The surface tension of a liquid, which drives most free-surface flows at small scales, is often measured with the pendant drop method due to its simplicity and reliability. When the drop is suspended in air, controlling the ambient temperature and humidity is usually an afterthought, resulting in evaporation of the drop during the measurement. Here, we investigate the effect of evaporation on the measured surface tension using experiments and numerical simulations. In the experiments, we measured the evolution of the droplet temperature, which can be drastically reduced by $\mathrm{\Delta }T\approx {10}^{\circ }\mathrm{C}$ due to evaporative cooling, thereby altering the measured surface tension by more than 1 mN/m. This finding can be reproduced by numerical simulations, which additionally allow for controlled investigations of the individual influences of further effects on the pendant drop method, namely, shape deformations by evaporation-driven flows in the gas-phase and in the liquid-phase, including the resulting Marangoni flow. We provide a simple passive method to control the relative humidity without requiring additional instrumentation. Our findings are particularly pertinent to Marangoni flows, which are driven by surface tension gradients and which are consequently highly sensitive to measurement inaccuracies. We apply our method with different aqueous mixtures of glycerol and various diols. Our results and insights have implications for various applications, ranging from inkjet printing to agricultural sprays. Finally, we meticulously documented our setup and procedure for future reference.

The impact of localized surface roughness on the development of a short laminar separation bubble (LSB) forming on the suction side of a NACA 0018 airfoil at an angle of attack of $6^{\circ }$ and a chord-based Reynolds number of ${\text{Re}}_c=100000$ is investigated experimentally. Direct force measurements and two-component particle image velocimetry (PIV) in multiple planes are used to characterize the effect on flow development compared to the baseline flow over a smooth airfoil and fully tripped model. Results show that localized roughness not only eliminates the downstream LSB but also induces significant three-dimensional modifications to bubble topology over a substantial spanwise region ($\sim \mathcal{O}\left(c\right)$) extending beyond the roughness element. This leads to a more substantial impact on aerodynamic performance than that expected from the relative spanwise extent of the localized roughness. The results suggest that bypass transition leads to mean flow reattachment in the spanwise proximity of the localized roughness. The produced three-dimensional, open LSB is characterized by the presence of notable spanwise flow in the separated flow region and spanwise variations of mean separation, transition, and reattachment. Consequently, changes are observed in the formation and development of shear layer vortices along the span, despite the dominant streamwise wavelength and frequency of perturbations remaining nearly unchanged. Furthermore, the modified LSB exhibits relatively low-frequency spanwise “breathing,” which induces mean flow deformations that modulate the stability of the LSB and contribute to the more complex vortex dynamics observed in this flow region.

We experimentally investigate the impingement of a gas jet onto a flowing liquid metal film, focusing on the resulting free-surface deformation and the subsequent evolution of surface waves. Our results show that the bulk flow significantly influences both the deformation of the free surface and the characteristics of the generated surface waves, which is different from the classical gas jet impingement on static liquid surfaces. Under steady gas jet impingement, the periodicity of free surface waves intensifies with a dominant frequency around 10 Hz at high gas Reynolds number ${\mathrm{Re}}_g$ for a stationary liquid surface. Critically, the interaction of the bulk flow with the gas flow establishes asymmetric coupling conditions, countercurrent flow upstream and cocurrent flow downstream, which cause the momentum exchange between the gas and the surface waves to exhibit opposite trends upstream and downstream as the liquid Reynolds number ${\mathrm{Re}}_l$ increases. In addition, under the impingement of a pulsating gas jet, we use the attenuation coefficient $c$ to correlate the wave amplitude with the jet momentum at different locations. We also find that the nonlinear interaction between the bulk flow and the forced wave accelerates the nonlinear evolution and energy dissipation of the wave. These findings can help engineers design liquid metal divertors to prevent excessive liquid evaporation, dry spots, and droplet splashing, which could damage the divertor substrate.

The fresh water equation of state exhibits a fundamentally important nonlinearity; the temperature at which it attains its maximum density occurs at roughly $4^{\circ }\mathrm{C}$ as opposed to at $0^{\circ }\mathrm{C}$. The form of the equation of state in this regime is quadratic and has the well-known implication that two fluid parcels may mix and produce a child parcel with a higher density; a process known as cabbeling. In this work we report on direct numerical simulations of the Rayleigh-Taylor instability in the cabbeling regime. We demonstrate that the mature, three-dimensional state of the instability leads to cabbeling, which, in turn, serves to sustain an instability that would otherwise saturate outside of the cabbeling regime. We present a new quantitative measure of strong cabbeling potential and use it, along with the mechanical energy, to demonstrate that the Rayleigh-Taylor instability is arrested in two ways that are unique to the cabbeling regime. Our results have implications for radiatively driven, under-ice flows in late winter during which ice prevents mechanical driving by the wind. While our focus is on the freshwater setting, we extend the derivation of the strong cabbeling potential to heat-salt systems, thereby extending its usefulness to the broader community.

Relaxation of the turbulent momentum and passive scalar fields generated by a specific staggered roughness distribution in the entrance region of an initially laminar channel flow is studied through direct numerical simulations. The computational domain is necessarily large, and a new and fast algorithm is introduced to efficiently resolve the flow characteristics. Staggered roughness elements of height 0.27 times the half width of the channel recover the entry zone either entirely or partly, prior to a smooth channel labeled as the control channel (CC) wherein both the turbulent flow and scalar fields decay, because the Karman number is significantly low and it is close to the subcritical limit. Despite the low Reynolds numbers, the roughness elements are able to trigger the bypass transition mechanism leading to massive clusters of coherent quasistreamwise vortices entering into the smooth channel. The characteristics of the turbulence decay at the CC centerline collapse reasonably well with those of a homogeneous isotropic turbulence. The inner layer responds relatively rapidly to the rough-smooth step change in the control channel while the outer layer recovery is gradual. The decays of the fluctuating streamwise velocity and of the passive scalar intensities are particularly slow. Despite the fact that the turbulent activity decreases and that the flow approaches the relaminarization, the Nusselt number averaged over large streamwise distances in the smooth channel remains close to an equivalent fully developed turbulent smooth-channel flow.

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.