The distinct dynamical roles of vorticity amplification (VA) and vortex tilting (VT) in three-dimensional homogeneous isotropic turbulence are investigated using direct numerical simulations of a modified Navier-Stokes system. By selectively suppressing VA while retaining VT, we demonstrate that gradient amplification by VA is strictly required to sustain the classical forward energy cascade. Progressively suppressing VA weakens small-scale velocity gradients, heavily depletes extreme fluctuations, and entirely eliminates the classical energy dissipative anomaly, causing the normalized energy dissipation to decay as ${\mathrm{Re}}_{\lambda }^{-1}$. In the limit of complete VA suppression, enstrophy emerges as the relevant inviscid invariant. Scale-by-scale budget analyses confirm that the dynamics transition to a purely forward enstrophy cascade, characterized by an anomalous enstrophy dissipation and a robust $E\left(k\right)\sim k^{-3}$ intermediate energy spectrum. We verify that these asymptotic scaling limits—including a ${\mathrm{Re}}_{\lambda }^{-1/2}$ finite-Reynolds-number correction for the enstrophy anomalous dissipation—are universal properties of the VA-suppressed dynamics, independent of whether the large-scale forcing is helical or nonhelical. Remarkably, despite the smoothing of the velocity field and the elimination of the energy dissipative anomaly, anomalous structural scaling and a broad multifractal spectrum persist. These results reveal a fundamental mechanistic separation: Although VA is responsible for amplifying intense localized fluctuations, geometric reorganization by VT alone is mechanically sufficient to sustain multifractal intermittency.

When a drop of a leaky dielectric fluid is suspended in another fluid and subjected to a uniform dc electric field, it becomes polarized, leading to tangential electric stresses that drive fluid motion both inside and outside the drop. In the presence of a second drop, the dynamics of the first drop are altered due to electrohydrodynamic interactions with the second, causing the drops to translate due to dielectrophoretic forces and hydrodynamic interactions. We present a semianalytical nonlinear three-dimensional small deformation theory for a pair of identical, widely separated leaky dielectric drops suspended in a weakly conducting fluid. This theory is valid under conditions of large drop separation, high drop viscosity, and high surface tension, ensuring that the drops remain nearly spherical. The resulting model is semiempirical, with selected higher-order terms retained rather than obtained through a systematic asymptotic expansion. For the first time, we develop a model within the Taylor-Melcher leaky dielectric framework that incorporates both transient charge relaxation and convection. This allows the model to capture the transition to Quincke rotation, a symmetry-breaking phenomenon in which drops begin to spontaneously rotate in sufficiently strong fields. We derive and numerically integrate coupled nonlinear ordinary differential equations for the dipole moments, shapes, and positions of the drops. Our results show good quantitative agreement with previous numerical and experimental work in the limit of zero charge relaxation and convection, and the model reduces to existing models for isolated drops and interacting solid spheres in the relevant limits. We also discuss the hysteresis in the onset of Quincke rotation of isolated drops observed in experiments. Various trajectories for pairs of drops undergoing Quincke rotation are presented, along with results for fixed drops, including their shape, the nature of electrohydrodynamic interactions (attractive or repulsive), and the conditions leading to Quincke rotation. In particular, it is shown that the onset of Quincke rotation for a pair of drops is qualitatively different from that for an isolated drop due to electrohydrodynamic interactions and from that for a pair of solid spheres due to straining flows present only in drops.

In the framework of the generalized, nonlocal Gross-Pitaevskii (GP) model, we study numerically the pressure- and size-dependent mechanisms of roton emission and vortex nucleation by objects moving in superfluid ${}^4\mathrm{He}$. For each of several pressures in the range from 0 to the solidification pressure of $\approx 25\mathrm{bar}$, we chose the parameters of the interatomic interaction potential such that the resulting excitation spectrum for the generalized, nonlocal GP equation approximates fairly accurately the pressure-dependent dispersion curve determined experimentally by Godfrin et al. [Phys. Rev. B 103, 104516 (2021)]. In the two-dimensional approximation, for circular obstacles (disks) moving in quiescent ${}^4\mathrm{He}$, we calculated two critical velocities—one corresponding to the roton emission and the other to the nucleation of quantized vortices—as functions of pressure and the obstacle's size. We also comment briefly on three-dimensional simulations of the roton emission and vortex nucleation by moving spherical obstacles.

