Interactions and reconnections of vortices are fundamental in many areas of physics, including classical and quantum fluids where they are central to understanding phenomena such as turbulence. In three-dimensional (3D) superfluids, quantum vortices are one-dimensional filaments that can intersect, reconnect, and recoil with irreversible dynamics described by near-universal scaling laws. We explore quantum-vortex reconnections in a four-dimensional superfluid, where a vortex is a two-dimensional surface. Using real-time numerical simulations, we find much richer behavior than in 3D, including stable intersecting vortex surfaces which do not reconnect, and unusual vortex reconnections which occur without significant energy dissipation, which may indicate quasireversible dynamics. Our work raises many interesting questions about vortex physics in extradimensional systems and may be further extended to look at vortex dynamics and turbulence in higher-dimensional spaces.

Bio-inspired $\vee$ flight formation is a well-known technique for energy saving among groups of fixed-wing aircraft, and as of recently, for groups of quad-rotors. Here we study the effect of the formation angle on the performance of each of the members of a five-member $\vee$ formation in terms of the flow field, and drag force. We employ axisymmetric cylinders, which are nonlifting in solo condition to reduce or eliminate the effect of the lift (lateral force) on the group performance, and use time-resolved, multi-illumination, consecutive-overlapping particle image velocimetry (PIV) to capture the velocity field around and between the members. Over a range of $\vee$-formation angles, we see various degree of drag reduction, with the highest drag reduction $(\sim 80\%)$ for the interior members of the tightest formation (formation with the smallest $\vee$ angle and the most overlap in frontal views). All formation members experience some levels of drag reduction up to a $\vee$ angle of around ${50}^{\circ }$, and in a formation with a $\vee$ angle greater than ${50}^{\circ }$, only the leading member experiences observable drag reduction. We explore the complex flow dynamics between the formation members in terms of wake-body and wake-wake interactions and the bleeding (gap) flow. We present the mean and fluctuating quantities, as well as the dynamics of the vortex shedding and circulation in the wakes of the members, and discuss how these flow characteristics relate to the drag of each member, as a function of both their position within the $\vee$ and the angle of the formation. This current study serves as a baseline for further explorations of wake-body and wake-wake interactions of flow past groups of bodies and demonstrates how changing formation angle can help achieve a desired group performance (like minimum drag).

The interaction between air shock waves and granular materials is fundamental in both natural phenomena and engineering applications. However, the role of particle morphology, particularly that of flexible fibers, remains unclear. Here we numerically investigate shock-induced dispersal and resistance in dense flexible fiber curtains, using a coupled Discrete Element Method and Computational Fluid Dynamics (DEM-CFD) framework. We find that the dispersal dynamics and shock attenuation are controlled by the competition between fiber interlocking and the internal solid volume fraction of clusters. Low aspect ratio fiber systems, which have high cluster volume fractions, exhibit nonuniform expansion, with instabilities at the downstream interface leading to pronounced granular ejections, resulting in rapid dispersion of the clusters. In contrast, high aspect ratio fiber systems, which possess lower cluster volume fractions, maintain integrity of the clusters for much longer periods due to the fiber interlocking contacts, thereby suppressing the interfacial instabilities. Consequently, stronger resistance to the shock by the fiber cluster is obtained at early stage of the wave propagation for the low aspect ratio fibers, and the stronger shock resistance occurs at a later stage for the high aspect ratio fibers. Fiber flexibility modulates these behaviors by promoting fiber bending deformation, effectively weakening geometric interlocking and reducing air drag. To describe the time evolution of the fiber curtain expansion, the fiber aspect ratio should be included in the scaling law to account for the effect of fiber shape on the air drag. For the very flexible fibers, an effective fiber aspect ratio is required to replace the nominal fiber aspect ratio in the scaling law, in order to take the effect of large fiber deformation into account. These findings offer a fundamental understanding of the shock-driven multiphase flows and dispersal of the elongated, flexible fibers.

