A wind tunnel experiment explores the interaction between a parallel jet and the tip vortex from a rectangular wing with jet nozzles beneath, designed to mimic a cruising aircraft in terms of the propulsive-to-lift force ratio. The wake is investigated over the full roll-up phase of the trailing vortex sheet—about 20 wingspans—enabled by the tunnel's long test section. A parametric study of the jet-to-wing-tip distance evaluates (i) the vortex influence on jet mixing, and (ii) the vortex response to the jet disturbance. Half of the symmetric wake is measured via stereo particle image velocimetry (PIV) in several transverse planes. Sufficiently downstream, the tip vortex dynamics appear largely unaffected by the jet, exhibiting growing oscillations (meandering) regardless of jet presence. The midwake region, associated with separated flow at the wing/mast junction, is found to promote transient horizontal oscillations. At the last measurement plane, the displacement mode aligns near ${50}^{\circ }$, possibly indicating the onset of long-wave vortex instability, whose presence has yet to be fully ensured. Jet mixing is tracked using seeding in the same PIV planes. The jet is entrained by the rolling tip vortex, especially when positioned outboard near the vortex, producing a spiraling plume that enhances mixing. For very short jet-to-vortex distances, the jet becomes trapped in the vortex core. A model-based analysis of particle motion shows that tip vortex meandering has little effect on jet spreading.

Transient size segregation of a bidisperse granular mixture flowing over a periodic chute is studied using the discrete element method (DEM) and continuum simulations. A recently developed particle-force-based size segregation model is used to predict the time-dependent flow properties of binary mixtures starting from rest. A two-way coupled continuum model that solves the momentum balance and convection-diffusion equations by incorporating the mixture segregation model along with the generalized inertial number-based rheological model is developed for predicting the evolution of segregation. The solids fraction dependence on the local mixture composition is found to be crucial for accurate prediction of segregation for larger size ratios. The predicted concentration profiles and other flow properties of the mixture are found to be in good agreement with the DEM data for a variety of compositions. The evolution of the center of mass of the two species with time is also very well captured for different initial configurations and size ratios using the particle-force-based segregation model.

Detonation-based propulsion devices, such as rotating detonation engines (RDEs), must be able to leverage the higher energy densities of liquid fuels in order for them to be utilized in practical contexts. This necessitates a comprehensive understanding of the physical processes and timescales that dictate the shock-induced breakup of liquid droplets. These processes are difficult to probe and quantify experimentally, often limiting measurements to macroscopic properties. Here, fundamental mechanisms in such interactions are elucidated through detailed numerical simulations of Mach 2 and Mach 3 shock waves interacting with $100\mu \mathrm{m}$ water droplets. Using a thermodynamically consistent two-phase formulation with adaptive mesh refinement, the simulations capture droplet surface instabilities and atomization into secondary droplets in detail. The results show that droplet breakup occurs through a coupled multi-stage process, including droplet flattening, formation of surface instabilities and piercing, and the shedding of secondary droplets from the ligaments of the deformed primary droplet. When considering the dimensionless timescale of Ranger and Nicholls $\tau$, these processes occur at similar rates for the different shock strengths. The PDFs for the diameters of secondary droplets are bimodal log-normal distributions at $\tau =2$. Modest differences in the degree and rate of liquid volume transfer into droplets less than $5\mu \mathrm{m}$ in diameter are hypothesized to partially derive from differences in droplet surface piercing modes. These results are illustrative of the complex multi-scale processes driving droplet breakup and have implications for the ability of shocks to effectively process liquid fuels.

The fragmentation of liquid jets within gaseous crossflows finds numerous applications in both natural and industrial situations. The thermophysical properties of the liquid and gaseous media significantly influence the instability waves along the liquid jet column, the breakup mechanisms, and the resulting droplet size and velocity distributions. The viscosity and density of liquid and gaseous phases can vary widely based on the application. In plasma spray processes, the gaseous Reynolds number and the liquid-to-gas density ratio reach approximately 30 and 12 000, respectively, well beyond the typical ranges in engines and wind tunnels. This study employs numerical simulations to gain insights into the breakup mechanisms within these unique and unexplored conditions, aiming to take a step towards comprehending the intricacies of liquid jet breakup in thermal spray environments. The finite volume scheme has been used to solve the incompressible variable-density Navier-Stokes equations, and a volume of fluid approach has been utilized to track the gas-liquid interfaces. The study presents a range of findings, including qualitative results such as instantaneous snapshots and liquid jet cross-section shapes, alongside quantitative data on breakup point locations, surface wavelengths, pressure distribution, and jet trajectory. Our observations demonstrate that a low momentum flux ratio predominantly drives the transition to Kelvin-Helmholtz instability, with high gaseous viscosity acting as a secondary factor that enhances liquid column breakup in plasma-like crossflow conditions. This behavior contrasts with the Rayleigh-Taylor instability, which is commonly reported at relatively high momentum flux ratios, high-density ratios $(\sim 1000)$, and high gaseous Reynolds numbers.

