Papers

We use high-resolution, interface-resolved direct numerical simulations (DNS) to investigate the origin of Kolmogorov (K41) scaling in bubble-induced turbulence (BIT). Region-wise velocity structure functions show that the 2/3 scaling appears only within bubble wake regions. Comparison with matched single-bubble DNS further indicates that the K41 scaling observed in the full BIT field arises from the superposition of individual bubble wakes. On this basis, we derive a scaling for the dissipation rate in dilute BIT that is consistent with experimental results from the literature.

This is the first in a series of papers aimed at understanding the statistics of coalescing particles in turbulent flow and their relation to collisionless ghost particles. We perform three families of Direct Numerical Simulations (DNS) under identical flow conditions: ghost particles without mutual interactions; particles that coalesce upon collision with lost monomers replenished at random positions (CR); and particles with the same collision-coalescence kinetics without replenishment (CN). All analyses are monodisperse and concern only monomers. Across $St=0.01\text{-}3.0$, the ghost-particle system has higher collision kernels ($K$) and radial distribution functions (RDFs, $g(r)$) near contact than the coalescing systems. A velocity-filtered RDF, $g_{\mathrm{G}}^{(-)}(r)$, provides a reasonable estimate of the CR contact RDF, $g_{\mathrm{CR}}(d)$. We show that the residual discrepancy between $g_{\mathrm{G}}^{(-)}(d)$ and $g_{\mathrm{CR}}(d)$, and between the corresponding kernels, arises from correlations among successive collisions in the ghost-particle system. A history-filtered ghost-particle kernel, excluding such correlations, reproduces the coalescing-system kernel. We introduce a collision-correlation time $\tau_{\mathrm{cc}}$ that quantifies how long current collisions influence future events and find that it has a finite, narrow range across the studied $St$. Filtering particles with collisions within a period comparable to $\tau_{\mathrm{cc}}$ yields a history-filtered RDF that reproduces those of both coalescing systems. Finally, the fraction of repeated collisions involving identical particles decays exponentially with $St$. These results unify the coalescing and ghost-particle systems as a history-filtered framework.

We study radial nonlinear instability of compactly supported nonrotating equilibria of the three-dimensional Euler–Poisson system with a physical-vacuum boundary. Let $n^u(\mu)$ denote the radial instability index furnished by the turning-point theory of Lin and Zeng. Under general structural assumptions on the pressure law, suppose that $n^u(\mu)>0$ and that the equilibrium is not a mass extremum, $M'(\mu)\neq0$. Conditional on the existence of a sufficiently regular radial solution on the relevant time interval, we establish two nonlinear escape criteria. First, every perturbation with Hamiltonian strictly below that of the equilibrium exits a fixed neighborhood on a logarithmic time scale controlled by the least unstable linear growth rate. For the subclass of data for which the associated Lyapunov functional is initially nonnegative, we also obtain an explicit exponential lower bound in the weighted displacement norm. Second, sufficiently small perturbations whose Riesz projection onto the finite-dimensional unstable subspace is not too small escape on a logarithmic time scale. The second argument uses the exponential trichotomy of the linearized Hamiltonian flow and an invariant-cone estimate. In the polytropic class, the conditional estimates combine with the radial physical-vacuum local theory to yield unconditional nonlinear instability in the corresponding classical-solution topology. The results complement Jang's nonlinear instability theorem for Lane–Emden stars by treating mechanisms that do not require initial alignment with a leading growing eigenmode and by applying, conditionally, to unstable branches for general equations of state.

Adaptive loss-balancing schemes for physics-informed neural networks rest on a premise that every residual should be driven to zero. For level-set advection with an eikonal regulariser that premise fails: the eikonal term penalises deviation of $\lVert\nabla\phi\rVert$ from unity, a property transport preserves only under rigid motion; where the exact solution departs from a signed-distance function the eikonal residual of the correct answer is nonzero, and driving it to zero moves the network away from that answer. We show that standard gradient-norm balancing fails in exactly this way, its weight remaining near its initial value throughout training on benchmarks where the property is violated, and we introduce SDF-Aware Weighting (SAW), which combines a residual-quantile gate with a gradient-norm ratio so that points exhibiting legitimate departure are excluded before the surviving term is scaled. Across four three-dimensional benchmarks SAW selects an eikonal weight within an order of magnitude of the value located by an eighteen-run manual sweep, spanning four decades from $10^{-1}$ to $10^{-5}$ with a single fixed configuration. On the slotted sphere, where the initial field is non-differentiable at reentrant edges, SAW attains a lower error than any weight in that sweep. Two smooth rigid benchmarks serve as controls: SAW is worse there, as expected when its premise does not hold. An ablation with the gate disabled shows the slot is nearly entirely filled while the relative $L_2$ error reads $1.06\%$, indistinguishable from a field that never represented the slot. We give a feature-restricted measure that separates the two cases.

