describe different mixing problems accurately with one model and coefficient set. We combine local front dynamics with global mass conservation in separate buoyancy–drag equations for the bubble and spike fronts. Rather than imposing shared or fixed empirical coefficients, the model retains separate inertia, buoyancy and drag coefficients on the two sides and allows them to vary independently with density ratio. Given the bubble-side state scalings, RT/RM similarity relations, a mean-composition profile and endpoint asymptotics jointly constrain all six effective coefficients without case-by-case fitting. A profile-shape parameter $c$ labels distinct internal composition states and is selected a priori from RT spike scaling measured in linear-electric-motor experiments. The model then cross-predicts the RM spike exponent without recalibration to RM spike data and, by construction, recovers low-Atwood-number bubble–spike symmetry and the high-density-ratio free-fall RT-spike and ballistic RM-spike limits. Tests against constant- and variable-acceleration RT mixing, post-impulse RM evolution and Nova laser deceleration show that one closure describes mixing-width evolution across density ratios and acceleration histories without case-specific retuning, while reducing excessive spike growth at high density ratio. This physically interpretable, asymptotically consistent framework enables cross-problem prediction of wide-density-ratio RT and post-impulse RM mixing.

This study investigates the Reynolds-number (Re_\tau) evolution of wall-pressure statistics beneath zero-pressure-gradient TBLs, and links their logarithmic variation to the increasingly energetic large-scale motions in the logarithmic region. The wall-pressure skewness is found to become more negative with increasing Re_\tau, owing to increasing contributions from large-scale wall-pressure fluctuations (that are negatively skewed) and their nonlinear interaction with the statistically invariant inner-scale fluctuations (that are positively skewed). The analysis draws on new, well-resolved simultaneous measurements of wall pressure and streamwise velocity spanning 5000 < Re_\tau < 11300 in the Melbourne tunnel, atmospheric surface-layer measurements at Re_\tau = O(10^6) and a published simulation dataset at Re_\tau = O(10^3). Particular attention is paid to the principal experimental limitations affecting wall-pressure statistics: spatial resolution, Helmholtz resonance, facility noise and statistical convergence. Helmholtz resonance is shown to contaminate inner-scale wall-pressure contributions even after conventional corrections, and reliable estimation of skewness is found to require acquisition durations of O(10^5) eddy-turnover times or longer. The inner-scaled wall pressure spectrum is Reynolds-number invariant over the small-scale regime, in contrast to turbulent channel and pipe flows, whereas at intermediate and large scales it grows substantially with Re_\tau, consistent with these internal flows. Linear and quadratic velocity–wall-pressure coherence link these intermediate- and large-scale contributions to two dynamically distinct coherent structures: the self-similar attached-eddy hierarchy and turbulent superstructures, respectively. These analyses establish the connection between the inertial region and the log variation of wall-pressure variance and skewness with Re_\tau

High-order CFD simulations provide detailed resolution of the heterogeneous interstitial flow in pebble-bed reactors, but their computational cost is high, especially during the initial flow-development period required to reach statistically stationary conditions. This work investigates the use of a Super-Resolution Graph Neural Network (SR-GNN) to improve the initialization of high-order NekRS simulations. Lower-order P = 2 velocity fields are used as inputs to reconstruct higher-order representations, which are then used as initial conditions for P = 7 restart simulations. The approach is evaluated using a 146-pebble bed at Re = 1000, Re = 2500, and Re = 5000, with pressure-drop convergence used as the main figure of merit. The SR-GNN models were trained using paired low- and high-order snapshots and were first evaluated through qualitative inference comparisons. High-order restart simulations showed that, for Re = 1000 and Re = 2500, the SR-GNN initialized cases produced pressure-drop histories similar to direct restarts from true P = 2 fields. For Re = 5000, however, the super-resolved field restart approached the statistically stationary P = 7 pressure-drop range faster than both the direct P = 2 restart and the reference P = 7 simulation initialized from a uniform velocity field. The trained Re = 5000 model was also applied to a larger 1568-pebble bed, demonstrating qualitative applicability of the workflow to a significantly larger packed-bed geometry. These results indicate that SR-GNN-based initialization is a promising strategy for reducing high-order flow-development cost, while also motivating further work on broader Reynolds-number and geometry generalization.