Supersonic particle-laden turbulent boundary layers (TBLs) over a flat-to-concave surface at Mach 2.7 were investigated for the first time using Eulerian-Lagrangian simulations. In the transition section, the concave surface's compressible effect creates a high-frequency collision zone and significantly increases the particle volume fraction. In the downstream concave section, Görtler-like vortices induced by concave surface dominate particle dynamics. Particles are transported from the outer to the inner TBL along interregions of Görtler-like vortices, while being entrained in large-scale low-speed regions and ejected from the inner to the outer TBL. Görtler-like vortices enhance particle preferential accumulation and increase particle mass exchange of high- and low-speed fluids, particularly for large inertial particles (${\text{St}}^{+}=75$). This leads to a decrease in Reynolds shear stress and an increase in skin friction due to concentrated drag feedback. In contrast, small inertial particles (${\text{St}}^{+}=15$) distribute uniformly and have minimal impact on turbulence due to their better flow tracking in the concave section. Additionally, the concave geometry enhances pressure gradients and drag forces, thickens the viscous sublayer, and drives particles toward the intrados, which significantly reduces particle-wall collisions and deposition in the wall.

Local eddy viscosity and diffusivity models are widely used to understand and predict turbulent flows. However, local approximations in space and time are not always valid for actual turbulent flows. Recently, a nonlocal expression for the turbulent scalar flux was verified using the direct numerical simulation (DNS) of homogeneous isotropic turbulence with an inhomogeneous mean scalar. A model for the nonlocal eddy diffusivity was proposed and validated using the DNS data. In this study, using a similar approach, a nonlocal expression for the Reynolds stress and the passive vector flux was investigated using the DNS of homogeneous isotropic turbulence with an inhomogeneous passive vector. The Green's function for the passive vector fluctuation was evaluated to obtain the nonlocal eddy viscosity. The nonlocal expression for the passive vector flux agreed with the value directly obtained from the DNS. The nonlocal effects accounted for the overestimation of the passive vector flux by the local expression as well as the phenomenon of the countergradient diffusion appearing in some regions. A model for the nonlocal eddy viscosity was proposed systematically in a customary manner in the statistical theory of turbulence. The nonlocal eddy viscosity obtained from the model agreed well with the DNS values, including its temporal behavior, and the nonlocal model reproduced the passive vector flux. Because it was already known that the nonlocal eddy viscosity for the passive vector flux can also be applied to the Reynolds stress, these results indicate that the nonlocal eddy viscosity model is useful for gaining insight into momentum transport in turbulence.

We present the results of a theoretical investigation into the existence and evolution of resonant triads of two-layer gravity waves confined to a cylinder of finite height. We consider a stable stratification, for which the lighter fluid lies above the heavier fluid, with the two fluids being separated by an interface and bounded above and below by rigid horizontal lids. We demonstrate that the lateral confinement can excite resonant three-wave interactions, resulting in pronounced interfacial sloshing and highly efficient energy exchange. Such interactions are absent in unbounded domains or rectangular cylinders and consist of a single vertical mode and a single interface. For a cylinder of arbitrary cross section, we prove necessary and sufficient conditions for three spatially correlated wave modes to resonate, with the existence of triads depending critically on the depth and density of each fluid. Upon deriving amplitude equations governing the long-time evolution of a resonant triad, we show that the triad evolution is generally periodic and determine conditions for which energy exchange is most propitious. We also identify a criticality condition exclusive to multilayer flows that describes the decoupling of the triad interaction. Finally, we discuss the implications of our findings on the formation of resonant internal wave interactions in geophysical basins.