In this work, viscous fluid flow governed by the Stokes equations in highly perforated domains is studied using physics-informed neural networks (PINNs). Perforated microstructures induce complex boundary conditions and fine-scale flow features that are difficult for standard neural networks to resolve. Conventional PINNs, even when combined with advanced training techniques, can suffer from a loss of accuracy and efficiency as the number of perforations increases. One important source of this difficulty is the soft enforcement of boundary conditions through penalty terms, which can lead to stiffness, gradient conflicts, and poor resolution of near-boundary flow structures. Hard constraints provide an alternative by encoding boundary conditions exactly into the network ansatz, but may introduce undesirable non-local effects due to the global nature of the approximation. To address these challenges, finite basis PINNs (FBPINNs), which are based on domain decomposition and localisation principles, are used together with hard boundary constraints that efficiently encode perforation-related boundary conditions. This approach helps mitigate spectral bias, improves overall accuracy, and exhibits convergence that is only weakly affected by the number of perforations, thereby providing an efficient and highly parallelisable neural network framework. The proposed approach is further supported with theoretical arguments, specifically focusing on the localisation and approximation properties of FBPINNs.

Squeezing of a liquid film between two approaching solid surfaces can generate a high-speed peripheral splash. Despite extensive studies on squeeze-film hydrodynamics, quantitative prediction of the splash velocity remains unresolved, with existing theory significantly overestimating experiments. Here, we present a theoretical framework to predict the ejection velocity of viscous liquid squeezed between two parallel circular disks. We show that discrepancy of theory from experiments arise due to incomplete treatment of liquid inertia and from using peak ejection velocity to represent splash velocity. By accounting for both local and convective inertia, and introducing a momentum-averaged ejection velocity, we obtain good agreement with experiments over a wide range of parameters.

The Atmospheric Boundary Layer (ABL) plays a critical role in influencing objects exposed to atmospheric conditions, making its study crucial. Due to the high cost of real-world testing, this thesis focuses on replicating marine ABLs in a wind tunnel environment. Two profiles were developed: one that served as a framework for establishing commonality among the various international wind engineering standards ('Profile 1'), and a second profile, which is more suitable for modelling the inflow to wind farms in the English Channel and the North Sea ('Profile 2'). The ABLs were generated using Irwin spires without floor roughness elements, and the flow characteristics were measured using Laser Doppler Anemometry (LDA) and a multi-hole probe (MHP). MHP showed a reasonably high accuracy when compared to LDA, with less than 1% deviation in the streamwise velocity and under 5% standard deviation in the streamwise, spanwise, and wall-normal velocity components. The profiles achieved good agreement with target metrics such as normalised velocity and turbulence intensity. Spanwise uniformity and spectral analysis confirmed the robustness of the simulation across varying inflow velocities. Overall, Irwin spires proved to be a cost-effective and reliable method for simulating marine ABLs, offering valuable insights for optimising offshore wind energy systems.

High-fidelity immersed-boundary simulation resolves the coupled motion of a deforming swimmer and its surrounding flow, but the resulting cost limits repeated evaluations for engineering design, parameter studies, and control. We develop neural-operator surrogates for temporal prediction of the hydrodynamic fields generated by planar and volumetric eel swimmers. The surrogates are trained on regular-grid fields exported from adaptive fluid–structure simulations and are conditioned on swimmer geometry and Reynolds number. The planar model jointly predicts two velocity components, scalar vorticity, and pressure. On five held-out high-Reynolds-number trajectories, its full-domain global relative L^2 error is 3.51 %. The volumetric formulation uses three target-specific models with a common multichannel input: one model predicts three-dimensional velocity, one predicts vorticity, and one predicts pressure. Their full-domain global relative L^2 errors on five held-out within-range trajectories are 3.44 %, 5.58 %, and 19.2 %. Together, the results demonstrate the feasibility of field-resolved neural surrogates for moving-boundary swimmer flows while identifying pressure accuracy and physical consistency as priorities for further development.