The physical mechanisms controlling the onset of gravity-driven spreading of elastoviscoplastic drops remain unclear because yielding, elastic deformation, and viscous dissipation can occur simultaneously in different regions of the material. To isolate these mechanisms, we perform direct numerical simulations of large axisymmetric drops resting on a thin precursor layer of the same material. Each drop is first equilibrated under gravity, $g$, before being subjected to an additional constant downward acceleration of varying magnitude. The drop rheology is described by the Saramito–Herschel–Bulkley model. Once the rate of deformation becomes negligible under the enhanced forcing, the additional acceleration is removed and the drop is allowed to relax again under gravity alone, enabling the global deformation to be separated into recoverable and unrecoverable components. We find that spreading does not occur simply because some portion of the material yields locally. At low imposed accelerations, yielded regions remain confined within a predominantly solid-like viscoelastic matrix, and the resulting deformation is mostly recoverable. Appreciable spreading is observed when these yielded regions connect to form a continuous fluidised pathway from the drop interior to the free surface, allowing radial material transport. The acceleration required for this transition is governed primarily by the yield stress, whereas elasticity controls the partition between recoverable deformation and spreading by regulating the extent and spatial distribution of yielded regions.

Fluid–structure interaction (FSI) experiments are typically built around mechanical dynamics and constraints imposed by the physical apparatus, so changing mass, stiffness, damping, or allowable motion often requires hardware reconfiguration. Here we present a reconfigurable cyber-physical framework in which these properties are instead assigned through software-defined dynamics. The system provides three translational and one rotational degree of freedom, each independently configurable as prescribed, load-responsive, or locked, with operating roles that can also be reassigned during a running experiment. Measured forces and torques are incorporated into real-time virtual dynamic models, while a common supervisory architecture coordinates multi-axis motion, mode switching, synchronized data acquisition, and diagnostic positioning. The prescribed-motion pathway is validated using a pitching hydrofoil by comparison with published thrust and power scaling trends, while the load-responsive pathway is evaluated using an active-heave/passive-pitch benchmark that reproduces the expected frequency-dependent resonant response over the tested conditions. The same platform is then reconfigured for intra-cycle active–passive pitching, coordinated vertical-axis turbine-surrogate motion, force-driven passive surge, and automated multilayer stereoscopic particle image velocimetry. These results demonstrate that distinct FSI boundary conditions and measurement requirements can be implemented within a common motion, sensing, and control architecture. By treating mechanical roles and constraints as software-defined experimental variables, the framework provides a reusable basis for reconfigurable FSI experiments without redesigning the underlying platform for each application.

Odd viscosity is a nondissipative component of the viscosity tensor that arises in fluids with broken time-reversal symmetry. Despite conserving energy, we show that odd viscosity can qualitatively alter hydrodynamic stability by generating exponentially growing modes that are absent in conventional fluids. For plane Poiseuille flow, we derive the odd-viscous generalization of the Orr–Sommerfeld–Squire equations and find a new instability that first emerges for spanwise perturbations and extends to oblique modes through the amplification of odd-viscous forces in critical layers. The instability originates from the non-normal dynamics of shear flows: conventional fluids support transiently growing disturbances through the lift-up mechanism, while odd viscosity provides a feedback between wall-normal velocity and vorticity that converts this transient growth into a self-sustaining exponentially growing mode. More generally, we show that an energy-conserving perturbation can destabilize a non-normal dynamical system only when the unperturbed system supports transient growth. Our results establish a direct connection between transient growth, non-normality, and instability induced by nondissipative forces, with implications extending beyond odd-viscous hydrodynamics.

We study the inverse energy cascade of two-dimensional turbulence by means of high-resolution numerical simulations forced at intermediate wavenumbers. To clarify the role of vortices generated near the forcing scale, we decompose the vorticity and velocity fields into vortex and background components. Although the vortex component carries only a small fraction of the total energy, it has a clear effect on the energy spectrum and produces deviations from dimensional Kolmogorov scaling, which is realized by the background flow. We derive a generalized von Karman–Howarth balance for the decomposed fields and obtain a relation involving the third-order correlation between vortex and background velocity increments. The simulations support this prediction, which we interpret as a constant inertial-range flux associated with vortex-background correlations.

Experiments on a flexible plate horizontally submerged in a wave tank are reported in this paper. The plate is held at a fixed depth at its upstream end, while its downstream end is free to move. The wave field is measured using a synthetic Schlieren technique, giving access to an estimate of the fractions of the incoming wave energy that are transmitted and reflected after encountering the region where the plate is submerged. Part of the incoming wave energy is shown to be dissipated by the plate. Flow field measurements in a vertical plane parallel to the wave propagation are performed to examine the wave-plate interaction. A jet-like flow is produced at the free end of the plate, with strong vortex activity similar to that produced by a flapping fin. The kinetic energy present in this jet-like flow is computed from the velocity field measurements, and the external dissipation produced by jet creation is estimated. Results highlight the efficiency of flexible plates in reflecting and attenuating waves. This study also showcases a change in jet direction, in particular the observation of a jet going upward toward the free surface for certain frequencies. Such a configuration, could be of great interest for wave energy conversion applications, while preventing harmful phenomena such as seabed erosion.