Vertical excitation of partially filled horizontal cylindrical tanks can induce large-amplitude sloshing, particularly when the forcing frequency approaches twice the fundamental sloshing frequency, leading to parametric resonance. Under these conditions, parametric resonance can trigger exponential growth of free-surface perturbations, leading to large-amplitude waves, interface breakup, and enhanced mixing. In this work, we experimentally investigate the sloshing regimes associated with this primary parametric instability. Experiments are conducted in a transparent horizontal cylindrical tank ($D=134.5\mathrm{mm}, L=336.3\mathrm{mm}$) over a range of fill ratios and excitation conditions. A data-driven, image-based methodology is developed to identify and classify sloshing regimes directly from high-speed visualizations. The approach combines multiscale proper orthogonal decomposition for feature extraction with prototype-based clustering and support vector machine classification. The results are summarized in a dimensionless regime map across three fill ratios ($H_l/D\in [0.40;0.67]$), distinguishing stable free-surface conditions, dominant longitudinal modes, and mixed or mode-interaction regimes. The map provides a structured characterization of the flow responses in the vicinity of the primary parametric resonance.

Direct numerical simulation is performed to investigate supersonic flows in a bent pipe with a developing turbulent boundary layer and a core-flow region. By comparison with a flat plate, a channel, and a straight pipe, instantaneous and time-averaged flow fields in the bent pipe indicate intricate flow phenomena, including waves, separation, secondary flows, and the Görtler instability. Expansion and compression waves are generated on the upper (convex) and lower (concave) sides, respectively. Separation is triggered by the combined effects of the adverse pressure gradient (APG) and flow deceleration on the upper wall, which significantly thickens the boundary layer and enhances the velocity fluctuations. Driven by the imbalance of the centrifugal force and pressure gradients, secondary flows (Dean vortices) are visualized in the circumferential boundary layer. On the lower wall, the quantitative evidence of the Görtler number distribution, the clustering and uplift of low-momentum fluids, and the presence of streamwise counterrotating vortices with large-scale wavelengths are related to the increase of the Görtler instability. The baroclinic effect induced by Görtler-type vortices promotes the formation of small-scale vortices and intensifies the Reynolds stresses and turbulent kinetic energy in the outer region of the boundary layer. The occurrence of favorable pressure gradient stabilizes the lower boundary layer and causes the turbulence decay. Quadrant decomposition analysis reveals that the increasing Görtler instability and APG can amplify ejections (Q2) and sweeps (Q4) of turbulence events, while the FPG will suppress sweeps (Q4).

Turbulence governs the transport of momentum, energy, and scalars in many geophysical and engineering flows. In large-eddy simulations (LES), parametrizing subgrid-scale (SGS) stresses remains a central challenge, as unresolved physical processes strongly influence turbulent transport. The SGS stresses are not uniquely determined by the resolved flow field due to the influence of unresolved fluctuations, thus SGS stresses could be better described by a conditional distribution. Here we introduce a conditional diffusion model (CDM) to reconstruct SGS stresses from coarse-grained velocity fields in direct numerical simulations of the atmospheric boundary layer. The CDM consistently outperforms traditional deterministic models in terms of spatial correlations and probability distributions for deviatoric stresses, and can be applied to unseen convective stability conditions and resolutions. By learning conditional distributions rather than pointwise values, this generative framework introduces a fundamentally new way for stochastic SGS turbulence modeling.

We present a theoretical model for the metal-pad-roll instability in laboratory-scale experimental models of reduction cells consisting of two stably stratified liquid layers subjected to a vertical electric current and magnetic field. In contrast to most previous studies, we do not rely on the shallow-water approximation and can account for viscous and capillary effects that are prevalent in small-scale experiments. In small cells, dissipation effects are largely attributable to laminar viscous damping, which we calculate analytically using a perturbative formulation of the Stokes boundary layers forming at all container walls and on both sides of the liquid interface. The derived damping rates, which are also useful for modeling liquid-liquid sloshing in rectangular containers, are validated against direct numerical simulations conducted with the coupled level set and volume-of-fluid solver ARCHER. On this basis, we derive analytical solutions for the growth rates and instability onsets of the metal-pad-roll instability, which we compare with different theoretical descriptions and existing experiments. The presented solutions are intended to serve as a foundation for future benchmarking of multiphase solvers.

