This work presents a fast and uncertainty-aware sequential data assimilation framework suitable for estimation of key aerodynamic states (e.g., instantaneous vorticity fields and aerodynamic loads) during severe gust encounters, where vortex-gust interactions strongly affect the flow dynamics. The framework comprises an ensemble Kalman filter (EnKF), designed to detect and reconstruct nearly impulsive flow disturbances with a wide range of strengths and orientations and introduced at arbitrary times. The forecast and measurement update (analysis) stages of the EnKF are each composed of learned operators in a low-dimensional latent space, obtained via a physics-augmented autoencoder. The forecast operator propagates the undisturbed baseline dynamics, but cannot predict random gust-induced deviations from these dynamics. Thus, the analysis stage frequently assimilates new surface pressure measurements to listen for disturbance signals and initiate deviation from the nominal trajectory. The methodology is trained and tested on flowfield snapshots from high-fidelity simulations of two-dimensional airfoil-gust encounters and corresponding sparse surface pressure data. Because assimilation occurs entirely within the reduced-order latent space, the updates are computationally efficient and ensure that aerodynamic states can be continuously estimated from streaming pressure data. The estimated instantaneous latent state remains physically interpretable via decoding to the original high-dimensional flow. Eigenvalue decomposition of the state and observation Gramians in the measurement update stage reveals the dominant correction directions necessary to capture the flow disturbance and quantifies how sensors inform the state corrections throughout gust interaction. The framework readily accounts for sensor failure; sensor dropout experiments show that the EnKF adaptively reweights neighboring sensors to compensate for lost information, preserving estimation quality even under degraded sensing configurations.

The complex dynamics of high-dimensional oscillatory flows can be simplified using phase-reduction analysis, providing a deeper understanding of the flow response to external perturbations. Although phase-based modeling and analysis have been utilized in recent studies on oscillatory fluid flows, their usage is often limited to single-frequency flows due to difficulties in addressing chaotic characteristics, emerging from multiple dominant frequencies with broadband spectra in turbulent flows. In order to overcome this limitation, we propose a data-driven framework that models the dynamics of turbulent flows with multiple dominant frequencies based on a set of oscillators. The representative oscillators are extracted from the flow field data by training specially designed autoencoders. The oscillator dynamics are modeled through a machine-learning technique using neural networks to accurately predict the multifrequency oscillatory behavior of turbulent flows. We verify the oscillator-based model of the oscillatory turbulent flows by applying the proposed data-driven method to the three-dimensional supersonic turbulent flow over a cavity. We show that the oscillators extracted from the spanwise-averaged pressure field represent the dominant large-scale flow features and reflect the physical characteristics of the turbulent cavity flow. The data-driven oscillator dynamics model with observation-based correction accurately forecasts the oscillatory behavior of the turbulent cavity flow for a long period. The proposed data-driven method for reduced-order modeling of turbulent flows with oscillators will enable deeper investigations of perturbation dynamics and control of turbulent flows.

This work investigates the impact dynamics of multicomponent droplets undergoing liquid-liquid phase separation upon impact on a water pool. Using a ternary ethanol-trans-anethole-water system, a classical Ouzo-type system, we show that rapid solvent exchange and delayed oil precipitation generate a dynamically evolving heterogeneous interfacial layer that strongly modifies cavity collapse and jet formation. Ethanol rapidly diffuses into the pool, whereas trans-anethole precipitates as oil-rich microdroplets once the local composition enters the Ouzo regime. While the early cavity expansion remains inertia-dominated, the subsequent collapse exhibits a two-stage relaxation process because phase-separation-induced interfacial roughness, Marangoni stresses, and viscous relaxation suppress coherent capillary-wave focusing. Jet formation is therefore not controlled by impact inertia alone: increasing impact inertia can amplify interfacial disorder and reduce the efficiency with which cavity-collapse motion is converted into an axial jet. We further show that the size of droplets emitted from the Worthington jet is selected primarily during inertial jet formation rather than during the final pinch-off. By introducing a jet Weber number based on the jet velocity and the effective interfacial tension, we obtain a unified scaling for the emitted droplet size. The final breakup of the already formed jet remains consistent with inertial-capillary necking, whereas the macroscopic droplet-size selection is governed by how phase separation reshapes cavity collapse and inertial focusing. These findings not only advance the fundamental understanding of multicomponent impact flows but also offer valuable insights for predicting jetting behaviors in industrial scenarios.