This study presents a comprehensive numerical investigation of the dynamic behavior and fluid-structure interactions (FSI) of metallic cylinders undergoing hydrostatic collapse in semi-confined fluid environments using a structured Arbitrary Eulerian-Lagrangian (ALE) formulation in LS-DYNA. The numerical model reproduces the experimentally measured collapse pressure of 3.69 MPa and predicts the first water hammer peak with a 1.01% error, demonstrating high predictive fidelity. Following validation, the effects of material type (aluminum and titanium), cylinder slenderness ratio (L/D), and confinement diameter on collapse behavior, pressure evolution, and fluid motion are examined. Titanium cylinders exhibited sharper collapses, higher water hammer pressures exceeding 70 MPa, and greater kinetic and strain energy accumulation than aluminum due to their higher stiffness and yield strength. Lower L/D ratios produced more abrupt collapses, whereas higher L/D ratios promoted more gradual, axisymmetric deformation. Larger confinement diameters intensified jet formation and increased fluid velocities. The simulations provide mechanistic insight into the coupling between structural deformation and surrounding fluid, showing that geometry, material stiffness, and confinement govern collapse-induced energy transfer. Full-field FSI analysis captures key phenomena, including radial jetting, peak fluid velocities, and internal cavitation, that are not evident from pressure-time histories alone. These findings provide quantitative guidance for the design and safety assessment of subsea pressure housings, marine pipelines, and other underwater structures subjected to extreme hydrostatic loading.

We perform three-dimensional variational data assimilation (3DVar) using a discrete adjoint approach to optimise the time-averaged momentum equations. The experimental data consist of sparse stereoscopic particle image velocimetry (PIV) measurements collected along $12$ cross-stream planes in the wake of a vehicle-like bluff body at a Reynolds number $Re_L = 5.64 \times 10^5$ based on the streamwise body length. Adjoint localisation is proposed and implemented to reduce the memory footprint of the discrete adjoint method for spatially-varying control variables in 3DVar by confining the control variable space to a user-defined subdomain. Restricting the control variable to $12$ % of the full control space yields a maximum reduction in peak memory of $64$ %, while producing assimilated fields of comparable fidelity with respect to mean velocity and the optimised momentum forcing field. The localised adjoint case improves upon the baseline Spalart–Allmaras turbulence model and recovers the correct asymmetric topology of the complex three-dimensional (3D) recirculation bubble. The assimilated Reynolds shear stress agrees well with the experiment, and the assimilated mean pressure is shown to be physically consistent when correlated with the in-plane vorticity fields. A data efficiency study is also performed, in which the number of planes provided for assimilation is progressively reduced, demonstrating that the data coverage must extend at least to the end of the primary recirculation bubble to adequately constrain the near-wake dynamics. The efficiency that adjoint localisation affords is crucial for assimilating sparse, experimental data for 3D separated flows on fine meshes that can tackle industrial problems of interest.

Autoregressive reduced order models suffer from compounding long horizon rollout errors, typically treated as unstructured noise. We demonstrate that for bluff body wakes across Re=100 to 800, this rollout error is highly structured and reveals what these models actually learn. For a convolutional autoencoder LSTM model, 95 % to 98% of the error is pure phase error, peaking sharply at the vortex shedding frequency. The network reproduces the attractor geometry almost exactly, matching limit cycle amplitudes within 0.15%, but traverses the cycle at slightly the wrong rate. This timing error, accumulating to just a few thousandths of a cycle over the entire rollout, drives the long horizon error even while one step validation errors appear virtually perfect. Because phase error drifts linearly, it can be corrected offline without retraining using just one parameter per latent coordinate, fitted on a short calibration window. The signal to noise ratio of this phase fit serves as a diagnostic that reliably predicts correction success (r=0.85 across 50 networks). While simple periodic baselines match this performance on stationary limit cycles, they fail by over an order of magnitude when applied to wakes driven by slowly varying inflows. Conversely, our phase correction requires only phase coherence, successfully removing roughly half of the rollout error during non stationary flow.

Dynamic electrowetting of conducting droplets under mechanical deformation is conventionally modeled as a quasi-static variable-capacitance system, in which the electrical response is assumed to be governed solely by the evolution of the droplet–electrode contact area. Under the assumption of instantaneous charge equilibration, this framework successfully describes the cyclic steady-state electromechanical response of the system. However, its validity for transient interfacial electrical dynamics remains largely unexplored. Here, the transient electrowetting response of mercury droplets confined between a polymeric dielectric-coated electrode (PTFE or PVDF) and an opposing copper electrode is investigated under periodic mechanical excitation with multiple waveforms at 2 Hz. The measured contact area and corresponding capacitance evolve closely as predicted from instantaneous surface-energy minimization, confirming that the liquid-interface mechanics remain quasi-static. In contrast, the measured transient current and instantaneous electrical power exhibit pronounced asymmetric excitation and relaxation phases that are independent of the excitation waveform, demonstrating that transient charge evolution cannot be inferred from the instantaneous geometric capacitance alone. This transient behavior is phenomenologically interpreted using constituent first-order interfacial dielectric charge-relaxation kinetics, indicating that the measured current arises from slow dielectric charging followed by dielectric relaxation over the timescale of the imposed periodic mechanical oscillations during discharging. These findings establish that transient electrowetting is governed by the coupled interplay of droplet electrohydrodynamics and dielectric interfacial polarization, requiring a constitutive description beyond quasi-static variable-capacitance models based solely on contact-line dynamics.