We use a simple method for generating droplets at the surface of a liquid bath by rapidly stretching a liquid ligament with a spring-loaded cylindrical probe. By varying the probe radius $a$ and retraction length $L$, we identify three regimes. Overstretching a thin ligament produces multiple drops, while insufficient stretching of a thick ligament yields none. The optimal regime for single-drop generation lies in between. In the single-drop regime, the drop radius scales as $R\sim a^{2/3}{L}^{1/3}$, consistent with volume conservation of the stretched ligament. This method enables repeatable generation of single droplets (with $<5\%$ variation in $R$) on both still and vibrating baths and of ordered droplet lattices for pilot-wave hydrodynamics experiments.

Wall slip is ubiquitous in molten polymer flows, yet its role in polymer diffusive instability (PDI)—a unique viscoelastic instability driven by polymer stress diffusion at vanishing Reynolds numbers—remains uncharacterized. Here, we combine linear stability analysis and direct numerical simulations (DNS) to investigate PDI in viscoelastic plane Poiseuille flow under Navier slip conditions ($u=b{\tau }_{xy}$). Four distinct PDI modes are identified: PDI-1 (negative phase velocity, including antisymmetric PDI-1a and symmetric PDI-1s) and PDI-2 (positive phase velocity, including PDI-2a and PDI-2s). Wall slip exerts differential regulatory effects: it stabilizes PDI-1 (PDI-1s fully stabilizes at $b=0.003$) but triggers PDI-2 instability under small $b$. Energy balance analysis reveals PDI-1 is dominated by base-state conformation tensor contributions, while PDI-2 is driven by base-state velocity gradients. DNS validates these linear predictions, showing consistent nonlinear evolution for symmetric/antisymmetric perturbations. Our findings provide a quantitative basis for PDI control in polymer processing.

This work presents a unified viscoelastic-viscoplastic continuum framework for modeling rate-dependent granular flows across regimes. The formulation incorporates two distinct rate-dependent mechanisms, namely, micro-inertia and viscoelastic dissipation, within a single continuum description. A central contribution is an explicit link between the coefficient of restitution and a continuum viscosity, derived from an analysis of wave attenuation in granular assemblies, thereby establishing a direct connection between particle-scale collision physics and macroscopic damping. This relation is introduced while retaining inertia-dependent plastic flow governed by the classical $\mu \left(I\right)$ rheology. The constitutive model is constructed by meticulously partitioning elastic and plastic responses within the model and corresponding stress-update routine, such that viscous dissipation governs wave propagation and collisional processes without altering the plastic flow rule. The framework is implemented within the material point method to simulate transient processes involving large deformations, material separation, and subsequent reconsolidation. A range of numerical examples, including steady, transient, vibrational, and impact-driven flows, demonstrates that the model captures wave propagation, diffusion, and rate-dependent granular behavior within a unified continuum setting.

The wall imprint of outer-layer motions in wall turbulence is inherently intermittent, yet most attached-eddy coherence analyses are ensemble averaged. Here we develop a time-resolved coherence framework to track the intermittent wall imprint of logarithmic-region motions, using the near-wall velocity record as an operational wall-signature proxy. The method diagnoses scale-local linear common variance between the near-wall and logarithmic-region velocity records; it does not identify individual eddy boundaries or imply a one-to-one geometrical correspondence between motions at the two heights. Synchronized two-point hot-wire measurements in a high-Reynolds-number, nominally zero-pressure-gradient turbulent boundary layer are analyzed (E2-type Melbourne dataset), with a near-wall reference $u(z_R,t)$ and a logarithmic-region signal $u(z,t)$. A time-varying squared linear coherence ${\gamma }_L^2(t,f)$ is obtained from wavelet coherence. Upon averaging, the wavelet estimator reproduces the classical coherence behavior: ${\langle {\gamma }_L^2\rangle }_t$ matches short-time Fourier estimates over the energetic band and collapses with established similarity trends when expressed versus ${\lambda }_x/\mathrm{\Delta }z$. To summarize event persistence, we define a critical streamwise scale ${\lambda }_s\left(t\right)$ from the first down-crossing of a windowed autocorrelation of the large-scale component of $u(z,t)$. Across heights, $\overline{{\lambda }_s}\left(z\right)/\delta$ increases, while ${\gamma }_L^2({\lambda }_s\left(t\right),t)$ decreases within the logarithmic region, consistent with a weakening wall imprint with wall-normal separation. We then couple ${\gamma }_L^2(t,f)$ to a third-order-increment energy-flux surrogate $\mathrm{\Pi }({\lambda }_x/\delta ,t)$ to form coherence-conditioned cascade measures. Conditioning on a strong wall imprint yields a systematic wall-normal dependence: The high-coherence conditional flux weakens with increasing $z/\delta$ for ${\lambda }_x/\delta \lesssim O\left(1\right)$ and approaches zero at the largest scales. Finally, collocated wavelet energy-coherence statistics quantify how outer-layer energy is redistributed across coherence levels and reveal a peak in high-coherence conditional mean energy within the logarithmic region.

