Papers

Experimental Fluid-Structure Interaction (FSI) often involves phenomena that occur simultaneously across vastly different spatial and temporal scales. For example, the separation bubble behind a cylinder and the vortex interactions in its wake, or the flow produced by an individual swimmer and the flow generated by the movement of the entire swarm. Imaging-based flow studies of such FSI phenomena are challenging and often lead to separate analyses of different flow regions. This work introduces simultaneous shadow and laser-based Particle Image Velocimetry (PIV) to obtain concurrent near-wall and far-field flow velocity measurements. The experimental setup developed here enables the first simultaneous comparison between shadow- and laser-based PIV, demonstrating that shadow velocimetry can achieve accuracy comparable to laser-based measurements at the macro scale. We then use this new combined flow measurement technique to fully capture the velocity field generated by a shrimp-inspired underwater robot, employing laser PIV to record the flow surrounding the robot and shadow PIV to focus on the actuators, imaging regions that the laser technique cannot resolve due to wall reflections and shadows behind the structures. The simultaneous application of shadow- and laser-based PIV offers a new experimental avenue for gaining insights into the physics of FSI phenomena.

I show that the initial conditions imposed by Balan [Phys. Fluids 35, 113108 (2023)] are incompatible with a nonzero retardation time, so that the problem solved is not impulsive start-up, but, as I prove exactly, the start-up of a plate ramped as $1 - \mathrm{e}^{-t/\lambda_2}$ on the retardation timescale $\lambda_2$ (a material parameter, not a setting in a rheometer). Values digitized from that paper's viscoelastic figures fall on the ramped-plate solution, not on Tanner's start-up solution. The large negative wall normal stress reported for the corotational model is a grid-dependent artifact due to the same error in the initial data. An open-source code repository provides annotated notebooks reproducing every figure and number in this Comment.

We explore the collision hydrodynamics of a ferrofluid droplet falling freely onto a sessile droplet of the same liquid, in the presence of a horizontal magnetic field; a configuration that couples droplet-on-droplet coalescence with concomitant field-governed wetting and spreading. Using high-speed imaging, we track the events through crown formation, radial spreading, and rim detachment (under specific conditions), across three ferrofluid concentrations, two substrates of different wettability (glass and PET), and a range of impact velocities and magnetic field strengths. The maximum crown height is noted to scale as $H_{c,\max}/D_t\sim Fr^{0.5}$ ($Fr:$ Froude number); well below the ballistic upper bound of $H_{c,\max}/D_t\sim Fr$. At zero-field, the maximum spreading collapses onto the boundary-layer scaling $\beta_{0,\max}\sim (We_0/Oh)^{1/6}$ ($We_0$: Weber number, $Oh:$ Ohnesorge number) when expressed in terms of the merged impact velocity, and coalesced-drop size . With the field applied, a bulk-dissipation energy balance predicts $\beta_{\max}\sim Z^{1/5}$, where $Z$ combines the magnetic-driving, and inertial-capillary-viscous terms, but the observations instead follow a markedly weaker $\sim Z^{1/11}$, a deficit traced to enhanced dissipation from the magnetoviscous effects, and manifested via an effective Ohnesorge number. Finally, rim detachment occurs beyond a field- and height-dependent threshold, described by a size-independent criterion $Fr^2Bo\approx 3550$ ($Bo:$ Bond number), above which the rim may fragment into daughter droplets. These scalings provide predictive tools for magnetically assisted printing, droplet-on-demand systems, and coating processes, where repeated droplet collisions occur on the residual liquid droplet or layer.

We investigate the dynamical and thermal behaviour of settling heavy inertial particles in bulk turbulent thermal convection. Direct numerical simulations are performed in a homogeneous Rayleigh-Benard convection setup, where a uniform mean temperature gradient drives statistically homogeneous convective turbulence seeded with passive inertial particles. We quantify the effects of dynamic and thermal inertia on particle statistics. In particular, we investigate how the fluctuations of particle velocity and temperature can be traced back to the correlations between particle and fluid variables, and how particle temperature statistics is affected by the interplay of settling and preferential concentration.