Periodic porous structures manufactured using additive manufacturing are candidates for intensified process devices. Detailed measurements of the velocity field are required to characterize the turbulent mixing generated by flow through the channel network. We used time-resolved single-shot spiral magnetic resonance velocity (MRV) imaging to noninvasively record snapshots of the velocity field for water flowing through a Schwarz Diamond monolith. The time-resolved velocity data lend themselves to more detailed analysis than is possible with conventional time-averaged magnetic resonance  methods. The turbulent energy spectra measured with MRV confirmed that the pore network places an upper size limit on the eddies that could exist in the flow. The $-5/3$ power-law scaling from Kolmogorov theory was only attained at a Reynolds number around 2000, indicative of a higher transition point to a fully turbulent regime than is usually reported for random porous media. The local Reynolds stress tensor showed considerable anisotropy within the network, which affects mass transport to the channel surfaces. The time-resolved MRV method offers valuable insights into turbulence in porous media that can inform the design and operation of novel geometries.

A comprehensive experimental study was conducted to explore the noise generation mechanism of a structured porous-coated cylinder (SPCC) in cross-flow. Coherence analysis between the velocity field, near-field surface-pressure fluctuations, and far-field noise was performed to identify the relative contributions of dipole and quadrupole sources to far-field sound in the case of the SPCC. The velocity field was measured using planar particle image velocimetry (PIV) along the streamwise direction, while near-field surface pressure was measured using pressure taps via a remote-sensing method. The results demonstrated that turbulent wake velocity fluctuations, particularly the vertical component associated with quadrupole-type sources, exhibit significant coupling with the cylinder-surface pressure response and the radiated acoustic field. This correlation behavior suggests a possible pathway by which wake-associated unsteady fluctuations influence the near-wall surface-pressure response, which provides an equivalent dipole representation of the body-induced acoustic radiation. Both dipole- and quadrupole-related source mechanisms were suppressed by the SPCC. Dipole suppression was influenced by two mechanisms—delayed vortex shedding and reduced turbulence energy—whereas quadrupole attenuation primarily resulted from turbulence reduction. Consequently, although dipole sources remained important contributors, the relative dynamic coupling of quadrupole fluctuations with the far-field noise was stronger than in the baseline case. This led to a mixed acoustic contribution for the SPCC, in contrast to the baseline, where dipole sources dominated tonal noise.

Understanding the breakup of evaporating nanofluid droplets under extreme aerodynamic loads is essential for applications in drug delivery, material deposition, defense, and propulsion. This study investigates the shock-induced atomization dynamics of an acoustically levitated TM-10 nanofluid droplet subjected to a coaxially propagating blast wave and subsequent compressible vortex ring, generated using a compact wire-explosion shock source. The blast wave imposes a sharp velocity discontinuity, followed by a decaying flow field and a vortex-dominated interaction that drives droplet disintegration. Laser-induced heating promotes evaporation, increasing nanoparticle concentration, viscosity, and agglomeration within the droplet. Progressive evaporation leads to interfacial nanoparticle accumulation, initiating a sol-gel transition when the local volume fraction exceeds the gelation threshold, and ultimately forming a solid outer shell as the maximum packing limit is approached. Shock interactions are systematically examined across three evaporation stages: (1) steady liquid phase, (2) gel-shell phase, and (3) solid-shell phase. Each regime exhibits distinct atomization responses due to the evolving interfacial morphology. In the gel-shell regime, deformation is resisted by the viscous shell, producing a bag-on-sheet mode, followed by puncture, jetting, and eventual shell delamination. In the solid-shell regime, interactions intensify, resulting in brittle fragmentation and catastrophic fracture. The findings reveal how evaporation-driven interfacial transitions fundamentally alter breakup mechanisms under transient shock loading. By linking nanoparticle transport, shell formation, and flow-droplet interaction across multiple timescales, this work establishes physical insights into the atomization of complex, multicomponent, multiphase, and transiently evolving droplets under extreme aerodynamic conditions.

The values of liquid odd-viscosity coefficients remain largely unknown, with only one experimental measurement reported to date [Nat. Phys. 15, 1188 (2019)]. In this work, inspired by the well-known consequences of dispersion surfaces in classical liquids from the work of Lighthill, we theoretically determine the shapes of constant-phase wave crests formed around obstacles moving at constant velocity in two- and three-dimensional odd viscous liquids, which may or may not undergo rigid rotation. From this analysis, we derive parametric relations that the odd-viscosity coefficients must satisfy, providing a framework for their experimental determination.