Understanding the flow of complex media is relevant for a wide range of research fields and industrial applications. Several numerical approaches exist by which approximate solutions can be determined for the Stokes equations that describe microhydrodynamic flows at the continuum level. However, achieving efficiency and accuracy for an incompressible fluid remains challenging. Here, we present an algorithm for solving the Stokes equations for an Oldroyd-B fluid using Fourier transforms. We gain efficiency by leveraging the “Fastest Fourier Transform in the West” (FFTW). We validate our approach for the well-characterized four-roll mill, which exhibits nearly singular points of stress at the extensional points of the flow. We capture this divergence and showcase the potential of our method without making the usual diffusive renormalization. We also focus on characterizing the power-law behavior and numerically assess the divergence criterion. Future work will concentrate on active systems, the introduction of moving boundaries, and application to microfluidic devices.

The mean resolvent operator predicts the mean linear response to forcing in the frequency domain and provides the optimal linear time-invariant approximation of statistically steady, time-varying flows [C. Leclercq et al., J. Fluid Mech. 968, A13 (2023)]. We first leverage the harmonic resolvent framework [N. M. Wereley and S. R. Hall (IEEE, Piscataway, NJ, 1990); A. Padovan et al., J. Fluid Mech. 900, A14 (2020)] to propose an algorithm for performing mean resolvent analysis of a periodic flow. Next, we propose an alternative approach which does not explicitly rely on the harmonic resolvent framework. The approach leverages the fact that the mean-flow resolvent approximates the mean resolvent operator, therefore the optimal forcing modes of the latter operator may be sought in a subspace spanned by optimal modes of the former. This projection approach does not require computing the adjoint dynamics about the attractor, which may be convenient for future extensions to more chaotic and turbulent flows. The present paper is however focused on periodic flows, where the convergence of the projection approach can be checked in comparison to the “ground truth” provided by the harmonic resolvent framework. This test is performed on a nearly incompressible axisymmetric laminar jet forced harmonically at the inlet. For the weakly unsteady case, the mean-flow resolvent captures the dominant receptivity peak but misses a secondary one present in the mean resolvent gain. For the strongly unsteady case, the mean-flow resolvent fails to predict the frequency of the vortex-pairing, while the mean resolvent correctly locates the corresponding gain peak. The projection method converges with a subspace dimension of 10 in the weakly unsteady case, while about 100 modes are required for accurate predictions in the strongly unsteady regime. Nonetheless, even a one-dimensional subspace correctly identifies the dominant receptivity peak.