Strikingly, when hydrogel particles are embedded in ice in a temperature gradient, they move through the solid ice towards warmer temperatures, while swelling as they warm up. This motion comes from a flow of unfrozen water through the hydrogel mesh, driven by a process known as `cryosuction'. Here, we show how one can use this behavior to measure – with extremely high resolution – a range of different hydrogel transport properties, and how these change as a hydrogel deswells. These properties include permeability, compressibility, and poroelastic diffusivity: all of which are challenging to measure, but widely important for phenomena involving swelling, dehydration, transpiration and filtration. We demonstrate the measurement technique using poly(ethylene glycol) diacrylate (PEGDA) hydrogels. The technique uses picoliter-scale hydrogel volumes, and yields measurements of hydrogel properties that are consistent with existing literature data. The high resolution of our measurements also allows us to test commonly-used, classical predictions for hydrogel properties (derived assuming an idealized, homogeneous polymer network in the hydrogel). We show that these classical predictions do not work well, highlighting the need for new models that can accurately describe real hydrogels.

Periodic unsteady flows are common in forced-motion and fluid-structure interaction problems. Their parametric analysis typically requires repeated high-fidelity simulations, whereas existing reduced-order and surrogate models generally rely on pre-generated flow-field or aerodynamic data. This study proposes a purely physics-driven framework for solving parametric periodic flows and finite-amplitude aeroelastic responses. First, a Periodic Physics-Informed Neural Network (P-PINN) is developed to directly solve periodic flows by imposing temporal periodicity over a single motion cycle, thereby avoiding the need to resolve the long transient evolution preceding the establishment of the periodic state. The flow conditions and motion parameters are further incorporated as network inputs to construct continuous parametric representations of the periodic flow field and aerodynamic forces. On this basis, the parametric aerodynamic model is coupled with the structural dynamic equation through first-order harmonic balance to solve the response amplitude and frequency of a single-degree-of-freedom aeroelastic system. This framework is validated using forced-motion cases of a circular cylinder and an airfoil, demonstrating accurate reproduction of periodic aerodynamic forces, surface load distributions, and instantaneous flow fields under different flow and motion parameters compared with time-marching results. Furthermore, aeroelastic analysis is conducted for an elastically mounted circular cylinder at subcritical Reynolds numbers, and the resulting aeroelastic response agrees well with fully coupled CFD/CSD results. Once trained offline, the parametric model can be repeatedly evaluated for different structural parameter states, enabling the complete aeroelastic response curve to be obtained online within seconds, without repeated long-time fluid-structure interaction time marching.

Lean premixed hydrogen flames are highly susceptible to thermodiffusive instabilities, which generate complex cellular structures and enhance propagation speed. In practical combustors, incomplete premixing introduces spatial variations in local equivalence ratio upstream of the flame. This work investigates how the length scale of inlet fuel stratification affects the structure and propagation of lean laminar hydrogen flames using direct numerical simulations with detailed chemistry and transport. Controlled sinusoidal perturbations of fuel mass fraction are imposed at moderate amplitude, leading to local equivalence-ratio variations of $\phi \simeq 0.45-0.55$ in the flame region. Seven stratification wavelengths, from $\lambda = 15.4\delta_f$ to $133.3\delta_f$, are examined at constant density-weighted global equivalence ratio. Additional unity-Lewis-number simulations separate geometrical effects from differential transport. The results reveal a strongly scale-dependent response. In unity-Lewis-number flames, stratification organises the front at the imposed wavelength and monotonically increases flame surface area and propagation speed with wavelength. With differential diffusion, large wavelengths ($\lambda \gtrsim 40\delta_f$) produce a similar large-scale organisation, with rich channels forming forward bulges and lean channels recessed cusps, while thermodiffusive cells remain superimposed. This increases flame surface area and global propagation speed. At smaller wavelengths ($\lambda \lesssim 29\delta_f$), composition gradients interfere with intrinsic thermodiffusive cellular dynamics, reducing flame surface area and propagation speed relative to the perfectly premixed reference. These findings identify stratification length scale as a key parameter controlling the interaction between moderate mixture inhomogeneity and thermodiffusive instability in lean hydrogen flames.

Recurrent invariant solutions provide a dynamical framework for interpreting turbulence, but their computation becomes increasingly difficult in spatially extended flows, where close whole-domain recurrences are rare. We study two-dimensional Kolmogorov flow in a [Lx,Ly] = [2pi,12pi] domain with Re = 10 using a distributed reduced-order model composed of a patch-based autoencoder and a neural ordinary differential equation. Near- recurrence candidates are refined by latent multiple shooting, decoded to physical space, screened under the full Navier-Stokes dynamics and supplied to a full-state Newton- Krylov solver. Fourteen candidates converge to relative periodic orbits (RPOs), with periods 3.65 < T <16.45. The catalogue contains both domain-filling states and RPOs with recurrent activity localised to a restricted cross-stream region. The weakly modulated surroundings generally remain finite-amplitude and distinct from the laminar solution. Selected localised RPOs persist under continuation in Reynolds number, and recurrent states can be reconverged after truncating substantial portions of their surroundings. In addition, the model trained at Ly = 12pi generates convergent RPO seeds at Ly = 6pi and 8pi without retraining. These results demonstrate that distributed learned dynamics can provide useful initial conditions for exact coherent states searches in extended domains and reveal recurrent solutions with strongly localised temporal dynamics.