A fast-converging and asymptotic-preserving adjoint shape optimization method is proposed for drag reduction of multiscale gas flows in vibrating micro-electro-mechanical systems. The convergence of the Boltzmann kinetic equation is accelerated by macroscopic synthetic equations, whose constitutive relations integrate continuum-limit terms and high-order kinetic corrections to faithfully characterize spatiotemporal rarefaction effects. As such, this method maintains near-continuum limit consistency while retaining high kinetic accuracy in rarefied flow regimes. Fourier stability analysis performed in an infinite domain demonstrates that the present method yields a spectral radius below 0.5, indicating that the numerical deviation from the converged solution is halved per iteration. Numerical simulations are conducted on an oscillating cylinder and a comb-shaped resonator. The results verify the high accuracy of the derived adjoint sensitivities and the excellent drag reduction performance of the proposed method across various Knudsen and Strouhal numbers. Compared with conventional kinetic iteration methods, the present method produces convergent primal and adjoint solutions within dozens of iterations and features asymptotic preserving behavior, permitting spatial cell sizes far larger than the molecular mean free path. This facilitates efficient design of vibrating micro-electro-mechanical systems.

The equations of fluid motion are known; retaining their physics after removing most degrees of freedom remains a fundamental problem. Closure must preserve the geometry of the dynamics it replaces. We introduce Symplectic Geometric Closure (SGC), a prognostic stochastic field theory carrying Euler's Hamiltonian, area-preserving transport into two-dimensional and $\beta$-plane turbulence. SGC couples resolved vorticity to a hidden stochastic reservoir. The coupling conserves augmented enstrophy while permitting bidirectional energy transfer. This yields a compact random attractor in the hyperviscous Navier–Stokes–$\beta$ realization. Numerically, SGC sustains jets, vortices and filaments in high-Reynolds-number turbulence with high fidelity to filtered DNS at an inertial-range cutoff, preserving geometric identities to machine precision. The induced transport folds, stretches and rearranges vorticity: cross-gradient coupling selects interactions through resolved–reservoir gradient misalignment, retaining geometric selectivity and memory. The same geometry addresses spurious sweeping decorrelation, a longstanding obstacle to Eulerian closure. The interaction vertex excludes uniform translation and is Random Galilean compatible. Eliminating the reservoir generates finite memory, stochastic backscatter and a Dyson–Volterra equation for the dressed propagator. Its one-loop, line-renormalized self-energy reproduces Kraichnan-type Direct-Interaction Approximation architecture with fourth-order infrared suppression of sweeping. Deformation-controlled memory and conservative triad constraints yield the $k^{-5/3}$ inverse-energy and $k^{-3}$ forward-enstrophy cascades under standard assumptions. SGC thus realizes Kraichnan's program through Eulerian field dynamics, opening a route to data-driven closures that learn admissible geometric interactions rather than unconstrained forces.

This study investigates the influence of the spatial distribution of flexibility along a propulsor on thrust generation and propulsive efficiency in wave-assisted flapping foils. While flexibility is known to enhance propulsive performance, the role of its chordwise placement remains poorly understood. Here, the effective flexible length is systematically varied by shifting the flexure location along the tail while maintaining constant flexural rigidity and total chord length. Experiments are conducted in quiescent flow at heave frequencies of 0.8 Hz and 1.25 Hz, and non-dimensional heave amplitudes of h* = 0.13 and 0.22. Simultaneous measurements of hydrodynamic forces, flow fields, and tail kinematics are used to quantify performance and elucidate the underlying fluid-structure and fluid-particle interactions. The fully flexible configuration consistently achieves higher propulsive efficiency (up to approximately 164%) across all conditions, which is attributed to enhanced jet persistence and increased streamwise vortex spacing, indicative of a more coherent and sustained momentum jet. In contrast, the mid-flexible configuration yields substantially higher thrust (up to approximately 66%) at the largest heave frequency and amplitude, driven by a pronounced increase in near-wake jet velocity and momentum flux. These results demonstrate that the chordwise distribution of flexibility governs the trade-off between thrust and propulsive efficiency by modulating wake coherence and momentum transfer. The findings establish flexibility placement as a key design parameter in flapping propulsion and provide physics-based guidelines for enhancing the performance and endurance of wave-driven unmanned surface vehicles.