The salinity of water and the slope of ice significantly influence the melt rate and surface morphology of ice, both highly relevant in the context of glacier and iceberg melting in oceanic environments. In this study, we conduct experiments on vertical and sloped ice blocks melting in quiescent saline water. Through the use of fringe projection profilometry, we measure the morphology of the ice's front face. In particular, we combine the spatiotemporal phase shifting and orthogonal sampling moire methods. The far field salinity in the experiments ranged from 0 g/kg to 35 g/kg, and angles are between $-{18}^{\circ }$ and ${50}^{\circ }$. The ice blocks are $L\times W\times H=12\mathrm{c}\mathrm{m}\times 23\mathrm{c}\mathrm{m}\times 32\mathrm{c}\mathrm{m}$ and submerged in water of approximately $20{}^{\circ }\mathrm{C}$, leading to $\text{Ra}=\mathcal{O}\left({10}^7\right)$. We identify and classify five surface morphologies and regimes arising from the flow regimes imposed by salinity and inclination, namely, scalloped, channelized, top-melting, bottom-melting, and incurved. The channelized morphology consists of vertical channels carved along the ice surface whose development originates from a Rayleigh-Bénard-type instability, and which are enhanced by bubbles released from the melting ice and rising along the interface. The scalloped regime is characterized by a rough dimpled pattern commonly referred to as scallops. We observe that increasing the salinity leads to scallops that are smaller, shallower, and more uniform in size. Additionally, a salinity dependence of the melt rate is found, showing a nonmonotonic behavior, while the inclination angle shows little influence on the overall melt rate.

Gravitational settling affects particle transport in turbulent flows in two ways; explicitly, by introducing a finite settling velocity, and implicitly, by modifying how the particles interact with the flow field. For wall-bounded flows, when the wall is horizontal (gravity perpendicular to the wall), both the explicit and implicit effects of settling impact the particle transport towards the wall, whereas when the wall is vertical (gravity parallel to the wall) only the implicit effect plays a role. Surprisingly, it was recently demonstrated that even when the settling parameter $\mathrm{Sv}$ (defined as the ratio between the Stokes settling velocity and the friction velocity) is very small, settling can play a very significant role in controlling the near-wall transport in a horizontal channel. In this paper, we use direct numerical simulations to explore how this finding is affected by the particle boundary conditions and whether it also occurs in vertical channels where only the implicit effect of settling plays a role. We show that the sensitivity of the particle transport to $\mathrm{Sv}$ depends upon the particle boundary conditions with elastic-collisions (that generate a zero mean particle flux) and absorbing-wall conditions (that generate a negative mean particle flux) exhibiting qualitatively and quantitatively different sensitivities to $\mathrm{Sv}$. It is found that for vertical channels the impact of settling on the particle transport is in fact negligible if $\mathrm{Sv}$ is small, and only becomes significant when $\mathrm{Sv}\ge O\left(1\right)$. Finally, we examine the physical mechanisms governing the settling velocity of particles in vertical channel flows, and find that low-speed streaks can play a significant role in suppressing the settling velocity of the particles near the walls, in contrast to the core region where the preferential sweeping mechanism leads to an enhancement of their settling velocity.

We perform direct numerical simulation of the incompressible Navier-Stokes equation with forcing at different spatial dimensions and measure turbulent and chaotic properties. Lyapunov exponents, $\lambda$, decrease with dimension, and $\lambda <0$ for all simulations in six dimensions up to ${\mathrm{Re}}_{\lambda }=21.2$. These six-dimensional simulations display non-Gaussian statistics and other behavior similar to well developed turbulence despite their lack of chaos. Further, we find that small scale perturbations do not extend to the largest scales and that this terminal scale between correlation and decorrelation shrinks with dimension. We theorize that this change is related to the increased rate of vortex stretching. We find the interplay between turbulent and chaotic properties changes with increasing dimension.