We analyze laminar-to-turbulent transition over a blunt capsule representative of Martian entry at Mach 26 using global modal and transient-growth analyses about a thermochemical base flow characteristic of high-altitude entry conditions. Across the Reynolds-number range considered ($Re_\infty = 10^4$–$10^6$), the axisymmetric global eigenspectrum remains stable, ruling out temporally unstable axisymmetric global modes as a viable route to transition. The flow nevertheless supports strong transient growth concentrated in the shear–entropy layer generated by bow-shock curvature. Energy-budget analysis reveals a two-stage process: Reynolds-stress production in the mean shear first amplifies kinetic disturbances, which then generate entropy fluctuations as they traverse the strong base-flow entropy gradient. The optimal gain scales linearly with the Reynolds number based on the capsule nose radius, whereas boundary-layer-localized disturbances become competitive at the highest Reynolds numbers examined. These results identify shear–entropy-layer transient growth as a plausible linear pathway for seeding transition in high-enthalpy blunt-entry vehicles.

Inertial propulsion in fluids generally arises from an unbalanced flux of momentum. For the case of wave-driven propulsion, momentum is transported away from an oscillating raft in the form of self-excited surface waves. While this mechanism has previously been analyzed for rigid rafts, the role of flexibility has yet to be investigated. In this work, we develop a fluid-structure interaction model for a periodically driven two-dimensional flexible raft resting at the free surface of a fluid. The raft is modeled as an Euler–Bernoulli beam and is coupled to a weakly dissipative quasi-potential model of the fluid beneath. Varying the flexural stiffness and forcing position reveals new features associated with the introduction of flexibility, including the possibilities of thrust enhancement and reversal. By projecting the raft response onto its free rigid-body and elastic modes, the fluid loading can be represented as a modal impedance, informing a computationally efficient reduced-order model. Analysis of the modal response and its symmetries facilitates physical interpretation of our key findings. For a uniform raft, excitation of any single mode in isolation is incapable of producing a net thrust, and thus efficient wave propulsion requires a blend of interfering modes with appropriately coordinated amplitudes and phases.

Self-similar dynamics are often described in terms of a single asymptotic scaling regime. Here we experimentally investigate the post-breakup recovery of a hydrodynamic interface over substantially wider temporal and spatial ranges than previously accessible. Beyond the previously identified scaling behavior, we find four successive self-similar regimes characterized by the $R_{\beta}$-scaling with $\beta=1/6$, 1/2, 1, and 2, connected by three distinct crossovers. All four regimes exhibit robust collapse near the interface tip, while geometrical dependence becomes detectable farther from the singular region. This systematic variation across space and scaling regimes is consistent with scale separation and enhanced universality closer to the breakup singularity. The characteristic scales associated with the different $R_{\beta}$-scalings become comparable at the common geometric scale $z_m \simeq R$. These findings demonstrate that self-similar dynamics can undergo multiple successive crossovers among distinct scaling regimes rather than directly approaching a single asymptotic self-similar state.

This work presents a consistent formulation of body-force and heat-source terms within a double-distribution-function lattice Boltzmann framework for simulating compressible flows of generic fluids. The proposed approach extends a recently developed kinetic framework for non-ideal compressible fluid dynamics by incorporating external forcing and volumetric heating through shifted quasi-equilibrium states. The standard lattice Boltzmann discretization is applied with a second-order accurate integration along characteristics and product-form equilibria on nearest-neighbor lattices are employed, supplemented by necessary correction terms. This formulation ensures the consistent recovery of the Navier-Stokes-Fourier equations, including the Korteweg stress tensor, across arbitrary equations of state, while maintaining independently controllable thermodynamic and transport coefficients. The methodology is rigorously validated and applied for two different flow regimes, with ideal-gas compressible flows and non-ideal/multiphase compressible flows, respectively, where a broad hierarchy of benchmarks is employed, including non-classical shock tubes, thermal Couette flows, and force-driven Poiseuille and Womersley flows. The framework's ability to capture complex thermodynamic processes using forcing and heating is further demonstrated through Rayleigh and Fanno flows, Joule-Thomson effects, and throttling processes. Furthermore, the model is validated for multiphase phenomena, including interface consistency and liquid-vapor co-existence. The results demonstrate excellent agreement with analytical solutions and reference data, while spatio-temporal grid-refinement studies confirm the expected second-order accuracy of the scheme. This establishes the model as a robust and efficient foundation for simulating highly compressible flows of generic fluids in the presence of numerical and physical s...