We investigate whether the two flow-index thresholds previously found for isothermal shock profiles persist when the full nonisothermal dynamics is taken into account in a hyperbolic power-law relaxation model of Rational Extended Thermodynamics. The nonisothermal profile problem is structurally different from its isothermal counterpart: restoring the energy balance determines the temperature along the traveling wave and feeds it back into the pressure, the relaxation production, the temperature-dependent consistency coefficient, and the characteristic structure. Under thermodynamic stability, $p_\theta\ge0$, and strict convexity of the reduced Hugoniot pressure, no nontrivial constant-temperature compressive profile can satisfy the full equations. We derive an exact global characteristic-ordering identity and prove that the positive nonequilibrium characteristic speed has its strict global minimum at the unperturbed upstream state. Consequently, a monotone continuous profile exists for $1<M_0<\Mst$, whereas for $M_0>\Mst$ the Boillat–Ruggeri theorem excludes a $C^1$ profile and any admissible piecewise-smooth connection must contain a subshock. Despite the thermomechanical coupling, the shock-thickness classification remains unchanged: $m=2$ is the weak-shock threshold and $m=1$ the near-critical threshold as $M_0\nearrow\Mst$. The corresponding exponents are constitutive-independent within the present class, while finite limiting values and prefactors depend on the equation of state, internal energy, and temperature-dependent consistency coefficient. For the Tait–Murnaghan example, increasing the reference temperature lowers the critical Mach number when the dimensional viscous–relaxation scale is fixed and, for the thermally thinning law considered, reduces the resolved shock thickness.

From a dynamical systems perspective of subcritical transition in shear flows, the basin boundary separating the laminar and turbulent attractors, along with the edge state that governs the long-term dynamics on that boundary, are of fundamental interest. As the Reynolds number is increased from small values, a multiplicity of simple exact coherent structures (ECS) appear in phase space, of which one often undertakes the role of the edge state. At higher values of the Reynolds number, however, the dynamics on the basin boundary and the edge state are sensitive to initial conditions, as shown by a wealth of numerical and experimental studies. The mechanism behind this transition remains unclear. To address this, we examine the subcritical regime of Taylor-Couette flow using a minimal computational box and reveal a generic mechanism whereby the edge state becomes chaotic. The first step in this process involves the formation of a heteroclinic tangle between a travelling-wave-type ECS and an independently engendered chaotic saddle. The interaction causes the basin boundary to incorporate the saddle, thus inheriting its fractal structure, while the edge state itself remains the simple ECS. The transition of the edge state to chaos requires a second step: the formation of a heteroclinic cycle involving the ECS and the chaotic saddle. In consequence, the observation of a simple non-chaotic edge state at given values of the parameters is no guarantee that the same situation will hold at nearby values.

The object of investigation in this paper are the nonlinear equations of motion for two-dimensional inviscid water flows with piecewise constant density stratification in a three-layer fluid with a flat bottom, a free surface and two interfaces. We establish a Hamiltonian formulation for the nonlinear governing equations in this setup. The Hamiltonian of the system and the equations of motion of the surface and of the interfaces are expressed with the help of the Dirichlet-Neumann (DN) operators, which are introduced for each of the layers. Then, the linear equations for small amplitudes of the elevation of the surface and of the interfaces in the leading order are derived from which a bi-cubic equation for the dispersion relation is obtained, whose solutions are analysed. The six real solutions for the possible propagation speeds (three positive, related to right-moving waves and three negative, related to left-moving waves) have magnitudes of different order. Upper and lower bounds for the previously mentioned roots are also given in terms of the coefficients of the equation. Subsequently, approximate formulae for the propagation speeds are derived. The importance of the DN operators is further illustrated in a separate analysis of the three-layer model with flat surface (rigid lid). The full nonlinear evolution equations are expressed again in terms of the DN operators, and the equations in the linear regime and the weakly nonlinear propagation regime (the Boussinesq approximation) are derived by a proper expansion of the DN operators. Limits to the two-layer free surface model are obtained as well. The obtained results are applicable to internal waves in lakes and in the ocean as well as to laboratory experiments with three superimposed fluid layers.

The development of a solid rind or carapace at the surface of lava flows and domes results in a transition in deformation mechanism from dominantly viscous to elastic or plastic. This transition has a significant impact on the rate and style of emplacement, including on the construction of channelized flows, over-steepened margins, and flow advance due to lava breakouts. These processes are particularly important in subaqueous, subglacial, and extraterrestrial environments in which cooling is accelerated, requiring models specifically calibrated for these environments. We present a new numerical model, Viscous-Elastic Numerically Unified Solver for Solidifying flows (VENUSS), for cooling and solidifying free surface flows. The model couples a viscous fluid interior with an elastic shell whose thickness grows in response to cooling. As a demonstration of the impact of including a solidified crust in the flow model, we show that a dome-like shape fed from below with an elastic shell coupled to the basal topography results in more lateral expansion and less vertical uplift than a comparable highly-viscous rind, demonstrating the need for lateral transfer of stress in solid layers to accurately interpret and predict dome deformation.

