We report the pinching of an elongated liquid droplet confined in a rectangular microchannel. A local variation of the channel topography induces the droplet pinching and can lead to its breakup. The modification of the channel topography is caused by either a reversible local dilation of the channel bottom wall or a confinement gradient irreversibly printed in the channel. Interestingly, in both cases, channel height contraction of a few micrometers leads to the droplet's pinching in the direction of the channel width. If this pinching is such that the droplet is no longer confined at the level of its deformation, i.e., the liquid thread becomes three dimensional, the droplet splits in two. By minimizing the surface energy of the droplet under the channel confinement gradient, we can predict its pinching or breakup, if any. The dynamics of the droplet deformation are then captured by a semianalytical model that relies on the observation that the deformation is self-similar and assumes that most of the viscous dissipation occurs in the gutters at the corners of the channel. Conversely, we show that this kinetic model can be used to extract the channel's average topographic variation, down to a few micrometers, by measuring the droplet pinching dynamics under a classical optical microscope.

We study low Reynolds number turbulence in a suspension of polar, extensile, self-propelled inertial swimmers. We review the bend and splay mechanisms that destabilize an ordered flock. The suspension is always unstable to bend perturbations. Using a minimal 1D model, we show that the splay-stable to splay-unstable transition occurs via a supercritical Hopf bifurcation. We perform high-resolution numerical simulations in 2D to study the varieties of turbulence present in this system transitioning from defect turbulence to concentration-wave turbulence depending on a single nondimensional number, denoting the ratio of the splay-concentration wavespeed to the swimmer motility.

Large-eddy simulation (LES) is one of the high-fidelity turbulence simulations by resolving large-scale motions while modeling the effects of unresolved subgrid scales. However, the predictive accuracy of LES is largely dependent on the subgrid-scale (SGS) model. Traditional SGS models, based on assumptions such as isotropy and scale similarity, have been successfully applied to canonical turbulent flows but often fail in complex flows. Recent advances in machine learning, especially neural network (NN), have opened a new paradigm for SGS modeling by learning complex, nonlinear relationships directly from high-fidelity data. In this paper, we review the limitations of traditional SGS models and examine the development of NN-based SGS models and their strengths and limitations. Toward universal NN-based SGS model development, we discuss critical issues related to extrapolation to high Reynolds numbers, generalization to untrained flows, physical consistency, and computational cost. By combining data-driven methods with physical intuition and principles, NN-based SGS modeling has the potential to enhance the fidelity and versatility of LES.

We present measurements of the near-wall velocity field in turbulent Rayleigh-Bénard convection with a partially rough horizontal surface. These measurements cover Rayleigh numbers ranging from $Ra=5.8\times {10}^{10}$ to $Ra=8.0\times {10}^{11}$, while the Prandtl number was fixed at $Pr=0.7$. The measurements have been undertaken in the large-scale convection experiment “Barrel of Ilmenau,” which provides a very high resolution in space and time. The measurements confirm the prominent role of the ratio between the thickness of the boundary layer ${\delta }_{th}$ and the height of the roughness elements $h$, although transition effects only appear below ${\delta }_{th}/h\approx 0.6$ in our experiments. In addition, we calculated the ratio between the turbulent kinetic energy and the average kinetic energy in the boundary layer. This ratio remains virtually constant up to $Ra=4.2\times {10}^{11}$ and increases beyond this value. This is another indication of a qualitative transition of the boundary layer flow field. We observed this transition above both the TOP and above the VALLEY regions of the rough surface, concluding that both regions may contribute similarly to an increase in heat flux. The transition in the flow field is purely induced by viscous effects. The Richardson number, based on the thickness of the boundary layer and the velocity of the mean wind, is much smaller than one for all Rayleigh numbers investigated. This indicates that viscous effects dominate the near-wall flow field, and buoyancy does not play any role in the variation of the flow field here. We have also analysed time series of the wall-normal velocity component $w$ in the plane where the temperature fluctuates at its maximum. The distribution of the fluctuations of $w$ deviates from a normal distribution for all investigated Rayleigh numbers. In particular, the distributions exhibit broader tails on both sides. However, the distributions show just a little asymmetry, which we would expect as a signature of thermal plumes.