A general physics-based model for the distribution of shear stress and surface pressure is developed for laminar flow over spheres. Although integral coefficients have been studied extensively for spheres, they do not capture the local surface distributions that govern phenomena such as heat transfer, phase change, and mass loss in multiphase and particle-laden flows. The model depends on the flow regime of the sphere ($Re_\infty$, $M_\infty$, $Kn_\infty$), local gas properties ($\gamma$, $\omega$, $Pr$), and surface conditions ($T_w/T_0$, $\sigma_t$, $\sigma_n$). The formulation incorporates boundary-layer scaling, flow separation, shock-wave physics, velocity-slip effects, and high-speed rarefaction, while recovering the known asymptotic behavior in the creeping-flow, hypersonic, and free-molecular limits. The proposed model is validated in the continuum and rarefied regimes using CFD and DSMC simulations from literature. In the continuum regime, it is compared with CFD simulations of flow over a sphere in air under subsonic, supersonic, and hypersonic conditions with varying surface temperatures. The model captures the CFD distributions very well over a wide range of $Re_\infty$, $M_\infty$, and $T_w/T_0$. In the rarefied regime, it is compared with DSMC simulations of flow over a sphere in a monatomic gas under subsonic and supersonic conditions with fully diffuse and partial surface accommodation. It shows good agreement with the simulated shear stress and surface pressure distributions over a wide range of $M_\infty$ and $Kn_\infty$, while accurately capturing the effects of surface accommodation around spherical bodies.

This paper presents a high-fidelity direct numerical simulation (DNS)-fluid-structure interaction (FSI) framework for rigid-liquid-flexible spacecraft dynamics under microgravity conditions. The liquid-gas flow is simulated with the incompressible two-phase solver implemented in DIVA, validated against FLUIDICS experiments conducted aboard the International Space Station (ISS). The flexible appendages are described by a rotating assumed-mode plate model that accounts for geometric stiffening. The fluid and structural operators are coupled through a Dirichlet-Neumann fixed-point algorithm with Aitken relaxation, and a closed-system mechanical energy balance is used as an a posteriori diagnostic to assess the energy imbalance of the partitioned discretisation. The coupling strategy is validated against an experimental free-decay sloshing benchmark, and its numerical consistency is assessed through spatial sensitivity studies of the energy-balance defect. Prescribed-motion, rigid open-loop, and flexible open-loop simulations of a spin-up manoeuvre are compared to isolate the effect of structural feedback on the sloshing response. Reduced liquid models identified from the different simulation architectures exhibit different predictive capabilities when embedded in the same rigid-flexible plant. A controller synthesized from the reduced model identified from the flexible simulation is replayed in the nonlinear CFD-FSI environment. The reduced model reproduces the principal attitude and actuator responses for the considered manoeuvre but does not recover the detailed nonlinear sloshing-load history. The framework provides a high-fidelity environment for analysing coupled spacecraft dynamics, identifying control-oriented models, and assessing reduced-model-based control strategies beyond their linear design representation.

We present a review of results concerning the properties of scales larger than the forcing scale in turbulent flows. In three-dimensional turbulence, when the power driving the flow is injected at a well-defined scale, the injection scale separates the small-scale range, where the Kolmogorov cascade takes place, from the large-scale range across which the mean energy flux is zero, suggesting that these modes are in equilibrium. We show that, in the case of spatially periodic forcing involving only a few modes, an equipartition energy spectrum is generated at large scales, and we discuss the deviations from equipartition observed with more complex forcings. In two-dimensional turbulence, the injection scale separates the direct enstrophy cascade toward small scales from the inverse energy cascade toward large scales. Because of the inverse cascade, one would not expect equilibrium statistical physics tools to be suitable for describing the large-scale structures. Yet this is precisely the situation in which such tools have been most widely used. We indeed show that the bifurcations observed between different largescale regimes of two-dimensional turbulence, both in experiments and in direct numerical simulations, can be qualitatively described by the Truncated Euler equations, whose solutions satisfy statistical equilibrium.