In this work, we first propose a diffuse-interface model for simulating immiscible N-phase flows with solid-liquid phase change. In this model, a phase-field approach is adopted to capture multiphase fluid interfaces, and an enthalpy-based formulation is used to describe the phase change. The volume changes resulting from density differences during phase change are incorporated by introducing a source term into the continuity equation. The method also satisfies the reduction-consistent property, allowing it to rigorously degenerate to both the conservative phase-field method for N-phase flows and the classical enthalpy method for solid-liquid phase change. Then, a coupled lattice Boltzmann (LB) method is developed to solve this diffuse-interface model. Some numerical tests, including film freezing, single droplet freezing, and compound droplet freezing, are performed, and the results are in good agreement with the analytical solutions and data reported in the previous works. Furthermore, the proposed method is applied to study freezing dynamics of complex systems with insoluble impurities, capturing the interaction between the advancing freezing front and embedded impurities. It is found that the proposed diffuse-interface method is accurate and efficient for studying N-phase systems with phase change.

Physics-informed neural networks (PINNs), a scientific machine learning framework for solving inverse and forward problems involving partial differential equations, are seeing many successes in fluid research recently. Based on PINNs, this paper develops a physics-informed framework for reconstructing incompressible Reynolds-averaged Navier-Stokes solutions from boundary data through the incorporation of Reynolds stress transport (RST) formulations without introducing empirical models for the unclosed terms. Specifically, the RST equations are first formulated with the exact forms for the advection and production terms as derived from the Reynolds averaging process while the unclosed terms that need empirical modeling in traditional turbulence models are absorbed into a single inadequacy term. The resulting underdetermined systems are then embedded via the PINNs approach to reconstruct turbulent flow fields based on the mean velocity components and Reynolds stress components at the domain boundary. A mechanism of enforcing the realizability condition for the Reynolds stress is further proposed to enhance the reconstruction performance, via a customized neural network design. The proposed approach is applied and evaluated via a set of flow cases, including a zero-pressure-gradient turbulent boundary layer flow, an adverse-pressure-gradient turbulent boundary layer flow, and a set of flow cases over periodic hills of parameterized geometries. The results show that for all the test flow cases, the mean flow quantities are reconstructed very accurately, and a decent accuracy is obtained for the turbulence quantities including both the normal and shear Reynolds stress components.

We develop a deep reinforcement learning framework for controlling a bio-inspired jellyfish swimmer to navigate complex fluid environments with obstacles. While existing deep reinforcement leaning frameworks for underwater navigation often use only kinematic and geometric state representations (e.g., position, orientation, velocity, and proximity distances), a key challenge remains in achieving efficient obstacle avoidance under strong fluid-structure interactions and near-wall effects. We augment the agent's state representation within a soft actor-critic algorithm to include the real-time forces and torque experienced by the swimmer, providing direct mechanical feedback from vortex-wall interactions. A path-planning module supplies a local pilot point along the computed shortest path to guide the swimmer, reducing the navigation task to reaching a nearby target while avoiding obstacles. This augmented state space enables the swimmer to perceive and interpret wall proximity and orientation through distinct hydrodynamic force signatures. We analyze how these force and torque patterns, generated by walls at different positions influence the swimmer's decision-making policy. Comparative experiments with a baseline model without force feedback demonstrate that the present one with force feedback achieves higher navigation efficiency in two-dimensional obstacle-avoidance tasks. The results show that explicit force feedback facilitates earlier, smoother maneuvers and enables the exploitation of wall effects for efficient turning behaviors. With an application to autonomous cave mapping, this work underscores the critical role of direct mechanical feedback in the reinforcement learning framework for improving navigation within complex fluid environments.

Existing literature reports inconsistent trends in the peak impact load (increasing, decreasing, or nonmonotonic) with plate size during flat-plate water entry. A prevailing view has long held that smaller plates experience higher peak loads due to reduced air entrapment, which weakens the buffering effect, an interpretation that remains qualitative and unverified. In this paper, the influence of plate size on peak impact load and the air cushioning dynamics are numerically investigated using both 2D and 3D models. Contrary to conventional expectations, we find that as plate size decreases, the entrapped air volume (both total and per unit impact area) reduces, yet the peak impact load, quantified by maximum slamming and pressure coefficients, also decreases monotonically. To elucidate the underlying mechanism, the compression dynamics of air layer, which physically govern the peak load, are analyzed via a control-volume framework bounded by the plate bottom and the free surface underneath. The analysis reveals that the air compression is dictated by two competing processes: contraction of the control volume and air outflow through the control surface (i.e., peripheral gaps). The former promotes air compression, whereas the latter mitigates it. As plate size decreases, both processes intensify; critically, the markedly enhanced air escape dominates, thereby attenuating the net compression of air layer and leading to a monotonic reduction in the peak impact load.