Viscous fingering instabilities occurring at reactive mixing interfaces prevailing in porous media are often driven by concentration-dependent viscosity of the constituent fluids and play a vital role in several environmental and industrial processes. The stability of such reaction fronts is usually modeled at the Darcy scale, often under the pretense of a constant and identical molecular diffusivity of both the reactants and the product. However, at the Darcy scale, evolution of mixing interfaces is generally governed by hydrodynamic dispersion rather than molecular diffusion, while the diffusion coefficients of the various species involved are often distinct. Yet, their impact on the stability of a reaction front remains hitherto unexplored. As such, in this article we perform a linear stability analysis to unravel the role of dispersion on the stability of a bimolecular reaction front with regards to viscous fingering, where all species have distinct molecular diffusivities. The dispersion tensor is assumed to be linearly dependent on the local Darcy velocity, and the viscosity is assumed to vary exponentially with species concentrations. The stability of the front is analyzed using a transient approach where an initial value problem (IVP) is solved for the perturbations. A second approach using a quasi-steady-state approximation (QSSA) is also adopted as a reference case. We show that although the results from QSSA and IVP eventually converge at sufficiently large times, significant differences persist during the early stages, depending on the precise nature of viscosity variation. In particular, the results from the IVP approach show that both longitudinal and transverse dispersion tend to suppress the growth of perturbations. We further establish that the stability characteristics of the front become independent of the ratio between diffusion-to-advection timescales (the Péclet number) when hydrodynamic dispersion is taken into account. We demonstrate that diffusivity contrast between the product and the reactants may suppress or promote instability. Notably, it is shown that enhanced diffusivity of the product in scenarios where it is the most viscous element may stabilize an otherwise unstable front. The results shown here may be relevant to applications such as contaminant remediation, enhanced oil recovery, and carbon sequestration.

The development of a free laminar jet from a fully developed Poiseuille profile to a self-similar Gaussian flow is investigated theoretically. While the far-field self-similar state is well understood, the near-field transition region presents a significant analytical challenge due to the interplay of axial convection and radial viscous diffusion. This study introduces a first-principles analytical model based on a linearly decaying reference velocity. The model determines the jet's velocity decay rate, $k$, through a self-consistent framework where its evolution is required to match an optimal trajectory defined by a Galerkin-constrained guidance model. Built on a two-mode Laguerre-Gaussian expansion, the model reveals a universal linear scaling for the dimensionless centerline velocity decay and demonstrates that the transition length, $z_t$, scales linearly with the Reynolds number. Predictions for both centerline velocity and full velocity profiles show excellent agreement with numerical simulations over a diverse range of Reynolds numbers $(\mathrm{Re}=20–1500)$. This work establishes a robust and physically insightful framework for describing the evolution of laminar jets with finite Poiseuille inlets.

Air curtains (AC) are contemporary devices that are used to minimize buoyancy-driven exchange flow across the doorway of a building. Under optimal conditions, they restrict up to 85% of outdoor fluid from infiltrating the indoor region. In the present study, we use large-eddy simulations and a Lagrangian analysis framework to investigate the spatial origin and transport mechanisms of fluid that penetrate an air curtain operating at Reynolds number $\mathrm{Re}=4000$ and Froude number ${\mathrm{Fr}}_0=28.4$. We further explain the saturation of sealing effectiveness at 85% by comparing transport characteristics of an AC with those of nonbuoyant jets and gravity currents. We observe that prior to the curtain establishment, most infiltration occurs via a gravity current, where particles initially near the wall are transported indoors along near-straight trajectories. Once the AC establishes, an entrainment-detrainment pathway becomes dominant. The outdoor fluid is first entrained into the turbulent core and subsequently detrained into the indoor region, either before reaching the wall or after its impingement. The present study thus highlights that it is the inherent entrainment of the outdoor fluid by the curtain which results in a loss of sealing by about 15 to 20%.

Accurate scaling of heat energy is critical for compressible turbulence modeling. In addition to the temperature-velocity relation, temperature transformations have received increasing interest recently, but their overall accuracy is still inferior to the velocity counterparts. In this work, we propose to use total enthalpy $H$ instead of temperature to construct the compressible law of the wall for heat energy. A critical justification is the structural resemblance between the equations of compressible $H$ and incompressible passive scalars. Also, $H$ reduces to static enthalpy at zero Mach number, meeting the requirement of self-consistency for transformations. To build the transformation, we first define and uncover the scalings of laminar and turbulent Prandtl numbers for $H$, and then reveal the strong analogy of heat flux budgets between compressible $H$ and incompressible passive scalars. Finally, a semilocal total enthalpy transformation of no fitted parameters is constructed for channel flows, which is structurally analogous and comparable in accuracy to the Trettel-Larsson velocity transformation. This new transformation can potentially serve as a wall model for energy equations to accurately predict the enthalpy or temperature in compressible turbulence.

