Feeding by marine invertebrate larvae depends critically on the low-Reynolds-number fluid mechanics of the feeding currents they generate. Yet the relative importance of gravity-driven versus drag-driven mechanisms in small invertebrate larvae has remained unresolved. Here, high-speed microscale imaging, micro-particle image velocimetry (μPIV), and an analytical axisymmetric Stokes-flow model are combined to quantify the feeding currents of free-swimming veliger larvae of the eastern oyster Crassostrea virginica. Despite their small body size ($<330$µm), the larvae possess a high excess density ($\sim 181\mathrm{kg}/{\mathrm{m}}^3$), shifting the force balance such that gravity-driven feeding currents dominate. μPIV measurements reveal flow fields with first-order (Stokeslet-type) spatial decay, yielding ecologically sufficient body-volume-specific maximal clearance rates of $\sim 2.5\times {10}^6/\mathrm{day}$. These values agree with predictions from the Stokes-flow model, which decomposes the clearance into gravity-driven and drag-driven components and shows that the former consistently outweighs the latter across observed swimming speeds. The model further explains how slow swimming modulates clearance by $\pm 44\%$ relative to hovering. Together, these results demonstrate that C. virginica veligers operate in a gravity-dominated feeding regime similar to that of larger calanoid copepods, and that their feeding strategy is shaped by an interplay of excess weight, swimming kinematics, and ciliary propulsion. This work highlights the fundamental role of gravity in larval feeding mechanics and underscores the need to incorporate excess weight when evaluating form-and-function relationships in marine invertebrate larvae, particularly for shelled bivalve and gastropod larvae with high excess density.

Interactions and reconnections of vortices are fundamental in many areas of physics, including classical and quantum fluids where they are central to understanding phenomena such as turbulence. In three-dimensional (3D) superfluids, quantum vortices are one-dimensional filaments that can intersect, reconnect, and recoil with irreversible dynamics described by near-universal scaling laws. We explore quantum-vortex reconnections in a four-dimensional superfluid, where a vortex is a two-dimensional surface. Using real-time numerical simulations, we find much richer behavior than in 3D, including stable intersecting vortex surfaces which do not reconnect, and unusual vortex reconnections which occur without significant energy dissipation, which may indicate quasireversible dynamics. Our work raises many interesting questions about vortex physics in extradimensional systems and may be further extended to look at vortex dynamics and turbulence in higher-dimensional spaces.

The offshore wind industry is rapidly expanding to meet clean and secure energy needs. New developments are now increasingly constrained to deeper waters, where the water column is seasonally stratified. Here flows past offshore wind infrastructure will increase water column mixing, although such processes and their extent are poorly understood. Studies have so far been limited to field-scale simulations, which make sweeping assumptions regarding flow-structure interactions and fine-scale stratified turbulence, and field observations, which are limited by the sparsity of measurement campaigns and data captured. To isolate and quantify the key processes governing water column mixing by infrastructure, we present fully structure-resolved direct numerical simulations of two-layer stratified flow past a vertical cylinder. We identify two wake regimes by systematically varying the flow Reynolds and Richardson numbers: (1) a weakly stratified regime, characterized by a narrow but highly energetic wake dominated by horizontal shear and (2) a strongly stratified wake, characterized by the emergence of a thermocline-spanning recirculation cell attached to the cylinder. Here strong vertical motions develop from the recirculation cell which are responsible for the formation of large-scale stationary internal waves. These waves account for up to 10% of the total energy budget and provide a mechanism for far-field energy propagation. The weakly stratified wake regime is characteristic of existing offshore wind sites where temperature gradients are relatively weak; the identified strongly stratified regime describes the dynamics to be expected in future deep water offshore wind sites. This difference between the two regimes offers an explanation for the previously enigmatic discrepancies in field observations regarding wake persistence and detectability. Future work must focus on narrowing the gap between idealized simulations and field-scale flows, for which the datasets herein will provide a critical benchmark for validation.