Numerical simulation of dynamic wetting processes remains challenging due to the multiscale feature of the moving contact line. This paper presents a finite element method for two- or three-dimensional dynamic wetting problems within the framework of the lubrication equation and the precursor film model. By reconstructing the disjoining pressure formulation, a mesoscopic precursor film model is implemented to enable a relatively thick precursor film to reproduce the intermediate-region interfacial behavior of a physically thin precursor film. The proposed model reduces the requirement for excessive spatial resolution near the contact line, thereby significantly reducing the computational cost while preserving the macroscopic flow dynamics. This method does not incorporate any moving boundary and easily handles topological changes. Its capability and accuracy are validated through various simulations, including the spreading, retraction, sliding, and coalescence of drops, as well as the breakup of liquid ridges. Numerical results (with the mesoscopic precursor film model adopted) show good agreement with the available exact solutions and asymptotic theories.

Carbon capture, utilization and storage (CCUS) is a key approach for reducing anthropogenic CO2 emissions. Currently the vast majority of CO2 stored is injected into depleted hydrocarbon reservoirs. Reactive transport in hydrocarbon-bearing carbonate reservoirs is controlled not only by the balance between reactant delivery and surface reaction, but also by the heterogeneous pore-scale flow field created by pore structure and fluid distribution. Here, we used time-resolved micro-CT imaging, pore-network analysis, and direct numerical simulation to investigate channelized dissolution during injection of CO2-saturated brine into oil-bearing Ketton limestone at 0.5 mL/min. The system remained in a high Pe, low Da regime throughout the 180 min injection. Despite the advection-dominated flow regime, dissolution became strongly localized. Preferential flow pathways were already present originally because the heterogeneous pore structure and remaining-oil occupancy restricted brine flow to a subset of the connected pore space. Dissolution progressively amplified these pathways. The associated reduction in hydraulic resistance further focused flow, producing a continuous tortuous channel by 180 min. Meanwhile, the effective reaction rate was only 1.6*10^5 mol/m2s,, approximately one order of magnitude lower than the batch reaction rate, showing that rapid advective transport did not translate directly into rapid overall dissolution under multiphase conditions. These results demonstrate that channel formation arose from the coupling between strong reactant delivery and pore-scale flow-field heterogeneity, rather than from the bulk Pe Da regime alone. Accounting for flow-field heterogeneity is therefore important for predicting reactive transport and pore-structure evolution during CO2 injection into hydrocarbon-bearing carbonate reservoirs.

A fundamental question in the statistical theory of homogeneous isotropic turbulence is whether the longitudinal velocity autocorrelation $f(r)$ remains non-negative and if it can be shown from first principles such as kinematic realizability. While incompressibility forces the transverse correlation $g(r)$ to exhibit a negative loop ($\int_0^\infty r g(r)\,dr = 0$), the sign behavior of $f(r)$ is subtle. We show that positive-definiteness via Bochner's and Schoenberg's theorems structurally fails to enforce pointwise positivity because the 3D spherical projection kernels are sign-changing. By mapping the problem to the one-dimensional spectrum $E_{11}(k_1)$ via the cosine transform and applying Pólya's criterion, convexity of $E_{11}(k_1)$ provides a rigorous sufficient condition for $f(r) \ge 0$. While pure Kolmogorov $-5/3$ scaling is strictly convex, physically realizable spectra with Batchelor ($k^4$) or Saffman ($k^2$) infrared scaling are necessarily concave near $k_1 = 0$. For mature broadband spectra such as the von Kármán–Pao model, high-precision quadrature confirms that the convex inertial bulk dominates, yielding strictly positive tails and demonstrating that apparent negative dips are discrete Fourier artifacts. Also, we construct a smooth, divergence-free, finite-energy narrowband initial field that produces a genuine negative loop ($\min_r f(r) \approx -0.083$), serving as a counterexample to universal non-negativity. Spectral bandwidth is shown as the governing physical parameter, with nonlinear triad interactions rapidly broadening narrowband fields over an eddy turnover time, systematically suppressing negative excursions and preserving $f(r) \ge 0$ in mature turbulence.

We assess computed lift coefficient data for flow past a circular cylinder to evaluate their suitability for practical applications. Specifically, we consider lift coefficient data for a circular cylinder over Reynolds numbers from 120 to 8000. The results are obtained from two-dimensional finite element simulations of the incompressible Navier-Stokes equations using pressure robust discretizations. We compare the computed lift coefficients with published experimental and numerical results, finding good agreement in some cases but significant disagreement in others. Because lift fluctuations are central to vortex-induced vibration concepts, these data therefore provide input for the analysis and preliminary design of bladeless turbines.