The offshore wind industry is rapidly expanding to meet clean and secure energy needs. New developments are now increasingly constrained to deeper waters, where the water column is seasonally stratified. Here flows past offshore wind infrastructure will increase water column mixing, although such processes and their extent are poorly understood. Studies have so far been limited to field-scale simulations, which make sweeping assumptions regarding flow-structure interactions and fine-scale stratified turbulence, and field observations, which are limited by the sparsity of measurement campaigns and data captured. To isolate and quantify the key processes governing water column mixing by infrastructure, we present fully structure-resolved direct numerical simulations of two-layer stratified flow past a vertical cylinder. We identify two wake regimes by systematically varying the flow Reynolds and Richardson numbers: (1) a weakly stratified regime, characterized by a narrow but highly energetic wake dominated by horizontal shear and (2) a strongly stratified wake, characterized by the emergence of a thermocline-spanning recirculation cell attached to the cylinder. Here strong vertical motions develop from the recirculation cell which are responsible for the formation of large-scale stationary internal waves. These waves account for up to 10% of the total energy budget and provide a mechanism for far-field energy propagation. The weakly stratified wake regime is characteristic of existing offshore wind sites where temperature gradients are relatively weak; the identified strongly stratified regime describes the dynamics to be expected in future deep water offshore wind sites. This difference between the two regimes offers an explanation for the previously enigmatic discrepancies in field observations regarding wake persistence and detectability. Future work must focus on narrowing the gap between idealized simulations and field-scale flows, for which the datasets herein will provide a critical benchmark for validation.

Nonaxisymmetric droplet shape oscillations are investigated by extending the numerical framework developed in Akbari et al. [Phys. Rev. Fluids 11, 033602 (2026)], which is based on a Galerkin method using spherical harmonics, to fully three-dimensional configurations. The study focuses on the role of shape symmetry and mode excitation of inviscid droplet shape oscillation. The numerical results confirm that the oscillation frequency is independent of the azimuthal wave number, in agreement with classical theoretical predictions. The discrete geometric symmetries of both the initial droplet deformation and the initial velocity potential are demonstrated to be preserved throughout the oscillation. Consequently, only modes compatible with these symmetries are excited. When the initial velocity potential breaks the symmetries of the droplet deformation, leading to a reduction in these symmetries, additional modes are excited compared to those for a zero initial velocity. A similar result is observed in the droplet shape oscillations of a single initial deformation mode and a superposition of two initial deformation modes. In the former case, only modes that satisfy the symmetries of the initial deformation are excited. In the latter case, the superposition reduces the overall symmetry of the droplet shape, leading to additional mode excitation through symmetry breaking. These results highlight the fundamental role of symmetry preservation in nonlinear droplet oscillations. By exploiting these symmetry properties, the computational effort could be reduced without compromising numerical accuracy, as modes that do not occur can be excluded from the solution approach prior to the simulation.

We numerically examine a kinematic dynamo driven by precession in a cylindrical geometry, with particular emphasis on the narrow range of Poincaré numbers where dynamo action is most likely at low and moderate magnetic Reynolds numbers. Using time-averaged velocity fields obtained from hydrodynamic simulations, we analyze the symmetry, oscillation frequency, and onset of the leading magnetic eigenmodes. Two competing families of magnetic fields are identified: a centrosymmetric, higher-frequency quadrupolar mode and a centroantisymmetric, lower-frequency dipolar mode. We then quantify how the dynamo threshold depends on the electromagnetic boundary conditions, including pseudovacuum versus true vacuum treatment and the presence of conducting and/or magnetically permeable vessel walls. We show that simplified vanishing-tangential-field boundary conditions systematically underestimate the critical magnetic Reynolds number, whereas realistic outer layers can either promote or suppress dynamo action depending on their electrical conductivity and on the selected hydrodynamic mean state. These results clarify the role of wall properties and mode selection for the forthcoming DRESDYN precession dynamo experiment.