This study examines the propagation characteristics and sources of linear noise generated by an underwater propeller, employing a tailored formulation of the Ffowcs Williams–Hawkings equation. The simplified formulation enhances efficiency of the noise calculations by assuming uniform propagation times for noise sources located at different points on the blade surface. Comparisons of the predicted noise under uniform and nonuniform inflow conditions show that azimuthally varying inflow significantly amplifies the overall sound pressure level across most emission angles. Notably, the noise directivity and decay rates exhibit substantial changes, particularly within the propeller disk plane. These variations are primarily attributed to the amplification and dominant contribution of blade passing frequency (BPF) loading noise. An equivalent emission point acoustic model, derived from the simplified formulation, offers intuitive insights into the propagation behavior and source distribution of the loading noise. In the near field, the noise radiation is determined by variations in both radiation distance and blade forces. The predominant BPF tone arises from elements associated with different harmonics of the blade force, with interference among these elements causing azimuthally asymmetric noise radiation under the nonuniform inflow condition. In the far field, the noise spectrum is governed solely by the force derivatives, and the force fluctuations under nonuniform inflow only amplify the BPF tones, as interblade interference suppresses components at other frequencies. Regarding the noise source distribution, the near-field BPF tone and far-field broadband noise under the uniform inflow primarily originate from the root of the blade suction side and the blade trailing edge, respectively. Under the nonuniform inflow condition, the dominant BPF tone in both near and far fields is driven by the interaction of azimuthally varying inflow with the leading edges of the blades.

Phase-resolved ocean wave models have recently garnered significant attention in wave forecasting, as they capture the phase information of each wave component, enabling the prediction of three-dimensional surface elevation distributions within a defined sea area. However, wave fields input into phase-resolved models often deviate from actual wave fields due to limitations in wave surface measurement and reconstruction processes. Moreover, wave evolution is a complex dynamical process influenced by multiple factors, such as wind, currents, and topography, which are challenging to accurately simulate in phase-resolved wave models. To mitigate the impact of wave field disturbances and enhance prediction performance for strongly nonlinear ocean waves, we propose a coupled approach that integrates observations into wave simulations by combining the pseudospectral Fourier-Legendre method with the ensemble Kalman filter. We first establish and validate an assimilation framework applicable to strongly nonlinear phase-resolved wave simulations. Next, we optimize the assimilation parameters for both two- and three-dimensional regular and irregular waves, revealing that optimal parameters for irregular waves can be inferred from those of regular waves. Using these optimal parameters, we analyze the assimilation performance for waves with varying nonlinearity and disturbances. The results demonstrate that the coupled simulation approach delivers accurate surface elevation predictions, with errors consistently decreasing over time, even in highly nonlinear wave scenarios.

Experiments on two-dimensional (2D) random water wave propagation in a large wave tank are analyzed when the effect of dispersion changes. A stereoscopic profilometry technique is used to measure the water surface displacement resolved in both time and space over a significant fraction of the wave tank. The wave regimes are characterized by analyzing the space-time spectral statistical properties of the wave field. At a given finite water depth, the effect of dispersion can be varied by tuning the peak frequency of the wave generation. In shallow water conditions, the waves are only weakly dispersive, and this enables the propagation of solitons. In these conditions, random wave forcing produces soliton gases. In deep water conditions, the waves are dispersive, and for wideband spectra, one observes the development of weak turbulence. A transition between these regimes is observed when changing the peak forcing frequency (dispersion) and the wave amplitude (nonlinearity), with a clear threshold between states with solitons and soliton-less states. The development of a soliton gas is associated with a strong change of the wave spectrum as well as a significant evolution of the distribution of the water elevation. We also observed a strong effect of the finite size of the tank due to the peculiar reflection laws of line solitons.