This study investigates the spatiotemporal evolution of hypopycnal intrusive particle-laden flows to determine how particle concentration and size regulate flow instabilities, horizontal propagation, and vertical transport. These processes are directly related to the effectiveness of ocean alkalinity enhancement (OAE), where alkaline mineral particles are added to the ocean surface. Using high-resolution pseudospectral simulations, we systematically vary particle concentration and diameter to quantify the entrained area and effective settling velocity. Following particle release, the flow dynamics is governed by the competition between horizontal spreading and vertical sedimentation processes. We find that the terminal propagation distance decreases monotonically with increasing the particle concentration and diameter. This terminal distance is limited by collective vertical sedimentation driven by convective instabilities at the base of the sediment layer. Consequently, the effective vertical particle settling speed can exceed the Stokes settling speed of an individual particle by one to two orders of magnitude. The settling enhancement factor, defined as the ratio of the effective settling velocity to the Stokes settling velocity, reaches up to 100 for fine particles (i.e., particle diameter $5$µm) and increases with particle concentration. However, a large fraction of particles in the upper part of the particle-laden flow still settle according to the Stokes settling velocity, as they are not influenced by convective instabilities. This leads to a bulk centroid velocity that is much smaller than that of the vertical sedimentation front driven by convective instabilities. We categorize the flow evolution into three morphological regimes, governed by the balance between spreading and settling. We find that intermediate particle concentration and size can maximize the surface entrainment area and homogeneity, offering an optimal configuration for OAE. These results demonstrate that collective instabilities, rather than individual Stokes settling, control particle residence times, potentially limiting the carbon removal efficiency of surface-release OAE strategies.

In this study, we report direct experimental observations of self-sustaining ${\mathrm{CH}}_4$-air rotating flames formed spontaneously in an unheated, open, circular Hele-Shaw cell. These flames are observed under fuel-rich conditions and exhibit stable traveling-wave patterns, with edge velocities that can significantly exceed the nominal flame speed of the unburned mixture. Planar laser-induced fluorescence (PLIF) measurements across the central plane reveal that the flame front consists of a bibrachial structure, with a diffusion branch gliding along the side edges of the cell and a premixed branch extending into the interior. Complementary numerical simulations suggest that the formation of rotating flames is driven by a dynamic balance between local flame speed and unburned-gas velocity near the cell edges, where both wall heat loss and flow expansion play critical roles in stabilizing the rotation pattern. A parametric study is conducted for various equivalence ratios, flow rates, and gap distances, from which the regime diagrams of flame modes and rotation frequencies are obtained. At low flow rates, the rotating state is characterized by a single rotating flame wave, whose rotation frequency increases with flow rate. For this type of flame, a semiempirical model is established to predict their rotation frequencies and shapes as functions of mass flow rate and surface temperature. At elevated flow rates, multiple rotating waves appear with approximately equal azimuthal spacing, and the product of the wave number and rotation frequency increases with flow rate. Mode transition from rotating flames to steady ring-shaped flames anchored at the burner edges occurs at sufficiently high flow rates, while at sufficiently low flow rates, flame extinction occurs due to thermal quenching. These findings can provide useful guidance for the advancement of microcombustion technologies.

We study the dynamics of gyrotactic microswimmers suspended in homogeneous and isotropic turbulence by using direct numerical simulations. The swimmers are characterized by three nondimensional parameters: their aspect ratio ($\gamma$), a dimensionless swimming speed ($\varphi$), and a dimensionless reorientation time ($\psi$). Strong gyrotaxis (smaller $\psi$) promotes vertical alignment of the swimmers, while weak gyrotaxis leads to nearly isotropic orientations. At low swimming numbers, the orientation distribution is largely shape independent with spheres and spheroids showing marginally greater vertical alignment than rods, whereas at higher activity the peaks of the distributions exhibit largely shape-independent behavior and the tails show a clear dependence on particle shape. However, at large $\psi$ rods exhibit a stronger alignment along the vertical. We observe that at small $\psi$ the rod-shaped swimmers respond to shear by aligning with the stretching direction of the strain-rate tensor, while at large $\psi$ the alignment with the vorticity vector is preferred. The orientation autocorrelation is found to decay exponentially, with a decay rate that scales as $1/\left(2\psi \right)$. Analysis of the mean-squared displacement reveals a transition from a ballistic motion at short times to a diffusive regime at longer times. To assess the efficiency of vertical migration, we compute the probability distributions of vertical displacement over a fixed time interval and the time taken to migrate a specific vertical distance. Furthermore, we use a simplified two-dimensional model for spherical swimmers that qualitatively reproduces the key trends observed in the full three-dimensional simulations.