Finite corner curvature is commonly omitted when rarefied cavity flows are represented using idealised geometries. This study examines how downstream corner rounding affects lid-driven cavity flow over 0.5 $\le$ Kn $\le$ 5. Direct simulation Monte Carlo calculations were performed for normalised corner radii of Rc = 0, 0.10 and 0.20. The model was assessed through published benchmark data and a local grid-sensitivity test. Velocity fields, centreline profiles, area-averaged speed, translational temperature, number density and temperature anisotropy were analysed. A single primary vortex persisted across all cases. Corner rounding modified the local turning of the downstream return flow but caused little change in the wider circulation. The root-mean-square differences between the rounded and sharp-cornered centreline velocity profiles remained below 0.007. The area-averaged normalised speed increased in all rounded configurations, with a maximum change of approximately 2.5%. The thermodynamic response showed a stronger dependence on rarefaction. Corner rounding reduced the mean temperature non-uniformity at Kn = 0.5 and 1, but increased it at Kn = 2 and 5. Changes in the mean density deviation remained within approximately 1.3%, while the mean translational-temperature anisotropy varied from about -3% to 2.4%. The results show that the sharp-corner approximation captures the global velocity structure under the conditions studied, but can omit local flow changes and small thermodynamic responses associated with finite corner curvature.

We use direct numerical simulations to study the turbulent transonic flow over a supercritical airfoil, spanning the transition from stable conditions to fully developed buffet at chord-based Reynolds numbers of $3\times10^5$ and $6\times10^5$. The Reynolds number determines the incoming boundary-layer state, thereby affecting the separation behaviour. Spectral proper orthogonal decomposition reveals a single dominant mode that emerges below onset and persists across the transition to buffet. The energy of this mode increases with the angle of attack while its spatial structure and fundamental frequency remain nearly unchanged, consistent with a global instability that saturates into a nonlinear limit cycle. Geometrical acoustics provides a first-order description of the global mode propagation and identifies two paths connecting the acoustic source, located in the near wake, to the shock. A shorter path impinges on the shock from behind, while a longer one circumvents the shock tip before reaching it from the front. Linearised shock–acoustic interaction theory predicts a stronger shock response to low-frequency, front-impinging acoustic disturbances. Space–time correlations link the establishment of a downstream path to complete boundary-layer separation, which is induced intermittently by the upstream motion of the shock. The sum of the upstream acoustic time along the front-impinging path and the downstream convective time is compatible with the measured buffet period at both Reynolds numbers. Together, these results are consistent with a unified picture of buffet, where an aeroacoustic feedback mechanism provides the physical pathways through which perturbations can sustain the global dynamics.

We investigate the fast-advection limit ($\varepsilon \to 0$) of the stochastically forced two-dimensional incompressible Navier-Stokes equations on the torus. Numerical simulations are performed at resolution $N = 128$ for four different forcing shells on both the square torus and a thin torus, with the advection parameter $\varepsilon$ varied over approximately one decade. We find that the stationary distributions become increasingly concentrated on the lowest Fourier modes as $\varepsilon \to 0$, with the energy-to-enstrophy ratio $E/\Omega$ and the fraction $R$ of enstrophy in the lowest modes both increasing monotonically. At finite $\varepsilon$ the degree of concentration depends on the forcing shell through the effective spectral value $B_1/B_0$, in agreement with the condensation bound of Sznitman and Widmayer. Linear extrapolation to $\varepsilon = 0$ suggests that the limiting values may be forcing-independent, with $B_1/B_0$ governing only the rate of convergence. The same qualitative behaviour persists on the thin torus.

We conduct direct numerical simulations to investigate the effects of dilute polymers on flow structure, statistical properties and energy transfer in 2D turbulence. As the Weissenberg number (Wi) increases, the flow undergoes a sharp but continuous crossover between a weak-elastic regime and an elastic-activated regime. In the weak-elastic regime, the flow remains close to its Newtonian counterpart and polymer stresses have weak dynamical effects. In the elastic-activated regime, elastic stresses attenuate vortical motions and promote shear-dominated filaments. Scale-by-scale energy analysis shows that polymer addition weakens both the inverse kinetic-energy cascade and the forward enstrophy cascade in the two regimes, whereas the kinetic–elastic exchange and the inter-scale redistribution of elastic energy differ between them. Kinetic-to-elastic conversion dominates over the analysed range of scales in the weak-elastic regime, whereas a partial transfer from elastic to kinetic energy emerges at small scales in the elastic-activated regime. The inter-scale transfer of elastic energy is dominated by inverse transfer over the large-scale range in the weak-elastic regime but by forward transfer over the small-scale range in the elastic-activated regime. These results link the crossover to the onset of strong elastic feedback from the polymers and the associated reorganisation of the scale-by-scale transfer pathways. Downstream-decay statistics also show the same qualitative two-regime behaviour.