Accurate simulation of wind turbulence over fast-propagating waves requires interface-capturing methods that suppress numerical artifacts while accurately resolving momentum transfer across the interface. In high wave-age regimes, numerical errors at the air-water interface can reach magnitudes comparable to the physical flow, directly affecting predicted turbulence statistics. This study examines widely used interface-capturing techniques to evaluate how curvature estimation and flux discretization influence wind-wave simulations through the resulting spurious currents and interface regularization. A systematic assessment is performed using static and translating droplet benchmarks, together with solitary and monochromatic wave cases, to identify and quantify the dominant numerical error mechanisms. In addition, comparison with experimental measurements reveals how these primary error sources manifest in coupled wind-wave simulations. These findings clarify the numerical origin of the observed discrepancies and underscore the importance of accurate curvature and flux treatment in high wave-age regimes, without which numerical artifacts risk being misattributed to genuine wind-wave physics.

Starting from limited measurements of a turbulent flow, data assimilation (DA) attempts to estimate all the spatiotemporal scales of motion. Success is dependent on whether the system is observable from the measurements, or how much of the initial turbulent field is encoded in the available measurements. Adjoint-variational DA minimizes the discrepancy between the true and estimated measurements by optimizing the initial velocity or vorticity field (the “state space”). Here, we propose to instead optimize in a lower-dimensional latent space which is learned by implicit rank-minimizing autoencoders. Assimilating in latent space, rather than state space, redefines the observability of the measurements and identifies the physically meaningful perturbation directions which matter most for accurate prediction of the flow evolution. When observing coarse-grained measurements of two-dimensional Kolmogorov flow at moderate Reynolds numbers, the proposed latent-space DA approach estimates the full turbulent state with a relative error improvement of 2 orders of magnitude over the standard state-space DA approach. The small scales of the estimated turbulent field are predicted more faithfully with latent-space DA, greatly reducing erroneous small-scale velocities typically introduced by state-space DA. Furthermore, latent-space DA is demonstrated to be robust to noisy measurements over the range of Reynolds numbers considered. These findings demonstrate that the observability of the system from available data can be greatly improved when turbulent measurements are assimilated in the right space, or coordinates.

Machine learning approaches to subgrid-scale (SGS) modeling are now well established in atmospheric and oceanic applications. Among these, online end-to-end learning, where the differentiable solver participates in the training, has shown particular promise. Yet existing studies are largely restricted to idealized periodic domains, with no mechanical boundaries, precluding them from addressing the dynamics of bounded rotating flows relevant to planetary interiors. Here we consider two-dimensional quasigeostrophic turbulence in a rapidly rotating annular bounded domain. We examine three configurations varying the geometry of the container and the rotation rate. The system exhibits key features such as zonal jets, Rossby waves, and, in the spherical shell geometry, a slow quasiperiodic inward drift of the jets. The spectral properties of the zonal and nonzonal flow can be understood in the framework of zonostrophic turbulence theory. We develop a differentiable solver for this system, which allows us to train SGS models online, over a time span of one turnover time, using coarse-grained data from direct numerical simulations. In all cases a SGS model trained on a single turnover time accurately reproduces global integrated diagnostics, energy spectra as well as long-term dynamical behaviours, such as jet migration, occurring on timescales which exceed the training window by one order of magnitude. The online-trained model further outperforms classical hyperdiffusivity and Leith closure schemes, for which reducing the radial resolution is impractical. The resulting speed-up paves the way to further investigations of long-term geophysical fluid processes beyond the reach of direct numerical simulations.

Many natural and industrial systems involve particle-laden interfaces. Because interfacial particles prevent the coalescence and coarsening of drops, they hold promise for various applications requiring stable emulsions. Despite their remarkable ability to stabilize emulsions, it remains challenging to characterize how particles influence the interfacial transport of dissolved solutes. Here we quantify the diffusion from a single particle-coated drop by confining it to a two-dimensional configuration. Using fluorescence microscopy, we extract the intensity profiles of the fluorescent dye as it diffuses from the drop, yielding spatiotemporal measurements of the concentration field. Over a range of particle sizes, the particles impose minimal resistance to diffusion. We explain this behavior with a mathematical model describing interfacial mass transfer across a particle-coated interface. The particle monolayer controls the temporal dynamics of interfacial flux, but hinders the overall transport only at extreme coverage fractions beyond the close-packing limit. This framework reveals why particles often fail to hinder diffusion, offering new pathways to harness mass transfer in particle-stabilized emulsions.