Bubble growth in silicate melts drives significant volume expansion, which has a first order control on magma transport dynamics. When magmas are exposed to external environments, heat and volatile loss at free surfaces can reverse bubble growth, leading to shrinkage and complex feedbacks between diffusion, rheology, and flow. To resolve how magma flow controls, or is controlled by, bubble expansion, we couple a micro-mechanical model for volatile diffusion into individual bubbles, with a macro-scale thermal evolution and fluid flow of the surrounding magmatic suspension. This two-way coupling captures the co-evolution of bubble size, melt viscosity, and pressure gradients, allowing both growth and resorption to emerge naturally from local conditions. We identify distinct dynamical regimes governed by (i) bubble growth limited by (a) viscous resistance or (b) diffusion at the bubble scale, (ii) viscous transport of the suspension, (iii) outgassing through permeable porous networks and exposed magma-fluid interfaces, and (iv) thermal quenching. Across these regimes, thin, high-viscosity boundary layers arising from temperature and volatile concentration gradients play a central role in modulating flow and bubble evolution. The model is implemented in a flexible, modular numerical framework (Multiscale Vesiculation, Fluid flow, Failure, and Interaction Nonlinear model: MVFFIN) enabling extension to a wide range of systems and applications, including conduit flow and pyroclast evolution. By resolving the interplay between internal bubble dynamics and external boundary conditions, this approach provides a unified framework for understanding multiscale degassing and its impact on magmatic transport and fragmentation.

An analytical solution for a wave velocity field scattered by a submerged permeable vertical plate-type breakwater under the linear monochromatic wave is obtained and the applications of the solution are presented. The water has an infinite depth, and the flow is assumed to be incompressible, inviscid, and irrotational, which leads to the two-dimensional potential wave theory. The permeable breakwater vertically occupies a finite interval beneath the water surface and the water flows through the breakwater. The porous boundary condition is linear, but it couples the normal velocity on the plate to the discontinuity in the velocity potential across it, so that the scattering problem does not reduce directly to a Riemann-Hilbert problem of standard form. This is resolved by a perturbation expansion in a small dimensionless parameter representing the permeability. The solution is expanded up to the first order: the leading order gives the wave scattered by the impermeable breakwater through a homogeneous Riemann-Hilbert problem, and the first-order term gives the correction for the permeability through a nonhomogeneous Riemann-Hilbert problem. The far-field amplitudes follow in closed form up to a single Cauchy principal-value integral. The effects of wavelength, breakwater length, and breakwater permeability conditions on the reflection and transmission coefficients are discussed in detail as an illustrative example of the application of the solution. An exact energy identity is also derived; it verifies the first-order solution and yields a closed-form energy-consistency bound $\varepsilon_{\max}(kb)$ on the perturbation parameter, beyond which the truncated expansion ceases to conserve energy. The hydrodynamic load on the plate is obtained to the same order, and the leading-order results are verified against the closed-form solution of Evans for the impermeable plate.

We demonstrate, by studying precession-driven flows, that inertial wave hydrodynamic turbulence can drive a robust magnetic dynamo action. Motivated by the stronger damping of large-scale geostrophic vortices in rapidly rotating planetary and stellar interiors, we introduce a controlled damping of the vortices, which usually accompany inertial wave turbulence and feed on wave energy. It is shown that even a small vortex damping results in a significant increase of the growth rate of the dynamo due to inertial waves in the kinematic regime, allowing it to persist for magnetic Prandtl numbers as low as $Pm \sim 10^{-3}$ and Poincaré numbers $Po\sim 0.025$. These critical values of $Po$ and $Pm$ for the dynamo onset decrease with increasing Reynolds number. The onset and growth of the dynamo appear to correlate with the coherent fluctuations of kinetic helicity. Spectral analysis shows that magnetic energy growth is primarily due to inertial-wave-induced induction over a broad range of scales. These results establish inertial waves as an efficient mechanism for magnetic field amplification in rapidly rotating low-$Pm$ flows relevant to planetary and stellar interiors.