The importance of nonlocality is assessed in modeling mean scalar transport for turbulent Rayleigh-Taylor (RT) mixing at different Atwood numbers. Building on the two-dimensional incompressible work of Lavacot et al. [J. Fluid Mech. 985, A47 (2024)], the present work extends the macroscopic forcing method to variable density problems in three-dimensional space to measure moments of the generalized eddy diffusivity kernel in RT mixing for increasing Atwood numbers ($A=0.05,0.3,0.5,0.8$). It is found that as $A$ increases, (1) the eddy diffusivity moments become asymmetric and (2) the higher-order eddy diffusivity moments become larger relative to the leading-order diffusivity, indicating that nonlocality becomes more important at higher $A$. There is a particularly strong temporal nonlocality at higher $A$, suggesting stronger history effects. The implications of these findings for closure modeling for finite-Atwood RT are discussed.

In this paper, we develop a lattice Boltzmann scheme based on the Vielbein formalism for the study of fluid flows on spherical surfaces. The Vielbein vector field encodes all details related to the geometry of the underlying spherical surface, allowing the velocity space to be treated as on the Cartesian space. The resulting Boltzmann equation exhibits inertial (geometric) forces that ensure that fluid particles follow paths that remain on the spherical manifold, which we compute by projection onto the space of Hermite polynomials. Due to the point-dependent nature of the advection velocity in the polar coordinate $\theta$, exact streaming is not feasible, and we instead employ finite-difference schemes. We provide a detailed formulation of the lattice Boltzmann algorithm, with particular attention to boundary conditions at the north and south poles. We validate our numerical implementation against two analytical solutions of the Navier-Stokes equations derived in this work: the propagation of sound and shear waves. Additionally, we assess the robustness of the scheme by simulating the compressible flow of an axisymmetric shock wave and analyzing vortex dynamics on the spherical surface.

The present study illustrates the effect of periodic heating on the onset of convective instability in a two-layer system composed of a fluid layer overlying a Darcy porous medium. The system is bounded below by a sinusoidally heated impermeable surface and above by a stress-free surface. A general thermal boundary condition depicts the heat transfer through the upper surface. Tangential and normal stress balances at the permeable fluid-porous interface are represented by the Beavers-Joseph-Saffman-Jones and Lions interface conditions, respectively. Linear and energy stability analyses are performed, and the resulting stability criteria are determined through numerical computations. The linear theory results indicate that varying modulation parameters can not only control the onset of instability but also induce a shift in the mode (fluid/porous) of instability when $\widehat{d}\sim 0.1$. The investigation is further extended to systems with varying configurations by altering the physical parameters such as Biot number, thermal diffusivity ratio, slip coefficient, and Darcy number. The energy method yields two nonlinear stability criteria—strong global and asymptotic limits—and hence dismisses the existence of global stability. These nonlinear bounds lead to the regions of subcritical instability and uncertain stability.

Condensation on vertical surfaces leads to fluid retention, which limits the efficiency of applications ranging from heat exchangers to atmospheric water harvesters. A common strategy is to structure the surface with grooves, yet whether grooves help drainage or worsen retention remains unclear. Here we use a high-throughput condensation setup to quantify retention on substrates patterned with parallel vertical grooves of fixed geometry ($d/w=1$) while varying the spacing $s$. We uncover two opposite regimes separated by the droplet detachment radius $R_d$. For large spacings ($s>R_d$), droplets grow and slide under gravity while grooves, acting as passive reservoirs, increase retention. For small spacings ($s<R_d$), grooves instead trigger active drainage, confining droplet growth and reducing retention to values even lower than on smooth surfaces. Two asymptotic models, a groove-volume reservoir model and a plateau-packing model, capture this transition and explain the scaling of retention with $s$. These findings show that groove spacing controls whether grooves act as drains or reservoirs, providing a simple geometric design rule for tailoring condensation retention in practical systems.

This work identifies the physical mechanisms at play in the different flow regions along an Eckart acoustic streaming jet by means of numerical simulation based on a modeling of the driving acoustic force including attenuation effects. The flow is forced by an axisymmetric beam of progressive sound waves attenuating over a significant part of a closed cylindrical vessel where the jet is confined. We focus on the steady, axisymmetric, and laminar regime. The jet typically displays a strong acceleration close to the source before reaching a peak velocity. At further distances from the transducer, the on-axis jet velocity smoothly decays before reaching the opposite wall. For each of these flow regions along the jet, we derive scaling laws for the on-axis velocity with the magnitude of the acoustic force and the diffraction of the driving acoustic beam. These laws highlight the different flow regimes along the jet and establish a clear picture of its spatial structure, able to inform the design of experimental or industrial setups involving Eckart streaming jets.

