The nonlinear evolution of multimode Rayleigh–Taylor (RT) mixing plays a crucial role in numerous natural phenomena and engineering applications, yet accurate characterization of its small-scale dynamics is severely restricted by limited spatial resolution in experiments and simulations. This resolution constraint motivates the development of superresolution (SR) techniques to reconstruct high-frequency flow features from coarsely resolved data. In this study, direct numerical simulations reveal that while horizontally averaged profiles and integral mixing width remain largely insensitive to resolution degradation, fluctuation variance ${\sigma }^2$ decreases sharply once grid spacing exceeds the interfacial thickness, resulting in systematic overestimation of mixedness $\theta$. To recover the lost multiscale information, we develop three convolutional neural network (CNN)-based superresolution models within a unified framework: a baseline CNN architecture, a residual-block variant (Res), and a physically conditional residual variant $(\text{Re}\mathrm{s}+\mathrm{h})$. These models substantially outperform bicubic interpolation. For spatial $\times 4$ and $\times 8$ upscaling of flows with varying initial perturbation phases, the CNN-based approaches reduce relative $L_1$ errors from 6.3% to 0.41% $(\times 4)$ and from 15.1% to approximately 4.5% $(\times 8)$. Furthermore, models trained solely on initial perturbation phase variations exhibit strong generalization to unseen perturbation amplitudes, interface thicknesses, and Reynolds numbers, maintaining high fidelity for the $\times 4$ SR task across parameter space. For the more demanding $\times 8$ task, minor oversharpening and spurious small-scale structures appear under certain conditions. These artifacts are effectively suppressed by enriching the training set with additional cases spanning amplitudes, thicknesses, and Reynolds numbers. These results highlight the strong potential of physics-informed machine learning approaches for exploring more complex three-dimensional RT mixing problems.

Near-surface turbulent flows beneath a free surface are reconstructed from sparse measurements of the surface height variation, by a neural network algorithm known as the SHallow REcurrent Decoder (SHRED). The reconstruction of turbulent flow fields from limited, partial, or indirect measurements remains a grand challenge in science and engineering. The central goal in such applications is to leverage easy-to-measure proxy variables in order to estimate quantities which have not been, and perhaps cannot in practice be, measured. In the application considered here, the aim is to use a sparse number of surface height point measurements of a flow field, or drone video footage of surface features, in order to infer the turbulent flow field beneath the surface. SHRED is a deep learning architecture that learns a delay-coordinate embedding from a few surface height (point) sensors and maps it, via a shallow decoder trained in a compressed basis, to full subsurface fields, enabling fast, robust training from minimal data. We demonstrate the SHRED sensing architecture on two types of turbulent data from recent studies [Aarnes et al. J. Fluid Mech. 1007, A38 (2025) and Babiker et al. Phys. Rev. Fluids 11, 054802 (2026), respectively]: fully resolved DNS data and PIV laboratory data from a turbulent water tank. SHRED is capable of robustly mapping surface height fluctuations to full-state flow fields up to about one integral length scale deep, with as few as three surface measurements.

Capillary retraction of liquid ligaments is well understood for Newtonian fluids, whereas viscoplastic effects remain comparatively unexplored. Here, we consider Herschel-Bulkley fluids, which incorporate both yield stress and shear-rate-dependent viscosity, thereby introducing a spatially varying effective viscosity that is absent in simpler yield-stress models (e.g., Bingham models). We focus on the low-viscosity regime, where droplet detachment in Newtonian fluids is controlled by the end-pinching mechanism. Using fully resolved axisymmetric simulations, we show that viscoplasticity and shear-rate-dependent rheology reorganize the routes by which a retracting ligament may pinch off, escape breakup, or stay motionless due to large yield stress. We identify two distinct routes by which a retracting Herschel-Bulkley ligament can escape end-pinching. In the shear-thickening regime, increased local viscosity during neck thinning leads to larger vorticity detachment from the curved neck, which opposes the capillary singularity. In the strongly shear-thinning regime, reopening is governed by curvature-induced pressure gradients. We show that this latter mechanism persists in the Newtonian limit of vanishing viscosity, yielding a purely inertial-capillary pathway for reopening. While previous Newtonian studies report end-pinching down to Ohnesorge number ${\text{Oh}}_K\approx {10}^{-4}$, suggesting breakup as the asymptotic low-viscosity outcome (Anthony et al. [Phys. Rev. Fluids 4, 093601 (2019)]), our results demonstrate that a purely inertial-capillary reopening mechanism can arise as ${\text{Oh}}_K\to 0$, indicating that end-pinching is not the route in the inviscid limit.