The flow over a slender body at low angles of attack generates concentrated vortical structures in the wake, which inevitably interfere with the hydrodynamics of a trailing body. This work elucidates the evolution of vortices shed from the leading body moving at low angles of attack ($<6.3^{\circ }$) and their influence on the trailing body through numerical and experimental approaches. Periodically shed vortex rings merge into vortex tubes, forming ladder-shaped packets of hairpin vortices, with the vortex tubes and vortex rings serving as the legs and head, respectively. These interconnected hairpin vortices undergo a topological disintegration process, characterized by the migration of the interconnections between adjacent hairpin vortices along the vortex legs towards the head. The wake vortices interfere with the nearby but nonimmersed trailing body by reducing the pressure asymmetry between its windward and leeward sides, rather than by locally lowering the surface pressure on the side adjacent to the vortices. The dependence of the interference on two nondimensional parameters representing the temporal vortex intensity and the launch spacing is quantitatively clarified. Finally, a theoretical model is developed to predict the hydrodynamic forces and moments acting on the two bodies, including the cross force, axial force, and additional contributions induced by body acceleration and by the shed vortices, with the axial distributions of these forces also characterized.

The stability of laminar boundary layers developing over spanwise-periodic surface modulations is investigated by means of numerical simulations and linear stability analysis. The configuration considered consists of a nominally flat plate with sinusoidal waviness in the spanwise direction, whose amplitude grows in the streamwise direction proportionally to the boundary-layer thickness of the Blasius case. The present approach allows a systematic assessment of both the base-flow characteristics, discussed in comparison with the Blasius boundary layer, and the evolution of plane Tollmien-Schlichting (TS) waves. The results show that spanwise surface waviness has competing effects on TS-wave stability. While the critical Reynolds number is increased, indicating an apparent stabilizing influence near the lower branch of the stability curve, enhanced amplification rates are observed further downstream, leading to an earlier transition with respect to the Blasius boundary layer. This behavior is traced back to curvature-induced inflectional velocity profiles developing in the valleys of the wavy surface, whose destabilizing effect strengthens as the waviness amplitude grows in the streamwise direction. These findings clarify the physical mechanisms underlying the apparently contradictory effects of spanwise surface waviness on boundary-layer stability, and provide qualitative trends and quantitative indications that are relevant for the interpretation and design of wavy-surface configurations aimed at modifying laminar boundary-layer stability.

While extended research has been conducted on solid particles settling in turbulence, most of them have focused on very dense particles like solid ones in air turbulence or on almost neutrally buoyant ones. The intermediate case of particles whose density is representative of solid particles falling in water turbulence has been scarcely explored in the academic literature. In the present work, we aim to bridge this gap. To this end, we perform Eulerian-Lagrangian point-particle numerical simulations to examine the settling of small particles in homogeneous turbulence with two values of particle-to-fluid density ratio, $\mathrm{\Gamma }=4$ and 14. The analysis of the results provides a comparison with the much more investigated case of very heavy particles with $\mathrm{\Gamma }=1000$ to compare and contrast the settling mechanisms between the moderate and large density ratios. The simulations are performed in one-way and two-way coupling for dilute particle-laden conditions and two turbulence Reynolds numbers, ${\text{Re}}_{\lambda }=40$ and 115. In two-way coupling, both particle self-disturbance and force-spreading operator related issues are handled by determining an effective particle diameter. The main results show that the settling increase is significantly smaller for moderate than large values of $\mathrm{\Gamma }$ and that the commonly reported centrifuge effect for high density ratios is not observed for the much smaller ones considered here. Under two-way coupling, it is found that for the moderate density ratios, the particle settling velocity is not mainly governed by the sampled fluid velocity as a consequence of a significant added mass contribution that tends to balance the dragged fluid motion. When particle inertia is large, the settling velocity is, on average, and as commonly reported in the literature, mainly modified by the mean fluid velocity sampled by the particles; however, a histogram-based data analysis reveals that the correlation between settling and sampled fluid velocities holds true for only a relatively small subset of individual particles. Furthermore, high particle inertia induces a severe local unbalance between gravitational and drag forces. This unbalance creates a nonhomogeneous distribution of particle acceleration, an effect shown to be further amplified by drag nonlinearity. While this latter finding has been addressed for very high particle-to-fluid density ratio, it is also expected to occur for moderate density ratios provided that particle inertia is high enough. The two considered values of the turbulence Reynolds number do not have a significant effect on the analyzed particle and flow quantities. Finally, as far as the existing literature allows for comparison, the experimental data used for comparisons of the settling velocity, fluid, and particle velocity, and acceleration statistics are in fair agreement with the simulations.

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.