When a bubble detaches, it produces a sound. While the frequency of this sound is well understood, there has been no consensus on what drives its amplitude. Although mechanisms based on shape oscillations, initial velocity of the bubble radius, neck collapse or Laplace pressure have been suggested, none of them has been confirmed experimentally. We performed experiments involving two methods of producing bubbles, which result in sound levels differing by two orders of magnitude. Our results show that the sound amplitude is given by the conditions of velocity and radius of the bubble at detachment, in line with the scenario of a free harmonic oscillator proposed by Strasberg in 1956. We refined this scenario by describing how the bubble radius velocity is affected by gas exchange though the closing neck. This “leaking bubble” model predicts that the bubble begins to produce sound prior to detachment, as observed experimentally. By feeding image analysis of the neck into the model, we obtained excellent agreement between the experimental and the calculated pressure signals.

In this work, two-phase flow scalings are derived, which enable the quantification of grid-point and time-step requirements as functions of Reynolds ($\mathrm{Re}$), Weber ($\mathrm{We}$), and capillary ($\mathrm{Ca}$) numbers. The adequate grid resolution is determined in the inertia-dominated regime with the aid of high-fidelity simulations of stationary two-phase, i.e., interface-resolved, homogeneous isotropic turbulence by evaluating convergence of total interfacial area, size distribution, Sauter mean diameter (SMD), and curvature distribution. Although standards for direct numerical simulations (DNS) for single-phase turbulence flow exist, there is a lack of similar guidance in two-phase flows. Therefore, length scale ratios of the Kolmogorov-Hinze to the Kolmogorov scale of ${\eta }_{\mathrm{KH}}/\eta \sim {\mathrm{We}}_{\mathcal{L}}^{-3/5}{\mathrm{Re}}_{\mathcal{L}}^{3/4}$ in the inertia-dominated regime and the Kolmogorov-viscous to Kolmogorov scale of ${\eta }_{\mathrm{KV}}/\eta \sim {\mathrm{Ca}}_{\mathcal{L}}^{-1}{\mathrm{Re}}_{\mathcal{L}}^{3/4}$ for the viscous-dominated regime, are constructed. These scalings imply a computational cost increase like ${\mathrm{We}}_{\mathcal{L}}^{12/5}$ and ${\mathrm{Ca}}_{\mathcal{L}}^4$, in the inertia-dominated and viscous-dominated regimes, respectively. A dimensionless number, referred to as the ratio of interface scales ($\mathrm{Ris}$), defined as $\mathrm{Ris}:={\eta }_{\mathrm{KH}}/{\eta }_{\mathrm{KV}}={\mathrm{We}}_{\mathcal{L}}^{2/5}/{\mathrm{Re}}_{\mathcal{L}}$, is proposed to aid in the classification of the turbulence regimes in the presence of an interface. Convergence of the total interfacial area, size distribution, SMD, and curvature distribution are observed for grid resolutions of $k_{max}{\eta }_{\mathrm{KH}}\ge 60$ for second-order schemes in the inertia-dominated regime. Furthermore, it is observed that this lower bound is the minimum required to capture intermittent events responsible for the increase of instantaneous total interfacial area. This criterion will be a valuable tool for determining grid resolution and time-step requirements a priori for DNS of two-phase flows and for estimating the corresponding computational cost. This work provides guidelines and best practices for numerical simulations of two-phase flows, which will accelerate physics discovery and model development.

