Liquid-fueled detonative flows involve heavily coupled droplet breakup, phase transition, and chemical heat release over extremely short timescales. In rotating detonation engines and related high-speed propulsion systems, whether liquid fuel remains coupled to the leading wave depends not only on droplet size or Weber number, but also on the total work extractable imposed by the compressible flow and the timescale over which vapor becomes available. This work develops a regime diagram for droplet dynamics in shock-driven and detonative environments using two dimensionless groups: a thermodynamic-load coordinate, which measures the ability of the surrounding gas to drive droplet disintegration, and a timescale ratio, which compares phase-change and aerodynamic-response rates. The diagram is constructed using physically based criteria for aerodynamic breakup, compressibility effects, and transcritical or supercritical interfacial behavior. Recent shock-droplet interaction experiments, liquid-fueled detonation studies, and rotating detonation engine data are mapped onto this framework. The resulting classification shows that water droplets generally remain in breakup-dominated regimes, whereas hydrocarbon fuels more readily enter compressible and supercritical-transition regimes where rapid vapor release can couple with detonation heat release. For liquid-fueled rotating detonations, sustained operation is favored when strong thermodynamic loading is combined with phase-change rates fast enough to synchronize vapor production with the wave cycle. The diagram provides a unified interpretation of breakup, vaporization, and sustained two-phase detonation, while highlighting the need for phase-change models valid across all the possible thermodynamic conditions.

We theoretically investigate the equilibrium state of a surfactant-laden liquid column subjected to a weak uniform transverse electric field within the framework of the Taylor-Melcher leaky dielectric theory in the Stokes-flow regime. Our second-order perturbation analysis yields an analytical expression for the deformation parameter $D$. The solution reveals that the uniform surfactant coverage ${\mathrm{\Gamma }}_0^{*}$ (normalized by the maximum packing concentration) and the elasticity number $E$—which quantifies the sensitivity of interfacial tension to surfactant coverage—modulate the steady-state deformation indirectly through the electric capillary number ${\widetilde{\mathrm{Ca}}}_E$, defined as the ratio of electric forces to the surfactant-modified interfacial tension. In contrast, the surface Péclet number ${\mathrm{Pe}}_s$ (the relative importance of convection to diffusion in surfactant transport) and the effective Boussinesq number $B_{\infty }$ (the ratio of surface to bulk viscous stresses) do not influence the steady-state deformation up to $O\left({\widetilde{\mathrm{Ca}}}_E^2\right)$. Owing to the cylindrical geometry, surface dilatational and shear viscosities yield identical dynamic responses, and their combined rheological effects can be lumped into an effective interfacial tension. Our parametric analysis shows that all surfactant-related dimensionless parameters (${\mathrm{\Gamma }}_0^{*}, E, {\mathrm{Pe}}_s$, and $B_{\infty }$) significantly modulate interfacial properties and bulk flow circulation. Specifically, increasing ${\mathrm{\Gamma }}_0^{*}$ or $E$ enhances deformation; decreasing ${\mathrm{Pe}}_s$ homogenizes the surfactant distribution, thereby suppressing Marangoni stress and strengthening flow circulation; and increasing $B_{\infty }$ attenuates circulatory motion. This work provides insights into the distinct roles of surfactant-mediated mechanisms in the steady electrodeformation of transversely electrified liquid columns, laying a solid theoretical foundation for understanding the behavior of surfactant-laden columns and jets in electric-field-based engineering processes.

The linear modal and nonmodal stability of plane Poiseuille flow of supercritical water (SCW) with pronounced nonideal property variations is investigated. Strong variations in thermodynamic properties near the pseudocritical region are coupled using the approach developed by Ren et al. [J. Fluid Mech. 859, 89 (2019)] for supercritical ${\mathrm{CO}}_2$. The parameter space governing nonideal effects is spanned by the composite dimensionless parameter $\mathrm{PrEc}$, which characterizes viscous heating intensity, together with the thermal boundary condition $T_w^{*}$. Compared with previous results for supercritical ${\mathrm{CO}}_2$, SCW displays distinct modifications in neutral curve topology within the transcritical regime of nonideal parameter space, including a three-stage evolution of the envelope with increasing $\mathrm{PrEc}$ and the emergence of isolated island branches. In the sub- and supercritical regimes, the deviation of the two-dimensional critical Reynolds number from the isothermal value follows an approximate power-law dependence on $\mathrm{PrEc}$. Nonmodal analysis indicates that the classical small-$\alpha$ scaling between the rescaled maximum transient growth ${\overline{G}}_{max}$ and $(k^2,\alpha \mathrm{Re})$ remains applicable in nonideal regimes, and this behavior is examined over a wide Reynolds-number range. Transient energy budget analysis further reveals that nonideal effects do not alter the underlying shear-driven lift-up mechanism but redistribute energy among production, thermodynamic, and viscous channels. The results provide a systematic stability map for SCW channel flows and offer quantitative benchmarks for assessing nonideal effects in linear stability analyses of nonideal fluid systems.

Taylor-Aris and generalized Taylor dispersion theories characterize the long-time spreading reached after transverse homogenization in bounded shear. The present work considers the preasymptotic approach to that regime for anisotropic microstructures transported through finite channels with non-Newtonian carriers. We use an established single-exponential memory closure to connect the exact short-time sampled-velocity variance with the long-time Taylor enhancement, and carry this reduction into bounded shear with varying transverse geometry, non-Newtonian rheology, and Brownian orientational dynamics. For scalar unit-reference problems with invariant release, the ratio of these two anchors defines the integral correlation time whenever sampled-velocity memory is governed by one slow mode. For the reduced rod problem, the same construction is used as a Green-Kubo-motivated two-anchor approximation to the dominant shear-generated contribution under a uniform but generally nonequilibrium transverse injection. Exact spectral solutions for isotropic dispersion in plane and circular power-law Poiseuille geometries and Newtonian Brownian-rod calculations with independently supplied rod generalized Taylor dispersion coefficients provide controlled benchmarks for this extension. Applied to a reduced Brownian-rod model in power-law channels, the carrier rheology enters through the imposed velocity and shear fields while the reference particle-scale diffusivities remain fixed. Lattice Boltzmann simulations of the corresponding anisotropic advection-diffusion equation retain the full tensorial direct-diffusion contribution and resolve the transient moment evolution. Across flow indices and rotational Péclet numbers, alignment and rheology-dependent shear sampling shape the raw transients, and the reduced variables follow common master curves to the reported accuracy. The resulting characteristic and tolerance-based development measures connect the approach to Taylor transport with physical residence times and downstream lengths in finite channels.

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.