Smectic bubbles as fluid structures with a huge surface-to-volume ratio represent unique examples of quasi-two-dimensional (2D) fluids. We investigate the behavior of islands, local regions with larger film thickness, in the presence of strong inhomogeneous electric fields. The islands, which can be considered here as 2D analogs of liquid droplets, become charged and are repelled by a needle-shaped electrode in contact with the film. The mechanism has strong similarities to electrospraying and electrospinning, but because of the constraint of the thin film, the motion is confined to the film plane. Interestingly, the phenomenon depends on the polarity of the electric field. This indicates that the charging of the islands is related to the asymmetric ion mobilities in the film material. To prevent sedimentation of the islands, the experiments were performed under microgravity conditions on parabolic flights.

The interaction between a single water droplet and a lean premixed hydrogen-air flame is investigated using two-dimensional detailed-chemistry simulations in an Eulerian-Lagrangian framework. A single cusp flame configuration is employed to impose a controllable curvature to the flame and isolate the effects of droplet-induced stretch. When the water droplet evolves in an inertia-dominated regime, it acts as a localized momentum and heat sink, generating a transient deformation of the flame front and a reduction in the local displacement speed. It is observed that curvature gradient generated by the droplet-flame interaction, contributes to the decrease in flame speed and heat release rate by reducing the reactants focusing effect. This result is confirmed by comparison with an equivalent simulation performed under a unity Lewis number assumption, where curvature-induced differential diffusion effects are artificially suppressed. The analysis of droplet-induced stretch further shows that the interaction produces a local curvature inversion of approximately $40\%$ of the initial flame shape, while the tangential strain rate component of stretch increases and counteracts this effect. After the interaction, the flame gradually recovers its original shape, and the curvature perturbation decays exponentially with a restoring time governed by the flame diffusion timescale. An analytical model using an analogy with a mass-spring-damper system is proposed to estimate the local flame displacement and displacement speed during the droplet-flame interaction.

Wake-induced lift is a key mechanism governing the initial destabilization of bubbles rising in a chain [Atasi et al., Phys. Rev. Fluids 8, 053601 (2023)]. Moore's wake model predicts limited interfacial vorticity and a relatively slender, spatially confined wake for clean spherical bubbles, suggesting that wake-mediated interactions weaken as the interbubble spacing increases. However, we observed pronounced large-scale lateral dispersion and strong bubble frequency dependence in controlled experiments where bubble diameter and generation frequency were independently varied, even when the interbubble separation exceed the characteristic wake length. A reduced-order model incorporating pairwise wake-induced interactions captured the onset of bubble chain destabilization but systematically underpredicted the subsequent emergence of large-scale dispersion. We demonstrate that bubbles rising in a chain collectively generate a mean upward liquid flow that modifies the local shear field, enhancing the lateral migration through shear-induced lift. Incorporating this self-induced weak flow into the model quantitatively reproduced both the dispersion magnitude and its frequency dependence. These results suggest that the dispersion of bubbles rising in a chain involves a two-stage mechanism, with initial chain destabilization mediated by wake interactions, followed by flow modification arising from two-way coupling between bubbles and the liquid. This collective mechanism highlights the importance of self-induced mean flow effects in continuum descriptions of bubble flows.

When a bubble detaches, it produces a sound. While the frequency of this sound is well understood, there has been no consensus on what drives its amplitude. Although mechanisms based on shape oscillations, initial velocity of the bubble radius, neck collapse or Laplace pressure have been suggested, none of them has been confirmed experimentally. We performed experiments involving two methods of producing bubbles, which result in sound levels differing by two orders of magnitude. Our results show that the sound amplitude is given by the conditions of velocity and radius of the bubble at detachment, in line with the scenario of a free harmonic oscillator proposed by Strasberg in 1956. We refined this scenario by describing how the bubble radius velocity is affected by gas exchange though the closing neck. This “leaking bubble” model predicts that the bubble begins to produce sound prior to detachment, as observed experimentally. By feeding image analysis of the neck into the model, we obtained excellent agreement between the experimental and the calculated pressure signals.