We present theoretical results related to the experimental findings of Matsubara and Alfredsson (2001) on the scaling of the energy spectra of the Klebanoff modes, i.e. streamwise-elongated vortical disturbances generated by free-stream turbulence in a flat-plate transitional boundary layer. The scaling is explained by a model that describes the streamwise evolution of the streamwise and spanwise energy spectra. The theoretical framework is based on the quasi-steady asymptotic solution of the boundary-region equations, on an axial-symmetric model of the free-stream spectrum, and on the spectral response of the boundary layer to the external perturbations.

Standard rheological measurements yield only selected stress components; thus, inferring tensorial constitutive equations from experimentally accessible observables is complicated. We propose a constitutive formulation written in terms of a deviatoric stress tensor, whose trace is zero, rather than the extra stress tensor. From rheometric data including shear stress, first and second normal stress differences under shear, and elongational stress under uniaxial elongation, we can construct a deviatoric stress state without the indeterminate isotropic stress. The deviatoric-stress dynamics is represented by a closure inferred through symbolic regression, constrained to satisfy material objectivity and a given linear Maxwell response. To demonstrate the proposed formulation, two closures inferred from stress responses of the Giesekus and Larson models successfully captured untrained transient-flow responses under planar elongation and mixed shear/uniaxial elongations at deformation rates around an inverse relaxation time. Steady rheological functions of the closures agreed with the original models in the linear-response regime and over a deformation-rate range connected to the training data, whereas deviations and divergent responses appeared at larger deformation rates outside the training regime. These results demonstrate that the proposed deviatoric-stress formulation provides a practical route for constitutive modeling of observable linear and nonlinear viscoelastic dynamics, while clarifying its range of validity under strong deformation.

We present a spectral element lattice Boltzmann method (LBM) for partial wetting on curved geometries. A non-ideal gas phase-field model is incorporated into the LBM framework to enable phase separation with a constant interface thickness and the potential form of surface tension force is used. We adopt the force-splitting approach, yielding significantly improved stability and accuracy. Complex boundaries are naturally handled using a flux bounce-back scheme, which resolves inconsistencies in normal vectors across adjacent elements. Additionally, a general wetting boundary condition is implemented to capture static contact line in a thermodynamically consistent manner. The method is validated through simulations of droplets on flat surfaces, 2/3-dimensional curved surfaces, and equilibrium droplets without boundaries. Results demonstrate that parasitic currents are significantly reduced on unstructured meshes with complex geometries, reaching residual kinetic energy levels on the order of $10^{-24}$ for wetting configurations and $10^{-30}$ for isolated droplets.

It is traditionally believed that the no-slip boundary condition is necessary for vorticity generation, as might be implied by the Lighthill vorticity generation mechanism. However, the investigations of Morton (1984) and Terrington et al. (2020) assert that the vorticity-generation mechanism is independent of the no-slip boundary condition. To investigate this hypothesis, we simulate viscous flow over a circular cylinder in the laminar periodic von Kármán vortex-shedding regime at Re = 170, without enforcing the no-slip condition at the wall. Instead, we close the wall tangential velocity and its normal derivative using one-sided finite-difference approximations. Accordingly, the wall tangential velocity is dynamically determined from the evolving interior solution rather than prescribed. The resulting flows exhibit qualitatively similar patterns of periodic vortex shedding across all three wall treatments (no-slip, second- and third-order one-sided approximations), although the mean drag coefficient, r.m.s. lift coefficient, and Strouhal number differ from those of the standard no-slip simulation. More significantly, the velocity distributions just outside the boundary layer closely match those of the standard no-slip simulation, regardless of the approximation order. In particular, the circulation evaluated along a contour at the edge of the boundary layer, which corresponds to the total vorticity contained within the layer in the no-slip case, is found to be remarkably insensitive to the wall treatment. These results suggest that the no-slip condition is not necessary for vorticity generation or periodic shedding. However, it may still be required for accurate quantitative prediction of the integral flow quantities and shedding dynamics.

The classical problem of a rigid body in an ideal fluid is a six-dimensional dynamical system with three conserved quantities. Despite its long history and its importance as a reduced model of many fluid-structure problems, basic questions remain, including the shapes and connectivities of the three-dimensional submanifolds of solutions, and the nature of chaotic motions on these. We explore the problem with a particular ellipsoidal body, beginning with integrable motions— steady linear translation and rotation and periodic planar tumbling and fluttering. The stability of these states depends on the relative magnitudes of linear and angular momentum or energy. Linear stability, including Floquet, analysis of lower-dimensional perturbed systems is consistent with direct integration of the full system. We document instabilities leading to a variety of regular and chaotic motions, including flipping and twirling, whose trajectories appear to follow paths near connections between the integrable states. Such indirect observation of these connections provides insight into the structure underlying the rich dynamics of this simple system. For the submanifold where linear and angular momentum are perpendicular, we further examine how solutions fit together to fill momentum space in different zones of stability of the integrable states, and thereby uncover additional bifurcations in connectivity and what appear to be new integrable solutions.