The Plateau–Rayleigh instability of liquid jets governs a wide range of natural and industrial processes. While the classical linear stability theory accurately predicts disturbance growth rates and dominant wavelengths, it cannot quantify the amplitude and frequency spectrum of nanoscale initial surface disturbances. This critical missing information prevents accurate forecasting of breakup lengths and droplet generation. Conventional optical imaging is constrained by the diffraction limit and lacks the capability to resolve such nanoscale surface fluctuations. Here we introduce a Mie-scattering-based measurement technique to characterize nanoscale surface disturbances on liquid jets. The method employs a thin laser sheet to illuminate the jet, with scattered light captured at designated azimuthal observation angles. Based on Lorenz–Mie theory, we develop an inversion algorithm incorporating cosine similarity and cross-correlation to reconstruct jet surface disturbances from measured scattering fringes, achieving a sub-nanometer resolution for detecting diameter variations, with an overall measurement precision limited by a background noise floor of 0.18 nm RMS. Comparative analyses of forward and rainbow scattering signals further confirm that the surface disturbances become axially symmetric as the amplitude reaches a few nanometers, and thus satisfies the assumptions of the scattering model. Synchronous validations against high–speed imaging and scanning electron microscopy corroborate the quantitative accuracy of our scattering method. Applied in the near-nozzle region, the technique identifies two intrinsic signatures of initial perturbations: stochastic pulse-like fluctuations and low-frequency oscillations.

Recent indoor experiments on small-scale hovering rotors have reported mid-frequency quasi-tonal peaks of uncertain origin in the residual (aperiodic) far-field sound spectrum, even without wake recirculation. This study investigates their physical origin using hybrid Reynolds-averaged Navier-Stokes/large-eddy simulations coupled with a Ffowcs Williams-Hawkings acoustic analogy, applied to a four-bladed ideally twisted rotor in hover. The high-resolution simulation reproduces the measured higher-harmonic blade-passage-frequency tones, confirming that they arise from the rotor flow itself and not from the enclosed-chamber test environment. Flow-field analysis attributes the tones to blade secondary vortex interaction (BSVI): the outboard blade sections, between approximately r/R = 0.88 and 0.96, are repeatedly impinged upon by coherent, S-shaped secondary vortex worms formed by entrainment of the wake shear layer into the primary tip vortices of preceding blades. These aperiodic secondary vortices produce blade-to-blade correlated loading, yielding a quasi-tonal signature distinct from both purely periodic blade-vortex interaction and mostly stochastic blade-wake interaction noise. Spectral proper orthogonal decomposition of the zero-mean upwash confirms that the mid-frequency (3-10 kHz) content is dominated by a single, low-rank, spatially coherent mode associated with the braids, whereas a lower-frequency mode near 1 kHz is linked to the primary tip vortex core. BSVI is thus identified as a distinct and previously uncharacterized source of aperiodic tonal noise in hovering rotors, with direct implications for the acoustic design of small- to medium-scale rotorcraft and electric vertical take-off and landing propulsors.

Two-dimensional Kolmogorov flow is a common proving ground for the dynamical systems picture of turbulence. Hundreds of unstable periodic orbits have been found for this system across many Reynolds numbers and domain sizes, although the most well explored is Re$=40$ on a square $2\pi\times 2\pi$ domain with a forcing wavenumber of $k=4.$ Here I present a catalog of 8952 exact steady states of the flow in this canonical parameter regime. These solutions provide a fixed constellation informing the dynamics of both turbulence and transients.