We study the simultaneous vanishing-viscosity and vanishing-resistivity limit of steady incompressible MHD flows in a disk. The boundary velocity is a small nonaxisymmetric perturbation of a rigid rotation with mean angular speed \(\alpha\), while the prescribed tangential magnetic trace has mean \(\beta\). Assuming \(\alpha\neq0\) and the non-Alfvénic condition \(|\alpha|\neq|\beta|\), we construct solutions converging on compact interior subdisks to a rigidly rotating ideal MHD core with constant vorticity and out-of-plane current density. A new MHD–Wood law determines the two core rotations from the boundary data: the velocity core is selected by a coupled kinetic–magnetic balance, whereas the magnetic core is fixed by the imposed mean circulation. Consequently, zero circulation gives complete interior magnetic expulsion, while nonzero circulation leaves a uniform magnetic rotation after the nonaxisymmetric modes are confined to a thin boundary layer. This provides a fully coupled realization of Prandtl–Batchelor selection and flux expulsion; unlike classical kinematic models, the magnetic field actively changes the flow and need not be weak. The proof combines a non-Alfvénic coercive theory for a periodic MHD boundary layer, global matching of the two fields, and a coupled stability estimate adapted to the magnetic boundary condition. A separate conditional rigidity argument, using exact viscous identities and local convergence but no interior asymptotic expansion, explains the same core structure for a broader single-eddy family.

Charge separation during the breakup of water drop has been recognized since the early studies of waterfall and spray electrification, yet the role of controlled drop fragmentation at structured liquid-repellent surfaces remains unclear. Here we show that water drops impacting superhydrophobic meshes generate charged secondary droplets as liquid penetrates and fragments through the mesh pores. By combining Faraday-cup charge measurements with high-speed imaging, we identify how the charge depends on the Weber number and on the pathway of spray formation. No measurable charge is detected below the penetration threshold. At low Weber numbers, recoil jet formation gives a high charge per unit spray mass, whereas at intermediate Weber numbers both recoil jets and impact-induced jets contribute to charging. At higher Weber numbers, pancake bouncing suppresses recoil jet formation, so charging is dominated by impact induced penetration and the total charge approaches a saturated value. We further show that smaller mesh pores enhance the charge-to-mass ratio and that conductive meshes provide stable charging under repeated impacts by dissipating residual surface charge. These findings provide design principles for superhydrophobic mesh platforms for spray charging and rain-driven energy harvesting.

Multiphase electrohydrodynamic (EHD) flows play a crucial role in various engineering applications. However, existing numerical studies on three-phase electrohydrodynamic systems predominantly rely on phenomenological models, often neglecting thermodynamic consistency and critical surface charge convection mechanisms. To address these fundamental gaps, this paper proposes a thermodynamically consistent three-phase EHD model derived strictly from the Onsager variational principle. This theoretical framework intrinsically guarantees thermodynamic consistency and accurately captures complex multiphysics interactions without requiring a priori assumptions. Furthermore, a mesoscopic lattice Boltzmann method is developed to solve the proposed model, enabling the natural capture of interfacial evolution and charge transport. The accuracy of the numerical framework are rigorously validated against several benchmark cases, including electroosmotic flow in microchannels, the spreading of a three-phase liquid lens, the equilibrium of static compound droplet, and the deformation of compound droplet under uniform electric field. Using this validated framework, we investigate EHD applications, specifically simulating the complex dynamics of double droplet coalescence and separation under electric field, as well as the behavior of droplets subjected to combined EHD and shear flow. Overall, this work provides a robust, thermodynamically reliable numerical tool for exploring the highly nonlinear behaviors of multiphase EHD systems.

Spatial confinement profoundly impacts the transport and self-organization of active matter across diverse biological systems. While the collective orders in confined active matter have been extensively characterized, how geometric constraints reshape near-field flows and the resulting inter-particle correlations remains largely unexplored. In this study, we combine experiments and hydrodynamic simulations to investigate inter-particle correlations within quasi-two-dimensional Chlamydomonas reinhardtii suspensions. We reveal two disentangled modes characterizing cell pairs: a dipolar mode and an entrainment mode, which exhibit a density- and distance-dependent competition. Combining single-cell flow field analysis, hydrodynamic simulations, and active-passive mixtures, we link these two modes to singular hydrodynamics and lubrication-induced entrainment. Our results demonstrate that spatiotemporal correlations in confined active matter are fundamentally rooted in the interplay of these two hydrodynamic mechanisms.