Capillary forces are commonly regarded as an energetically closed channel in multiphase turbulence, redistributing kinetic energy across scales without net gain or loss. Here, we show that this picture breaks down in bubble-laden turbulence when short-range near-contact interactions are active. A spectral analysis of the kinetic-energy budget reveals that the cumulative capillary power does not vanish at statistical stationarity, but instead retains a finite negative residual. This apparent imbalance is exactly compensated by the work of short-range repulsive forces, which is negligible at large and intermediate scales and becomes positive only at small scales. Near-contact interactions therefore open a distinct small-scale pathway in the interfacial energy transfer, rather than acting as a mere regularization of unresolved thin films. The proper scale-by-scale description is thus an extended interfacial transfer, combining capillary and near-contact work, rather than a purely capillary one.

The influence of free-stream conicity on flow over a slender sharp cone was investigated. A unified parameter $d$, relating to the degree of freestream conicity, is defined; both theoretical analysis and numerical simulation were conducted for a range of flow conditions. Results show that conicity can strongly alter surface pressure, boundary-layer thickness, edge density, and wall heat flux compared to parallel flow, while the shock shape is less sensitive. Inviscid analysis reveals that the conicity response is governed by the hypersonic similarity parameter $K$ and streamwise coordinate $S$; normalized distributions for identical $K$ collapse into the same curve, indicating that conicity acts primarily as a streamwise scaling. At high Mach numbers, strong viscous interaction modifies the effective body shape and degrades the accuracy of analytical predictions, disrupting the scaling collapse. Thermochemical nonequilibrium has a minor effect on conicity corrections, although species distributions do not follow the scaling because they are controlled by finite-rate chemistry. Empirical transition assessment shows that conicity can delay or even suppress transition by increasing the transition Reynolds number and reducing the local edge Reynolds number. Since large conicity significantly affects the flow over slender cones, it is essential to first quantify the conicity level in experiments. If the conicity is non-negligible, its effects must be accounted for; when strong viscous interaction invalidates analytical scaling, CFD corrections should be introduced. The conicity metric is not restricted to conical nozzles and can be extended to other divergent free streams using the Mach number gradient.

The differential equations describing the self-similar profiles of velocity moments in turbulent round jets are investigated by the Lie-symmetry method. From this, solutions are constructed, which depend on free functions. Truncated Taylor expansion of the free functions yields expressions for the profiles. If the Taylor expansion is truncated after the leading term, the classical Gaussian profile for the mean velocity is recovered, constituting the first rigorous derivation of this well-known empirical result. Comparison to DNS data shows good agreement of the derived expressions with the actual profiles.

The primary instability of the wake behind a two-dimensional freely falling circular cylinder is investigated. Numerical simulations are carried out by using the arbitrary Lagrangian-Eulerian (ALE) lattice Boltzmann flux solver, with which the critical Reynolds number ${\mathrm{Re}}_{cr}$ for the Hopf bifurcation is identified. Results show that ${\mathrm{Re}}_{cr}$ decreases from 46.1 for a fixed circular cylinder to approximately 42.3 for a light freely falling body with the density ratio of ${\rho }^{*}=1.01$. A series of stability analyses for various degree of freedom (DOF) combinations are performed, indicating that the streamwise degree of freedom exerts marginal effects on the primary instability of the wake, whereas the transverse motion can significantly destabilize the wake. In contrast, the rotational motion exhibits a stabilizing effect, thereby increasing the critical Reynolds number ${\mathrm{Re}}_{cr}$. It is also demonstrated that, as the density ratio increases, the primary instability characteristics gradually converge to those of the fixed circular cylinder, confirming that the larger inertia weakens the structural mobility. Finally, the underlying mechanism is interpreted through the maximum energy of the perturbation velocity $k_{\max }$, which gives a robust scaling law to quantify the primary instability of the wake.