Estimating collision rates is of immense importance in particle-laden flows. An economical way of doing this is to directly identify incidences of caustics, or extreme clustering, by tracking particle velocity gradients in the neighborhoods of individual particles. The objective of this work is twofold. (i) We find conditions under which caustics form in point-vortex flow and in two-dimensional turbulence. While caustics are known to form in regions of strain, we show that the velocity alignment with strain directions is key. Particles must remain in compressional strain throughout the process to form caustics, whereas survivor particles, which visit high strain but do not form caustics, briefly go through extensional strain during the early part of the process. This enables survivor particles to attain significantly straighter paths and to move faster, whereas caustics particles follow paths of high curvature and move slower. As a result, caustics particles stay longer in high-strain regions than survivors. (ii) We ask about the effect of finite particle density, where the particle is denser than the background fluid. We show that finite-density particles need to sample stronger background strain than infinite-density ones to trigger caustics, but our other findings are universal across particle density.

Classic turbulence models often struggle to accurately predict complex flows. Although data-driven techniques have addressed these shortcomings, most existing research has concentrated on two-dimensional (2D) cases. In this study, we bridge this gap by enhancing a data-driven turbulence model, the shear stress transport-conditioned (SST-CND) model, which was originally trained on 2D separated flows, in three-dimensional (3D) scenarios. An additional correction term ${\beta }_{3\text{D}}$ is introduced to account for 3D effects. The distribution of this term is determined through a 3D field inversion process using high-fidelity data obtained from the flow around a cube. An algebraic expression for ${\beta }_{3\text{D}}$ is then derived through symbolic regression and formulated to degrade to zero in 2D cases. The performance of the resulting SST-CND3D model is evaluated across a range of flows. In 2D flows, the SST-CND3D model performs identically to its 2D-trained predecessor. However, the model exhibits superior performance in 3D flows, such as the flow around the complex JAXA standard model high-lift configuration. These findings indicate that a sequential approach, constructing a 3D correction term that vanishes in 2D on top of a 2D-trained model, constitutes a promising method for developing data-driven turbulence models that perform accurately in 3D while preserving their effectiveness in 2D.

In this study, we investigate the drag regimes of acoustic liners in the absence of external acoustic excitation. Friction coefficients $C_{\text{f}}$ are estimated in a turbulent channel flow over a wide range of Reynolds numbers using mean pressure-drop measurements. Two main drag regimes are identified: a viscous regime and a transitional regime in which pressure drag becomes significant. Within the transitional regime, two distinct behaviors are observed. The first exhibits low to moderate $C_{\text{f}}$ increments relative to the smooth-wall reference, consistent with $d$-type roughness trends. The second exhibits large drag increases associated with the onset of aeroacoustic resonance at the liner resonance frequency, which significantly distorts the mean velocity profiles. Despite the one-decade range of Reynolds numbers investigated, no fully rough regime is reached, questioning current approaches to modeling acoustic liner drag. Finally, liner hierarchy in terms of $C_{\text{f}}$ within the transitional regime correlates satisfactorily with a geometric dimensionless parameter ${\lambda }_{\text{f}}$, analogous to the frontal solidity used in roughness studies, offering insight into the role of orifice geometry in liner drag.

In this Letter, we report on the self-sustained capillary flow of a liquid, which is approximately $1000000$ times more viscous than water, over a long-lasting period of time. The ultraslow flow is primarily driven by the negative curvature pressure sustained by the liquid meniscus that forms inside a horizontal capillary tube. The dynamics reveal a natural infiltration process with long-term diffusive behavior dictated by dominant bulk dissipation. In contrast, the early stages, although spanning more than 24 h of flow, show a clear dependence on the dissipation induced by the moving contact line. We embark on a 30-day experimental journey following the flow of a high-viscosity liquid through a capillary tube to assess how existing theoretical models, which also account for the dynamic nature of the contact angle, perform in long-term imbibition processes.

Wind turbines operating in the atmospheric boundary layer are constantly exposed to time-varying flow conditions. These disturbances often occur on similar timescales to wind-turbine controllers, which may interfere with wind-farm control strategies that operate under steady-flow assumptions. This study aims to investigate the significance of such time variations on wind-turbine wake dynamics, focusing on slow timescales representative of quasisteady processes in large wind farms. Experiments are conducted at high Reynolds numbers ($R{e}_D=4\times {10}^6$) in a pressurized-air wind tunnel, with a wind turbine forced in periodic rotation-rate oscillations by means of a time-varying generator torque at low Strouhal numbers ($St=0.04$). Flow measurements in the wake of the turbine demonstrate that disturbances propagate through the wake as traveling waves, which are advected nonlinearly at the velocity of the wake rather than that of the free stream. The wake behavior can be described in a quasisteady manner, but only after wake advection is accounted for by a Lagrangian transformation. Even in the quasisteady regime, the spatiotemporal evolution of the wake can be controlled by independently varying the turbine thrust and tip-speed ratio. The results suggest that wake advection is important to consider for wind-farm modeling and control, and that time-varying control may allow wind-turbine wake interactions to be tuned even in nominally quasisteady conditions for optimal wind-farm performance.