Dense non-Brownian suspensions undergo a viscous to inertial transition with increasing shear rate ($\dot{\gamma }$), from a regime of constant viscosity at low shear rates to a regime where the viscosity varies linearly with the shear rate. The shear rate associated with this transition has been shown to vary dramatically between different experimental systems. Using the discrete element method, we show that in the regime where frictional contacts are absent, the characteristic shear rate for the transition to an inertial state is sensitive to the volume fraction ($\varphi$) of the suspension and exhibits a critical behavior at the jamming volume fraction (${\varphi }_m$) for the system. By uncovering the presence of a microstructural length scale ($L_c$) that controls the emergence of inertial effects in the suspension, it is shown that the criticality emerges as a consequence of $L_c$ diverging at jamming. We further show that in contrast to the conventional Stokes number $St=\rho d^2\dot{\gamma }/{\eta }_f$, the definition of a modified Stokes number $S{t}_{\mathrm{cluster}}=\rho L_c^2\dot{\gamma }/{\eta }_f$ correctly quantifies the inertial effects within the suspension and leads to a collapse of the rheological data.

The pinch-off of bubbles in viscoelastic liquids is a fundamental process that has received little attention compared to viscoelastic drop pinch-off. While these processes exhibit qualitative similarities, the dynamics of the pinch-off process are significantly different. When a drop of a dilute polymer solution pinches off, a thread is known to develop that prevents breakup due to the diverging polymer stresses. Conversely, our experiments reveal that this thread is absent for bubble pinch-off in dilute polymer solutions. We show that a thread becomes apparent only for high polymer concentrations, where the pinch-off dynamics become very sensitive to the size of the needle from which the bubble detaches. The experiments are complemented by numerical simulations and analytical modeling using the Oldroyd-B model, which capture the dilute regime. The model shows that polymer stresses are still singular during bubble pinch-off, but the divergence is much weaker as compared to drop pinch-off. This explains why, in contrast to droplets, viscoelastic bubble threads do not appear for dilute suspensions but require large polymer concentrations.

When wind blows over the surface of a viscous liquid, a clear transition from irregular small-amplitude streamwise-oriented wrinkles to well-defined nearly two-dimensional regular waves is observed at a critical wind velocity. We examine how free-stream turbulence in the air influences the growth of wrinkles and regular waves, as well as the transition between these two regimes. Experiments are carried out in a wind tunnel, in which air is blown over a tank filled with silicone oil whose viscosity is 50 times higher than that of water. The free-stream turbulence is enhanced using upstream grids, achieving relative turbulence intensities up to $8\%$. Surface deformations are measured using free-surface synthetic Schlieren with micrometer accuracy. Velocity measurements are performed using hot-wire anemometry above the interface and particle image velocimetry in the liquid. Results reveal two primary effects of grid-enhanced free-stream turbulence: an increase in the wrinkle amplitude and a reduction in the critical wind speed at the onset of regular waves. Nevertheless, the wrinkle-wave transition still corresponds to an approximately constant friction velocity. We also observe a nonmonotonic evolution of the wave amplitude with fetch, which we rationalize using a wave energy balance model that accounts for the downstream decrease in friction velocity.

We investigate uncertainty growth and chaotic dynamics in statistically steady, stably stratified three-dimensional turbulence. Using direct numerical simulations of the Boussinesq equations, we quantify the divergence of initially infinitesimal perturbations via twin simulations and decorrelator diagnostics. At short times, perturbations exhibit exponential growth, allowing us to define a (largest) Lyapunov exponent. We systematically examine how this exponent depends on stratification strength, quantified by the Brunt-Väisälä frequency and the Froude number, in a parameter regime relevant to oceanic flows. We find that increasing stratification leads to a monotonic reduction of the Lyapunov exponent, indicating suppressed chaoticity. Despite this reduction, uncertainty growth retains the universal temporal sequence observed in homogeneous isotropic turbulence—initial decay, exponential growth, and saturation. The growth phase is characterized by self-similar decorrelator spectra, but exhibits strong anisotropy: uncertainty spreads much more slowly along the stratification direction than horizontally, with the disparity increasing with stratification strength. An analysis of the decorrelator evolution equation reveals that the suppression of chaos arises primarily from strain-mediated alignment dynamics rather than direct buoyancy coupling. Our results provide a quantitative characterization of predictability and uncertainty growth in stratified turbulence and highlight the utility of decorrelator-based methods for anisotropic geophysical flows.