Active wing deformation in natural organisms provides remarkable maneuverability in complex environments. While numerous studies have examined bioinspired morphing mechanisms, relatively few have systematically compared the principal morphing strategies employed across biological flight and swimming. This study investigates and compares the wake structures and force dynamics associated with fundamental structure-deforming submodes in biological wing motion. Five principal morphing submodes, including pitching, bending, extending, flapping, and twisting, are examined to characterize their aerodynamic performance. The results reveal unique frequency-dependent lift enhancements, where the bending mode provides superior lift at lower frequencies, while the pitching and twisting modes become more effective in lift enhancement at higher frequencies. However, drag remains relatively insensitive to frequency variations in both the bending and extending modes. The dynamic spectra exhibit prominent peaks at deformation frequencies and their harmonics, indicating strong structural implications on flow dynamics. As the deformation frequency approaches the flow passing frequency, the flow dynamics begin to be locked, leading to vortex uniformity and homogenization of the dynamic forces. These effects arise because structural morphing stabilizes vortex shedding, thereby suppressing the formation of secondary, irregular vortices. The wake modal analysis further indicates that the generation of leading-edge vortices leads to lift enhancement, and their reattachment to the wing surface tends to suppress lift burr-fluctuation. Furthermore, the superposition of specific submodes effectively enhances lift without increasing drag, providing new strategies for the design and control of future actively deforming airfoils.

Zero-pressure-gradient boundary layers over high-skewness surfaces are studied via direct numerical simulations (DNS) in computational domains of up to $135\delta$ long with friction Reynolds numbers up to ${\text{Re}}_{\tau }\approx 4500$. Monoculture and multiculture biofouling-type surfaces were utilized at a planar solidity of approximately ${\lambda }_p\approx 40\%$. It is found that both the evolution of the main boundary layer quantities, as well as of the total drag, scale with the mean roughness height, $\overline{h}$, regardless of the roughness element shape and distribution. The same conclusions are made with respect to the roughness function $\mathrm{\Delta }{U}^{+}$. The outer-layer similarity is also investigated under different scalings and verified in both the first- and second-order turbulence statistics. Furthermore, the roughness impact on the flow dynamics in both a quantitative and qualitative manner is also explored by means of quadrant analysis. Finally, an attempt is made toward adapting the Schlichting's boundary layer equations for rough walls through a height-based occupancy ratio, that successfully captures most of the DNS-expected boundary layer evolutions.

The accidental release of ship fuel oils has been responsible for coupled environmental, economic, and engineering challenges. In marine oil-spill response, fluid-mechanical considerations are crucial for predicting spreading, entrainment, emulsification, adhesion, recovery, and transport. However, many practical countermeasures remain industry-driven and are only weakly connected to academic advances in multiphase flows, in particular, interfacial phenomena and rheology. This gap has become more critical after IMO 2020, as the low-sulfur fuel oil (LSFO) has been widely adopted. Compared with conventional heavy fuel oils, LSFO exhibits distinct composition-dependent rheology and interfacial behavior, including strong temperature sensitivity, wax-related viscosity increase, and partial solidification. The MV Wakashio spill in 2020 highlighted the limitations of conventional remediation methods for such fuels. This perspective reviews the compositional and rheological differences between conventional fuels and LSFOs, while focusing on fluid-dynamic challenges across stages ranging from spreading prediction to transport for onshore storage. We further discuss future opportunities, including AI-assisted methods and multiphase-flow strategies for improving recovery robustness and transport efficiency.

Pairwise hydrodynamic interactions of microswimmers form the fundamental building blocks for understanding their more complex collective behaviors. In this work we revisit the canonical problem of two interacting squirmers swimming along their common line of centers in both Newtonian and shear-thinning fluids. For the Newtonian case, we first derive an exact, closed-form solution for the axisymmetric Stokes flow generated by the interacting pair, thereby complementing prior analyses based on the reciprocal theorem approach by providing direct access to the detailed knowledge of the flow around the swimmers. The analytical solution is then used to cross-validate numerical simulations based on the finite element method. The combined theoretical and numerical investigation reveals coswimming configurations in which the two squirmers develop identical velocities over a range of separations. We rationalize these behaviors through symmetry arguments and quantify their propulsion performance in terms of the speed and energetic cost of swimming. Furthermore, motivated by the prevalence of shear-thinning biological fluids encountered by microswimmers, we examine how this ubiquitous non-Newtonian rheological behavior modifies the propulsion characteristics of these coswimming pairs. Taken together, our results provide a systematic characterization of an idealized model of pairwise squirmer interactions in Newtonian and shear-thinning fluids, establishing quantitative benchmarks for future studies of more complex and realistic swimmer configurations.