In this study, we investigate the influence of shear-thinning on the instability of a prototype time-periodic flow, the Stokes layer, in Carreau fluids. The time-dependent base flow was solved using a numerical method and a binomial expansion method. The expansion is conducted in terms of the nondimensional characteristic time ($\mathrm{\Lambda }$), which quantifies the fluid response time in viscosity to changes in shear rate. The expansion method shows good agreement with the numerical solution, provided that $\mathrm{\Lambda }$ remains small. To understand the effect of shear-thinning on time-periodic flow instability, a Floquet analysis was conducted to examine two key parameters of the Carreau model, i.e., $\mathrm{\Lambda }$ and the power-law exponent $n$. Our results show that decreasing $n$, which signifies stronger shear-thinning behavior, has a monotonic stabilizing effect on the flow within the range of investigated $n$. In contrast, increasing $\mathrm{\Lambda }$ has a nonmonotonic effect on the flow instability, which can be observed in both the weakly and strongly shear-thinning regimes. To clarify the instability mechanism, we perform an energy analysis showing that instability arises when the perturbation field is in phase with the oscillatory base flow, enabling efficient energy extraction from the time-dependent shear. A phase mismatch suppresses this transfer and stabilizes the flow. This mechanism parallels the classical energy-production process in steady shear flows, where streamwise and wall-normal velocity perturbations exhibit a characteristic phase difference. Crucially, it is identified here in a time-periodic shear flow.

Oscillatory flows in compliant confinements underpin processes ranging from physiological transport in blood vessels and airways to flow control and pumping in soft microfluidic devices. To understand the fundamental physics behind such processes, we study how hydrodynamic forces induce deformation at the fluid–solid interface in a slender two-dimensional (2D) channel bounded below by a rigid bottom surface and above by a slender elastic layer. The nonlinear coupling between flow and deformation, along with the attendant geometric asymmetry caused by flow-induced deformation, produces a streaming effect (a nonzero cycle-average despite time-periodic forcing). Surprisingly, flow inertia provides another nonlinear coupling, tightly connected to deformation, that enhances streaming, termed “elastoinertial rectification” by X. Zhang and B. Rallabandi [J. Fluid Mech. 996, A16 (2024)]. We adapt the latter theory of how two-way coupled fluid–structure interaction (FSI) produces streaming to a 2D rectangular configuration, specifically taking care to capture the deformations of the nearly incompressible slender elastic layer via the combined foundation model of T. G. J. Chandler and D. Vella [Proc. R. Soc. A 476, 20200551 (2020)]. We put this elastoinertial rectification theory to a stringent test against direct numerical simulations performed using a stabilized, conforming arbitrary Lagrangian–Eulerian (ALE) FSI formulation, implemented via the open-source computing platform FEniCS. We examine the axial variation of the cycle-averaged pressure as a function of key dimensionless groups of the problem: the Womersley number and the elastoviscous number. Assuming a small compliance number, we find excellent agreement between a perturbative calculation based on elastoinertial rectification theory and the simulations for both the leading-order and cycle-averaged pressure and deformation across a range of conditions. Finally, unlike previous literature, the combined foundation model also predicts nontrivial horizontal displacements in confined 2D layers, consistent with the simulations.

An experimental investigation was conducted on the wake of a rounded-edge slanted afterbody over a Reynolds number range of ${\mathrm{Re}}_D=40\mathrm{K}$ to ${\mathrm{Re}}_D=200\mathrm{K}$. High-speed particle image velocimetry (PIV), surface pressure measurements, and high-accuracy drag measurements provided substantial insight into this complex flow. In particular, they revealed an undocumented wake-state transition from a previously observed centerline-separated (CS) vortex state to a new centerline-attached (CA) vortex state between ${\mathrm{Re}}_D\approx 130\mathrm{K}$ and $180\mathrm{K}$. This wake transition was accompanied by a significant drag reduction and the transition of the upstream boundary layer from laminar to turbulent. The CS vortex state shared characteristics with laminar separation bubbles and produced spatially diffuse vortices that exhibited two distinct instabilities: a low-frequency flapping instability that governed the vortex dynamics and a high-frequency short-wave instability that drove shear layer breakdown and reattachment. The reduction in recirculation length was attributed to diminished viscous damping at higher Reynolds numbers, enabling earlier shear layer transition. In contrast, the CA state exhibited neither frequency signature and lacked a separated region, indicating a fundamentally different underlying dynamical mechanism. The vortices in the CA state were highly structured and spatially coherent, further distinguishing them from the diffuse and unsteady vortices observed in the CS state. These results provide new physical insight into the interplay between upstream boundary-layer transition, separated shear layer dynamics, wake topology, and their collective effect on global aerodynamics in terms of drag. Together, they provide a more comprehensive and unified understanding of the wake states and their transition between CS and CA for bluff body wakes.