Collective locomotion of swimming and flying animals is fascinating in terms of individual-level fluid mechanics and group-level structure and dynamics. Here we bridge and relate these scales through a model of formation flight that views the collective as a material whose properties arise from the flow-mediated interactions among its members. We build on and revise an aerodynamic model describing how flapping flyers produce vortex wakes and how they are forced by others' wakes. While simplistic, the model faithfully reproduces a series of physical experiments carried out over the past decade on pairwise interactions of flapping foils. By studying longer in-line arrays, we show that the group behaves as a soft “crystal” with regularly spaced member “atoms” whose positioning is, however, susceptible to deformations and dynamical instabilities. Poking or wiggling a member excites longitudinal waves (flow-mediated phonons, or “flonons”) that pass down the group while growing in amplitude, and indeed the internal excitation from flapping is sufficient to trigger instabilities. Linear analysis of the model explains the aerodynamic origin of the lattice spacing, the springiness of the “bonds” between flyers, and the tendency for disturbances to resonantly amplify. Other properties, such as the timescales for instability growth and wave propagation, seem to involve the full nonlinear behavior. These findings suggest intriguing analogies with physical materials that could be generally useful for understanding and analyzing animal groups. Several properties displayed by our system seem particularly relevant to biological collectives, namely, group cohesion and organization, sensitive detection of and response to perturbations, and transmission of information through traveling waves.

Mosquitoes exhibit unique motion patterns that have attracted growing interest from researchers aiming to understand their underlying aerodynamic mechanisms. However, previous studies have primarily focused on hovering flight. In the present study, we measured for the first time the kinematic and morphological data of mosquitoes Aedes togoi in forward flight using three orthogonally aligned and synchronized high-speed cameras, and numerically computed the forces acting on the wing and the surrounding flow. The results show that mosquito wing kinematics in forward flight exhibit two distinctive features that differ from those observed in most other insects. One feature is that the mosquito's stroke plane remains nearly horizontal; the other is that its wing pitching motion is remarkably asymmetric between the downstroke and upstroke. More specifically, the pitch-down acceleration at the beginning of the stroke and the pitch-up amplitude in the middle of the stroke are highly asymmetric. By establishing the kinematic-fluid-aerodynamic link, two novel thrust-generation mechanisms in mosquito forward flight are revealed: asymmetric pitch-down acceleration mechanism and asymmetric pitch-up amplitude mechanism. The mass-specific power of mosquitoes in forward flight is found to be comparable to that of hovering, and approximately 27% lower than that of the smaller mosquitoes Aedes aegypti, potentially offering larger mosquitoes an energetic advantage in seeking and feeding on hosts. These findings not only deepen our understanding of mosquito flight mechanics but also provide new insights for the kinematic design of micro flapping-wing vehicles in forward flight.

Large aperture telescopes are pivotal for exploring the universe, yet even with state-of-the-art manufacturing and launch technology, their size is limited to several meters. As we aim to build larger telescopes—extending tens of meters—designs in which the main mirror is based on liquid deployment in space are emerging as promising candidates. However, alongside their enormous potential advantages, liquid-based surfaces present new challenges in material science, mechanics, and fluid dynamics. One of the fundamental questions is whether it is possible for such surfaces to maintain their precise optical shape over long durations, and in particular under the forces induced by the telescope's accelerations. In this paper, we present a model and a closed-form analytical solution for the non-self-adjoint problem of the dynamics of a thin liquid film pinned within a finite circular domain. We use the 50-m Fluidic Telescope concept as the case study and examine the liquid dynamics of the telescope under both slewing actuation and relaxation regimes, elucidating the role of geometrical parameters and liquid properties. The solutions reveal a maneuvering “budget” wherein the degradation of the mirror surface is directly linked to the choice of maneuvers and their sequence. By simulating 10 years of typical operation, we show that, while the maximal deformation might reach several microns, the spatial distribution and propagation rate of the deformation allow the telescope to maintain its optical functionality for years, with at least a substantial portion of the aperture remaining suitable for astronomical observations. The model provides valuable insights and guidelines into the performance of liquid-film space telescopes, marking a crucial step toward realizing the potential of this innovative concept.