Spatial flow measurements support underwater navigation, but distributed sensing is constrained by robot size and sensor layout. We use a causal observer to estimate current lateral velocities from a finite history of measurements collected by a single sensing unit, supplying the inputs of a fixed navigation controller. In two-dimensional wake simulations with access to body-frame ambient velocity, this virtual sensing interface reduces simultaneous flow sampling from three points to the robot center. Trained only in a circular-cylinder wake at Re = 100, the flow-history observer achieves 84.4% and 80.6% success at held-out Re = 205 and 240 without retraining. These rates are 7.4 and 4.6 percentage points below direct spatial sensing and more than 30 points above a matched current-only observer. Past flow remains beneficial when past goal and yaw information is available. Across obstacle geometries, performance remains close to direct sensing in square-prism wakes but declines in triangular-prism wakes. Component replacement identifies the lateral velocity difference as control-relevant, while controlled perturbations reveal sensitivity to error persistence. The results demonstrate the closed-loop utility of single-point flow histories under the assumed observation model.

Families of explicit analytic solutions of the magnetohydrodynamic equilibrium equations are presented, equivalent to steady incompressible Euler flow. The solutions are non-axisymmetric and possess exact nested toroidal flux surfaces. No expansion is made in inverse aspect ratio or in the deviation from axisymmetry. The magnetic field and flux surfaces are given explicitly in Cartesian coordinates using elementary functions. The field, current density, and scalar pressure are smooth over the toroidal domain. The pressure gradient vanishes only on the magnetic axis. One family of solutions has uniform rotational transform $\iota=2$, while another family has a sheared $\iota$ profile. These counterexamples to Grad's conjecture are valuable for understanding the existence and regularity of 3D equilibria and for testing numerical codes.

This work examines sub-threshold triadic responses to a vortex-ring-induced perturbation of an internal gravity-wave field, using sparsity-promoting dynamic mode decomposition (spDMD) to diagnose wave structures from experimental observations. Compared with a standard approach to dynamic mode decomposition (DMD) that selects modes by truncation of the singular value spectrum, spDMD, an alternative approach that instead seeks to minimise reconstruction error, is shown here to robustly identify previously indistinguishable oscillatory signals of high frequency in cases of both triadic resonance instability (TRI) and sub-threshold sustained triadic response (STR). These signals are consistent with wave–wave interaction products composed of a primary internal wave with frequency $\omega_0$, and secondary TRI waves with frequencies $\omega_1$ and $\omega_2$ respectively, leading to signals with frequencies $\omega_3 = \omega_0 + \omega_1$ and $\omega_4 = \omega_0 + \omega_2$. We show that these signals satisfy conditions for resonance, but fail to satisfy the dispersion relation for internal waves, indicating that they are confined, non-propagating oscillatory signals rather than freely propagating internal waves. A hierarchical analysis of wave–wave interactions provides evidence that feedback between both branches of the TRI secondary waves gives rise to these signals. Whilst we expect our observations to generalise to many classes of wave–wave interaction, we cannot exclude the possibility that the particular observations we make in the laboratory may arise due to reflections of the primary wave from a free surface. However, beneath strongly density-stratified regions of the ocean we would expect to find these interaction pathways faced with the same geometric configuration, so we are confident our findings will transfer directly to the natural environment.

The induction region of a model wind farm is investigated experimentally as an adverse pressure gradient (APG) turbulent boundary layer problem, using hot-wire anemometry. An array of porous discs, with diameter $D=50$\,mm representing the farm, in multiple configurations across two turbulent boundary layers of different depths, with farm-present and farm-absent configurations compared throughout. The farm imposes a spatially developing adverse pressure gradient in the approach flow. Spanwise-averaged measurements reveal systematic farm-scale global blockage extending to at least $10D$ upstream in all cases. The farm-induced turbulence intensity increase, which reaches up to $7\%$ relative to the farm-absent reference for the shallowest boundary layer, is shown by cumulative variance decomposition to be carried predominantly by large-scale motions of the boundary layer, whilst the small-scale turbulence intensity is only weakly affected. This selective large-scale energisation is consistent with the outer-layer amplification driven by an adverse pressure gradient. The concentration of farm-induced turbulence energy at scales comparable to or larger than the rotor diameter has direct implications for turbine fatigue loading, preferentially exciting coherent rotor-scale load fluctuations at the frequencies most damaging under fatigue. The results establish a quantitative link between wind farm global blockage and APG boundary layer physics.