Superhydrophobic coatings are used to separate surfaces from the surrounding liquid by trapping an air layer called plastron in its microstructures. The durability and therefore the performance of these surfaces lie in the capacity to retain this plastron, which might be destabilized by excessive stresses or dissolution. Plastron monitoring is therefore essential to quantify the amount of gas shielding the surface from the liquid and to determine its temporal evolution. Such air layers, which may blend multiple length scales ranging from nm up to cm, are challenging to probe. In this paper, we develop a versatile technique based on the acoustic resonance of the plastron, which allows passive probing of the total volume of air trapped in the surface roughness. Validation of this technique is performed by comparing the mean acoustic thickness against direct optical observations and shows very good agreement. As this acoustic method uses portable transducers and is sensitive to the air layer's volume regardless of the superhydrophobic surface, we foresee that it can pave the way toward plastron monitoring under more realistic conditions such as complex geometries in different flow regimes. Additionally, this technique is shown to efficiently monitor plastron on timescales of a few milliseconds, enabling real-time characterization necessary to better assess destabilization mechanisms leading to the collapse of a plastron.

Unsteady load alleviation is crucial for engineering applications such as tidal turbines. Herein, we present an experimental study into the load alleviation capacities of constant-section airfoils with flexible trailing-edges. The trailing-edge studied here consists of two independent flexible skins, enabling large skin deformations and enhanced load alleviation compared to conventional flexible trailing-edge designs. We test high-amplitude plunging kinematics (up to peak-to-peak amplitude of one chord length) at reduced frequency $k=0.2$ and Reynolds numbers $\mathrm{Re}=\mathcal{O}\left({10}^4\right)$. To quantify the role of airfoil flexibility, we introduce two Cauchy numbers (${\mathrm{Ca}}_u$ and ${\mathrm{Ca}}_v$), which normalize the freestream and plunging velocities, respectively. We demonstrate that both the trailing-edge deflection and the resulting lift alleviation scale with these Cauchy numbers provide a fundamental framework for understanding flexible airfoil dynamics. Furthermore, we propose semi-empirical models for unsteady lift alleviation, which agree with our measurements. These findings lay the groundwork for fully predictive low-order models, advancing the design of passively morphing airfoils for efficient load control in unsteady flow environments.

Cerebrospinal fluid (CSF) flow is modelled in human perivascular spaces (PVSs) that surround brain penetrating arteries. It is proposed that the outer PVS boundary oscillates due to brain pulsations, and the arterial wall motion is driven by a blood pressure wave. Lubrication theory is employed to derive a mathematical model for the CSF flow, which is then solved numerically. A parametric analysis is undertaken to investigate the effect of the brain pulsations, which shows that pulsations magnify the net axial CSF flows created by the arterial wall motion. The findings suggest that net axial CSF flows are almost entirely positive (deeper into the brain), with arterial wall motion highly dependent on PVS-penetrating artery configurations. Given the glymphatic hypothesis, the findings support the clinical practice of treating dilated PVSs as indicators of an increased likelihood of neurodegenerative conditions, such as dementia.

This paper is associated with a poster winner of a 2024 American Physical Society's Division of Fluid Dynamics (DFD) Milton van Dyke Award for work presented at the DFD Gallery of Fluid Motion. The original poster is available online at the Gallery of Fluid Motion, https://doi.org/10.1103/APS.DFD.2024.GFM.P2692828.

This paper is associated with a poster winner of a 2024 American Physical Society's Division of Fluid Dynamics (DFD) Milton Van Dyke Award for work presented at the DFD Gallery of Fluid Motion. The original poster is available online at the Gallery of Fluid Motion, https://doi.org/10.1103/APS.DFD.2024.GFM.P2676604.

This paper is associated with a poster winner of a 2024 American Physical Society's Division of Fluid Dynamics (DFD) Milton van Dyke Award for work presented at the DFD Gallery of Fluid Motion. The original poster is available online at the Gallery of Fluid Motion, https://doi.org/10.1103/APS.DFD.2024.GFM.P2685195

This paper is associated with a video winner of a 2024 American Physical Society's Division of Fluid Dynamics (DFD) Gallery of Fluid Motion Award for work presented at the DFD Gallery of Fluid Motion. The original video is available online at the Gallery of Fluid Motion, https://doi.org/10.1103/APS.DFD.2024.GFM.V2560348.