The displacement of air by a noncolloidal particulate suspension between two parallel plates can trigger interfacial instabilities and two seemingly intertwined patterns: deformation of the fluid-fluid interface and dense particle clusters within the suspension, hereafter referred to as plumes. While prior studies have primarily examined the onset and source of this instability, the emergence and coupling of these patterns remain unresolved. Notably, existing investigations have been limited to radial geometries, where continuous outward expansion of the interface weakens plume-plume interactions. Here, we experimentally displace air with an oil suspension in a rectangular Hele-Shaw cell. Confinement within a constant-width channel amplifies interactions between neighboring plumes, giving rise to previously unreported regimes of pattern formation, including plume merging and plume shedding. Image analysis reveals strong coupling between interfacial deformation and plumes and characterizes the interaction between adjacent plumes. Employing the suspension balance model, we demonstrate how net particle flux toward the interface drives particle accumulation and establishes the conditions for pattern formation. Namely, particle clustering at the interface locally slows the advancing interface and produces concave plume tips that become preferential sites for plume initiation. In addition, we develop a simple scaling for the size of the interfacial deformation based on the interplay between upstream pressure, interface concentration, and plume concentration.

A laboratory investigation was conducted to quantify the influence of background rotation on nearly zero-mean turbulence generated within an off-axis mounted isotropic box. High-resolution particle image velocimetry measurements were performed at the box center under varying rotation rates to examine the onset and development of anisotropy. In the absence of rotation, the turbulence exhibits nearly isotropic behavior, with radial and azimuthal velocity fluctuations closely matched and energy spectra consistent with Kolmogorov scaling. As the inverse turbulent Rossby number, ${\text{Ro}}_{\varepsilon }^{-1}$, increases, spectral anisotropy becomes increasingly pronounced, and the range of scales over which the radial and azimuthal spectra diverge broadens. The lower bound of this anisotropic range follows the scaling $({\kappa }_L-{\kappa }_{DI})\eta ={\text{Ro}}_{\varepsilon }^{-1}/40$, indicating a progressive influence of the Coriolis effects. A generalized Taylor transformation applied to spatial and temporal spectra yields characteristic convection velocities $U_r^{*}$ and $U_{\theta }^{*}$, which exceed the local rms fluctuations and scale as $U_r^{*}\sim 3u_r^{\prime }$ and $U_{\theta }^{*}\sim 2u_{\theta }^{\prime }$. Direction-specific turbulent rotation numbers exhibit a linear dependence on ${\text{Ro}}_{\varepsilon }^{-1}$, linking integral-scale rotational dynamics to small-scale anisotropy. The results provide experimental support for theoretical predictions of energy redistribution, quasi-two-dimensionalization, and wave-eddy interaction in rotating turbulence. The empirical scalings may offer compact constraints for turbulence closures in noninertial frames and establish a basis for future studies of scalar transport and dispersion in geophysical and astrophysical flows.