Surfactant adsorption at solid-fluid interfaces strongly influences contact line dynamics, yet most surfactant-laden phase-field models neglect solid adsorption and rely on Cahn-Hilliard-type equations. We develop a thermodynamically consistent and conservative Allen-Cahn-Navier-Stokes model for surfactant-laden contact line dynamics with solid adsorption. A unified free-energy formulation accounts for surfactant transport, adsorption, and wetting dynamics, yielding consistent wetting and adsorption boundary conditions. Second-order Allen-Cahn-type equations govern both the phase field and surfactant concentration, avoiding the numerical complexity of fourth-order formulations. A classical linear constraint ensures exact conservation of total surfactant mass, whereas a generalized nonlinear conserved quantity is introduced for the phase field to improve geometric volume conservation. The resulting weighted Lagrange-multiplier correction vanishes in the bulk phases and is confined to the diffuse interface, suppressing the leading-order curvature-induced bulk shift associated with the linear constraint while preserving the energy-dissipation structure. Matched asymptotic analysis shows that the nonlinear formulation can achieve formal second-order geometric-volume accuracy. A lattice Boltzmann method is developed to solve the coupled system. Numerical results confirm the predicted second-order convergence, demonstrate enhanced volume preservation for high-curvature droplets, and reproduce wetting responses induced by preferential solid adsorption, including hydrophilization and autophobing. Under shear flow, the results also show that solid adsorption can significantly influence contact line recession and droplet detachment.

The trajectories of point vortices after a division using reverse collapse route are studied. In this setting, an unexpected peculiar phenomenon appears, corresponding to the shadowing of the vortex breakup. This occurs at least for a finite time, when the system evolves from three to five vortices after a breakup. An analytical study reveals that this observed numerical phenomenon is related to the condition of scale invariance, a condition necessary for the finite time singularity. Further simulations agree with our analytical findings and indicate that shadowing can occur with more than five vortices, and as well with higher order singularities. This phenomenon leads to question what a vortex is actually measuring, triggering speculations if this shadowing property could be generalized to other Hamiltonian systems with finite-time singularities.

This study investigates the aerodynamic feasibility of high-speed evacuated tube transport (ETT) using an integrated CFD-machine learning framework for pod geometry optimization and a staged converging-diverging (CD) tube concept for supersonic operation. The pod geometry is parameterized using composite cubic Bezier curves with seven design variables. Latin Hypercube Sampling is used to generate 200 configurations across subsonic and supersonic regimes, which are evaluated using two-dimensional axisymmetric ANSYS Fluent simulations validated against published compressible-flow data. The resulting CFD dataset is used to train surrogate models for rapid drag prediction. XGBoost provides the best overall performance, achieving a test R^2 of 0.9524, and is coupled with Differential Evolution and Particle Swarm Optimization to identify low-drag geometries that are subsequently verified using CFD. The study further examines a staged CD tube architecture combining controlled area variation with gradual pressure reduction to mitigate choking during supersonic acceleration. In the idealized axisymmetric simulations, the proposed strategy enables transition from atmospheric entry at Mach 1.6 to near-vacuum cruise at Mach 2.5 and a blockage ratio of 0.50 without forming a choked annular flow region. Total drag decreases from 68,913.7 N under atmospheric supersonic conditions to 120.5 N in the final near-vacuum stage, associated with a transition from wave-drag-dominated to viscous-shear-dominated resistance. The results demonstrate the potential of combined pod-shape optimization and staged pressure-area management for reducing aerodynamic resistance in supersonic ETT systems.

Thermosolutal dendritic solidification involves interface evolution, solute diffusion, heat transfer, and melt flow over markedly different time scales. In lattice Boltzmann simulations, a single numerical time interval may place different transport processes in unfavorable relaxation ranges, while asynchronous updates require consistent transfer of phase-change contributions. To address these issues, a unified multirate multiple-relaxation-time lattice Boltzmann method is developed for thermal, solutal, and thermosolutal dendritic solidification. The coupled fields share a common moment-space framework but evolve at different update rates. The concentration and temperature source terms are separated into transport-related and phase-change contributions, and each resolved phase increment is used to immediately transfer the corresponding solutal and latent-heat contributions. The method reproduces characteristic dendritic morphologies and tip-velocity trends under pure diffusion and forced convection, with weak sensitivity to the tested update factors. Directional solidification over Lewis numbers \(Le=1\)–\(1000\) captures the transition from nearly planar to cellular and strongly branched growth, including vertically aligned dendrites and solute-rich interdendritic channels for saline water, in qualitative agreement with experiments. Source-coupling ablation shows that delayed coarse-step transfer produces increasingly strong local source pulses and eventual loss of numerical stability as time-scale separation increases, whereas phase-step instantaneous transfer remains stable over the tested conditions. These results demonstrate the applicability of the proposed framework to dendritic solidification with strongly separated transport time scales. The source code is publicly available in the DendriteLBM repository.