One challenge in developing a statistical field theory of turbulence is the analysis of the functional equations that govern the complete statistics of the flow field. Simplified models of turbulence may help to develop such a statistical framework. Here we consider the advection and stretching of an incompressible passive vector field by a spatially linear stochastic field as a model for small-scale turbulence. The model encompasses non-Gaussian statistics due to an intermittent energy flux from large scales to small scales, thereby displaying hallmark features of turbulence. We explore this model using the Hopf functional formalism, which naturally leads to a decomposition of the complex non-Gaussian statistics into Gaussian subensembles based on different realizations of the advecting field. We then characterize intermittency of the model using a numerical implementation, which takes advantage of this statistical decomposition.

Interfacial deformation under electric fields is a common phenomenon in many industrial processes. Particularly, we are interested in the dynamics of sessile soap bubbles in a parallel-plate electric field which exhibits a stable deformation regime followed by conical instability. Using side-view imaging, we track the equilibrium shapes, the transition to the unstable regime, and the pre-jet apex dynamics within one experimental system. In the stable regime, the meridional profile is well described by an ellipsoid-of-revolution fit, and the aspect ratio collapses across initial bubble sizes onto a single steady-state branch when plotted against the dimensionless field $E^{*}=\sqrt{{\mathrm{Bo}}_e}$ for data acquired within a fixed ambient session where the electric Bond number ${\mathrm{Bo}}_e$ is defined as ${\varepsilon }_0{E}_0^2{R}_0/\left(2\gamma \right)$. The end point of this branch marks the transition to the unstable regime. Above the onset of instability, the apex sharpens into a cone with half-angle $30.0^{\circ } \pm 0.6^{\circ }$, below the classical Taylor value. We interpret this smaller angle as a dynamic pre-jet angle rather than as a modified static Taylor-cone angle. To quantify the late pre-jet stage, we define the axial distance $\ell \left(t\right)$ from the instantaneous apex to a fixed reference vertex determined from the terminal cone geometry and measure its evolution. The corresponding rate grows as jetting is approached, and a near-tip inertia-capillary model captures the observed logarithmic trend as an approximation. Together, these measurements establish a single-system experimental benchmark in which stable electrocapillary deformation is organized by a single steady-state branch that leads into conical instability and pre-jet dynamics.

The mixing dynamics of a coalescing sessile and impacting liquid droplet on a solid surface is studied numerically. The numerical simulations utilize the volume of fluid method coupled with an advection-diffusion equation to assess diffusive mixing within the droplets. The simulation methods are extensively validated against analytical and experimental results confirming their ability to capture diffusion in droplet systems. Using dimensions and properties relevant to inkjet printing systems, the timescale for droplet mixing in printing and other microfluidic applications that concern the impact and coalescence of droplets is determined. Results show little mixing occurs during the impact and relaxation of the printed droplets, with complete homogenization driven mainly by molecular diffusion over a much longer timescale than the impact. The effects of key printing parameters, including droplet size, printing separation and substrate wettability are explored to quantify their impact on droplet mixing times. Understanding the effect of these parameters on the timescale for droplet mixing gives potential avenues to enhance or suppress droplet mixing before the mechanisms of evaporation or curing become relevant.

This study investigates the wake dynamics and force responses of transversely rotating spheres in isolated and tandem configurations at moderate Reynolds numbers ($\text{Re}=100$, 300, 1000). Using direct numerical simulations of transitional and weakly turbulent flow, we explore how rotation rate ($\alpha =0–5$) and interbody spacing ($L_x=2D, 5D$; $D$ is sphere diameter) influence wake topology, vortex shedding, and fluid forces. At lower $\text{Re}$, rotation suppresses unsteadiness, inducing double-threaded vortical structures, whereas at higher $\text{Re}$, centrifugal effects destabilize shear layers, generating multiscale vortices and weakly turbulent wakes. In tandem configurations, wake-body interactions promote instabilities even when rotation stabilizes the isolated sphere wake. The force coefficients exhibit a nonmonotonic dependence on $\alpha$ due to competing effects of Magnus-induced pressure asymmetry, shear layer separation, and wake unsteadiness.