We develop a perturbation-based frequency-response framework for analyzing amplification mechanisms that are central to subcritical routes to transition in wall-bounded shear flows. By systematically expanding the input-output dynamics of fluctuations about the laminar base flow with respect to forcing amplitude, we establish a rigorous correspondence between linear resolvent analysis and higher-order nonlinear interactions. At second order, quadratic interactions of unsteady oblique waves generate steady streamwise streaks via the lift-up mechanism. We demonstrate that the spatial structure of these streaks is captured by the second output singular function of the streamwise-constant resolvent operator. At higher orders, nonlinear coupling between oblique waves and induced streaks acts as structured forcing of the laminar linearized dynamics, yielding additional streak components whose relative phase governs reinforcement or attenuation of the leading-order streak response. Our analysis identifies a critical forcing amplitude marking the breakdown of the weakly nonlinear regime, beyond which direct numerical simulations exhibit sustained unsteadiness. We show that this breakdown coincides with the onset of secondary instability, revealing that the nonlinear interactions responsible for streak formation also drive the modal growth central to classical transition theory. The resulting framework provides a mechanistically transparent and computationally efficient description of transition that unifies nonmodal amplification, streak formation, and modal instability within a single formulation derived directly from the Navier–Stokes equations.

Controlling water motion on surfaces is critical for applications ranging from thermal management to passive water harvesting to self-cleaning coatings. Yet stabilizing continuous water films, desirable for their high surface coverage and drainage capacity, remains challenging with pure water, due to its high surface tension. Existing strategies rely on extreme wettability achieved by coating or fine-scale patterning, which are costly, fragile, or complex to scale. A robust, purely geometric solution is still lacking. We demonstrate that a pair of laser-engraved grooves on a moderately hydrophilic vertical substrate can laterally anchor water and stretch a continuous thin film, without any other surface treatment. Once stabilized, the film extends vertically over 100 capillary lengths ($>30\mathrm{cm}$), with thickness tunable via both flow rate and groove geometry. At the groove extremities, the end of anchoring triggers a cyclic instability, characterized by film rupture, retraction, and droplet release. The thickness of the film and retraction height obey predictive models, while droplet mass varies systematically with spacing and surface tension. This groove-based method offers a straightforward and scalable approach to creating, sustaining, and controlling thin water films. It opens new directions for passive liquid control in condensation, surface cleaning, and 2D millifluidic systems.

We develop a reduced-order theoretical framework for inertial spheroidal particles in turbulent Navier-Stokes flow, representing their orientation with a single unit vector (the director) instead of using a full rotation matrix. This symmetry-based simplification, analogous to Jeffery's classical description of neutrally buoyant spheroids, yields a compact set of evolution equations with fewer degrees of freedom. In the limit of small inertia, the director obeys Jeffery's equation which we consider as the equation on direction of distance between two infinitesimally close trajectories of a chaotic system. This implies that the particle's director is uniquely determined by its position, defining a director field that, in turn, induces a smooth, weakly compressible effective flow through which the spheroids move. This effective flow is distinct from the underlying incompressible turbulent flow, thereby generalizing Maxey's result for spheres. In homogeneous, anisotropic turbulence with zero mean fluid flow, the effective particle flow can acquire a nonzero mean; for example, in rotating turbulence, particles drift uniformly along the rotation axis. We show analytically that prolate spheroids align with the major Lagrangian stretching direction of the turbulent flow, whereas oblate spheroids align with the major Lagrangian compression direction. In spatially inhomogeneous flows (e.g., a wall-bounded channel flow), particle anisotropy can alter turbophoretic drift, possibly reversing the usual migration toward quiescent regions. We also show that inertial spheroids exhibit preferential concentration. Finally, when gravity is included, we derive analytic expressions for the mean settling velocity in the weak-gravity regime. This settling velocity increases monotonically with the particle aspect ratio, from $8/9$ of the Stokes settling velocity of an equivalent sphere for disklike particles to $4/3$ for rodlike particles. In the strong-gravity limit, the driving of spheroids by the Navier-Stokes turbulence can be effectively described as white noise. We show that very small oblate spheroids settle edge-first, but small ones settle broadside-on. The orientation-dependent settling velocity field is spatially varying and weakly compressible, providing a new mechanism for multifractal preferential concentration. Thus, this director-based framework provides a unified, physically transparent generalization of Jeffery's and Maxey's theories, yielding multiple new analytical predictions for the transport of nonspherical particles in isotropic, anisotropic, and stratified turbulent flows and environments.