We demonstrate that the area rule of velocity circulation – traditionally associated with the turbulent inertial range but shown not to be exact – is strictly satisfied in the large-scale absolute equilibrium of two-dimensional (2D) homogeneous isotropic turbulence under enstrophy equipartition. We also derive a novel perimeter rule from the 2D inviscid loop equation, which posits that the probability distribution function (PDF) of velocity circulation depends solely on the loop perimeter rather than its area. This perimeter rule holds strictly in the large-scale absolute equilibrium characterized by energy equipartition. At the intermediate states determined by both enstrophy and energy, these two regimes are separated by a characteristic equilibrium scale $l_\text{eq}$: the area rule governs loop statistics when $l\ll l_\text{eq}$, while the perimeter rule emerges for $l\gg l_\text{eq}$. These statistical laws remain robust even for loops with extreme aspect ratios as low as $0.03$, a value that inertial-range studies never achieved. Our findings provide a new steady-state solution to the 2D loop equation and suggest additional solutions, paving the way for exploring previously undiscovered geometric invariants of turbulence.

Alternate bars are ubiquitous bedforms in alluvial rivers, and excessive bar-height growth can increase flood risk and disrupt ecosystems. Predicting bar-height variability requires quantifying the dependence of bar growth rate on water discharge, yet this has rarely been achieved because conventional flume measurements interrupt the flow and cannot continuously capture bar evolution. Here we conducted laboratory experiments under four discharges and four channel slopes (16 conditions) and continuously mapped bed topography using Stream Tomography, a nonintrusive, flow-through measurement technique. Bar height exhibits sigmoidal growth and is well described by the Landau equation, allowing robust estimation of the growth rate and equilibrium height. The inferred dimensionless growth rate tends to increase as discharge decreases, but its sensitivity is weaker than that predicted by stability theory for a single alternate-bar mode. This discrepancy becomes more pronounced at lower discharge, indicating limitations of linearization and the influence of interactions among multiple bar modes. Furthermore, numerical flow simulations over the measured bed topography reveal that, during bar development, lower-discharge conditions produce a relatively larger bar height-to-depth ratio, making the flow more prone to deflection. In such cases, sediment transport is restricted downstream of depositional areas, thereby limiting bar migration. Consequently, flow and sediment transport become concentrated in the scour zones, enhancing local scour and promoting the growth of bar height. These results provide benchmark constraints for bar stability theories and help improve predictions of how bar height responds to changes in discharge.

Reported maxima of the advancing contact angle scatter from $87^\circ$ to $147^\circ$ in a single systematic study, and liquids on surfaces with static angles as low as $5^\circ$ reach dynamic maxima near $90^\circ$. We show that both observations follow from the hinged motion of the free surface near a moving contact line. The local Stokes solution for a wedge rotating about its contact line has two singular angles of opposite character: at $90^\circ$ the hinged motion generates no wall shear and the rotation is free, and at $\theta_h = 128.73^\circ$, where $\tan 2\alpha = 2\alpha$, a resonance with the $r^2$ eigensolution arrests the rotation through an $r^2 \ln r$ term. Between the two angles lies a band that a transient advancing angle cannot leave while the interface near the contact line remains a quasi-steady wedge. A compilation of 68 liquid-solid systems from nine sources and five configurations confirms the band and its two exits: systems not limited by the apparatus, with $\theta_s \le 40^\circ$, reach $87^\circ$ to $119^\circ$ regardless of chemistry, and every exceedance of $\theta_h$ occurs either where chemistry places the static angle above the band or where the flow leaves the quasi-steady regime. The record of a waterline on a vertical wall exhibits the band within a single unsteady experiment, together with a distinct quieting of the local contact angle at the crossing of $90^\circ$.

The theory of the perturbed convective wave equation for compressible flows (cPCWE) is generalised to spatially varying mean-density fields. The resulting equation is an exact scalar reformulation of the acoustic perturbation equations and describes sound generation and propagation in moving inhomogeneous media using a single unknown. The intermediate variables of the associated workflow, in which a Helmholtz decomposition problem, a Poisson equation and the cPCWE are solved successively, are related to the vortical, entropy and acoustic modes of Kovasznay, providing a physical interpretation of each processing step. The quantitative accuracy is assessed against fully compressible direct numerical simulations (DNS) of two-dimensional isothermal mixing layer and Lighthill's analogy computed in the same framework at Mach numbers between M=0.2 and M=0.4, based on the velocity difference across the layer and the ambient speed of sound. Over this range of Mach numbers, the radiated power spans several orders of magnitude. For M>=0.25, the sound power levels obtained using the three methods agree within 0.9dB, and within 0.5dB for M>=0.3. At M=0.2, where the acoustic fluctuations are weakest relative to the hydrodynamic ones, Lighthill's analogy over-predicts the radiated power by 2.8dB. In contrast, the cPCWE deviates from the DNS reference by only -1.2dB. This closer agreement is because the cPCWE source term is confined to the vortex-pairing region, while convection and refraction are represented by its convective wave operator. Beyond reproducing the far-field sound, the cPCWE resolves the acoustic field within the shear zone itself, where the DNS' fields are masked by vortical fluctuations.