The deposition of a viscoplastic fluid onto a substrate can be achieved by moving apart two plates initially separated by a fluid-filled gap, where the footprint shape depends on the initiation of a fingering instability. Here, we present an approach for controlled deposition of a viscoplastic fluid by designing the macroscopic structure of the solid substrate. Through experiments in a lifted Hele-Shaw cell, we explore how slot, square, pyramid, and triangular patterns affect the dynamics of liquid deposition. The substrate structures directly control the symmetry and final shape of the deposited viscoplastic footprint, while having little systematic influence on the maximal normal adhesive force or on the force-gap scaling exponents once the total entrapped volume is accounted for through an effective initial gap. We develop a scaling description for the normal force of a Herschel–Bulkley fluid, showing that the measured force decay reflects a superposition of capillary, yield stress, and viscous contributions. For experiments producing stable patterning, the measured effective exponents are consistent with the theoretical range predicted by this model. Finally, we interpret the pattern-selection mechanism through a dynamical permeability analysis where the substrate texture creates an anisotropic permeability field whose angular maxima correlate with the preferred inward propagation directions of the invading air. Our results highlight a direct link between substrate geometry, interfacial dynamics, and the final deposited morphology, showing how millimetric deposition patterns can be programed using submillimetric surface structures.

Vortex stretching is a fundamental aspect of Navier-Stokes turbulence and is commonly understood in analogy to the stretching of infinitesimal material lines. However, the parallel alignment of material lines and vorticity cannot be maintained due to the role of viscosity in the directional realignment of vorticity. In Navier-Stokes turbulence, the result is relatively modest quantitative differences in the alignment and stretching rates of vorticity compared to material lines. In this study, the qualitative effect of viscous tilting of vorticity is demonstrated directly by surgically removing it from direct numerical simulations of isotropic turbulence. The result is a drastic change to the fundamental structure of the flow, including a substantial deviation from the −5/3 inertial range scaling of the energy spectrum brought about by the infiltration and prevalence of viscous effects beyond the smallest scales. These observations demonstrate that the viscous tilting of vorticity is an essential characteristic of fluid turbulence. By extension, the same may be said of the difference in orientation and stretching rates for vorticity and infinitesimal material lines.

The continuous, constant-influx release of a dense fluid into a lighter one is investigated via a direct numerical simulation study. The heavier fluid forms a gravity current that propagates along the horizontal bottom of a rectangular domain. The effect of the turbulent entrainment of the lighter ambient fluid into the gravity current on the mean flow dynamics is examined. The unsteady gravity current is horizontally divided into three regions with distinct entrainment characteristics: the hydraulic jump, the body, and the head. Classical entrainment hypotheses, originally developed for steady continuous currents, successfully model the entrainment mechanism of the unsteady continuous current along the hydraulic jumps. Downstream, along the body region and specifically in the wake of the head, the effects of billows shedding from the head preclude the applicability of the classical theory. Investigating the depth-averaged flow properties along the current reveals how its dynamics deviate from standard entrainment hypotheses. The relationship between the bulk entrainment coefficient across the hydraulic jump and the source properties is examined.

Direct Numerical Simulations (DNS) of premixed hydrogen-air flames anchored in a fully developed turbulent channel flow (TCF) are performed at a friction Reynolds number of ${\mathrm{Re}}_{\tau }=530$ and thermochemical conditions susceptible to the emergence of intrinsic thermodiffusive (TD) phenomena acting on the turbulent flame. Two premixed flames are studied: a slower flame ($\phi =0.25$), predominantly propagating within the core flow, and a faster one ($\phi =0.35$), reaching closer to the channel walls and intermittently quenching on it. The present DNS database provides new insights into the characteristics of premixed flames susceptible to TD phenomena and propagating in realistic near-wall shear turbulence. The influence of varying turbulence intensity, and of wall-distance dependent time and length scales, on the flame propagation characteristics is evaluated through a detailed analysis of the local stretch factor $I_0$, quantifying reactivity enhancements caused by TD phenomena. At $\phi =0.25$, the flame response to the fluid motions is mainly forced by the weaker turbulence present in the core flow. This results in an augmented $I_0$ compared to the laminar reference value, suggesting reactivity enhancement by the strongly nonlinear interaction of TD phenomena with (relatively) weak turbulent motions present within the core flow. At $\phi =0.35$, as the flame propagates from the core flow towards the channel walls, the flame response is forced by turbulence of increasing intensity, resulting in a corresponding augmentation of the Karlovitz number. Crucially, as the flame propagates into the near-wall region, the peak value of $I_0$ is colocated with the peak Reynolds stresses ($y^{+}\sim 10$). This observation suggests a strong (local) synergistic interaction between TD phenomena and wall turbulence, ultimately resulting in significantly enhanced flame speed.