This research explores the modulation of Rayleigh-Plateau instability by adjusting the orientation angle and eccentricity of a wire within a nozzle. We demonstrate that both the angle and eccentricity significantly influence the Rayleigh-Plateau instability regimes. They both also influence characteristics, such as bead velocity along the wire, bead spacing (wavelength), and bead volume. Notably, when wires are both angled and eccentric, the effect of angle prevails. Our approach includes an empirical scaling analysis, comparing gravity, and viscosity forces on a single bead, yielding a unified empirical viscous force law, and enhancing understanding of Rayleigh-Plateau regime dynamics. This framework enriches our understanding of the forces at play in Rayleigh-Plateau instability and provides practical insights into the manipulation of fluid dynamics in industrial applications.

We investigate the 3D stationary flow of a weakly conducting fluid in a cubic cavity, driven by the Lorentz force created by two permanent magnets and a weak constant current. Our goal is to determine the conditions leading to efficient mixing within the cavity. The flow is composed of a large recirculation cell created by one side magnet, superposed on two recirculation cells created by a central magnet perpendicular to the first one. The overall structure of this flow, obtained here by solving the Stokes equations with Lorentz forcing, is similar to the tricellular model flow studied by Toussaint et al. [Phys. Fluids 7, 2587 (1995)]. Chaotic advection in this flow is analyzed by means of Poincaré sections, Lyapunov exponents, and expansion entropies. In addition, we quantify the quality of mixing by computing contamination rates, homogeneity, as well as mixing times. Though individual vortices have poor mixing properties, the superposition of both flows creates chaotic streamlines and efficient mixing.

I study turbulence in self-gravitating superfluids by performing direct numerical simulations of the three-dimensional (3D) Gross-Pitaevskii-Poisson (GPP) equation, which is also a model for dark-matter halos around galaxies. In the absence of self-gravity, the spectrally truncated Gross-Pitaevskii (GP) equation shows the emergence of Kolmogorov's $5/3$ scaling in the incompressible kinetic-energy spectrum. Introducing self-gravity, I observe the formation of different structures, from sheetlike to spherically collapsed structures, which introduce a minimum in the kinetic-energy spectrum that corresponds to the sizes of these structures. The system shows early convergence towards statistically stationary states, which I show by the onset of thermalization in the compressible kinetic-energy spectrum, where $E_{\mathrm{kin}}^c\propto k^2$. I also show that the formation of such large-scale structures suggests that the particles (bosons) move from small to large scales through an inverse cascade, supporting a mechanism for the formation of large-scale structures, such as dark-matter halos, around our galaxy Milky Way.

Liquid marbles, droplets coated with hydrophobic micro/nanoparticles, exhibit unique post-impact behaviors. This study experimentally investigates the oscillations and bouncing dynamics of liquid marble on a hydrophilic surface, and compares it with a mass-spring-damper model, to better understand the influence of parameters such as the Weber number (We), Bond number (Bo), and Ohnesorge number (Oh). Theoretical and experimental analyses were conducted to evaluate liquid marble's impact across different viscosities, volumes, and impact velocities. The MSD model describes liquid marble oscillations in two phases: (A) free oscillation during bouncing between two consecutive impacts, and (B) oscillation following the final bounce when the liquid marble is in contact with the surface, achieving a total error of less than 5%. The findings reveal that an increase in the Oh, Bo, and We results in a higher, lower, and higher damping ratio. As a proof of concept, this study highlights the potential for measuring key physical properties of liquid marble's core fluid by analyzing its oscillation damping ratio. Moreover, the number of bounces decreases with rising Oh, driven by heightened viscous dissipation. Greater We values intensify energy loss through deformation and inertial effects, further limiting the number of bounces.

The impact of interfacial deformations on the hydrodynamic force and torque exerted on a spherical particle with surface slip moving along a gas-liquid interface is investigated. Following a two-parameter asymptotic modeling approach, we perturb the interface from its planar state and apply the Lorentz reciprocal theorem to the zeroth- and first-order approximations to analytically calculate the drag and torque on the particle. This allows us to explicitly account for the effect of physical parameters like the three-phase contact angle, the Bond number, and the slip coefficient on the particle motion. In addition, we study the interactions between two translating and rotating particles at a large separation. The interaction forces and torques exerted by the flow-induced deformations are calculated via the linear superposition approximation, where the interaction forces are identified as dipolar in terms of the azimuthal angle.

This study investigates turbulent flows over rough-wall periodic hills using large-eddy simulations with the curvilinear immersed boundary method. Five rough surface configurations (R1–R5) are generated by randomly oriented ellipsoids with minor semiaxes ranging from $r=0.048h$ to $0.160h$, where $h$ denotes the hill height, at a Reynolds number ${\mathrm{Re}}_b=10595$ (which is defined based on the bulk velocity and the hill height). The analysis reveals that surface roughness significantly alters flow statistics, reducing streamwise velocity, enhancing wall-normal momentum transfer, and redistributing Reynolds stresses. It monotonically increases the separation bubble length from the smooth-surface case to the R5 case, while inducing upward and downstream displacement of the bubble center $(x_c,$ $y_c)$. Notably, the downstream movement of $x_c$ saturates beyond R3. A key finding is the geometric similarity of separation bubbles under coordinate transformation. By aligning bubble centers and rescaling coordinates using semiaxes $d_x$ and $d_y$, we demonstrate the collapse of bubble outlines and zero-velocity isolines across rough surface configurations. Moreover, this similarity extends to smooth-surface cases at varying Reynolds numbers. Analysis based on momentum balance reveals a dual role of the rough surface: it reduces the available momentum in the near-wall region of lower hills, while simultaneously counteracting the adverse pressure gradient induced by hill slopes. This dual role alters the flow separation mechanism, with the adverse pressure gradient caused by hill slopes being the dominant factor under low surface roughness conditions and near-wall momentum loss due to surface roughness prevailing under high roughness conditions.

Storage of sperm in the female reproductive tract occurs across species that reproduce by internal fertilization, modulating availability and preserving fertility. For instance, the sperm of the insects from the family Drosophilidae are stored in and released from the seminal receptacle—a long, slender, coiled tube. The sperm flagella, longer than any straight portion of the tube, must be flexible enough to navigate the twists and turns of these tightly coiled organs. As a step towards studying the coupled system of fluid, tube geometry, and flexible flagella, we present here a framework to study flagellar motion in tubular enclosures. The basic swimmer is modeled as a flexible Kirchhoff rod comprised of regularized Stokeslet segments, while the rigid surfaces that constitute the enclosure are represented by regularized Stokeslet surfaces. Swimming kinematics is not prescribed, but emerges from time-varying preferred curvatures. This approach allows for swimmer-wall interactions and, in turn, the evolution of swimming behavior near rigid boundaries. We first investigate the effects of flagellar bending rigidity, beat frequency, and the presence of inactive flagellar regions on swimming performance in free space. Next, we study the effect of confinement levels on swimming performance inside straight tubes. We find that swimming speed increases as the tube diameter decreases, with a more pronounced boost in speed for stiffer flagella. We also find that the swimmers, whose preferred beat is planar, drift towards the tube walls if the diameter of the tube is large enough. Finally, our work demonstrates that the model flagellum can navigate through a curved tube, which will enable studies aimed at understanding the coevolution of female reproductive tracts and sperm morphology in different organisms.

We develop a robust numerical method for thin plates falling in inviscid fluid that allows for leading-edge vortex shedding. The inclusion of leading-edge shedding restores physical dynamics to vortex-sheet models of falling bodies, and large-amplitude fluttering and tumbling are observed in inviscid simulations. Leading-edge shedding is achieved by introducing a quadrature rule and smoothing procedure for the Birkhoff-Rott equations. The smoothing error is controlled by a projection procedure similar to fencing. We find a transition point between fluttering and tumbling that is consistent with previous viscous simulations and experiments, and other falling motions such as looping and autorotation are also observed as the plate density increases. The dipole street wakes behind the fluttering plates resemble those in experiments. We consider plates bent into V shapes and study the effects of density and bending angle on the qualitative falling dynamics. At small densities, increasing the bending angle stabilizes the falling motion into fluttering, while at large densities, decreasing the bending angle stabilizes the falling motion into autorotation. In the autorotation regime, the magnitude of angular velocity increases as time cubed before it reaches a terminal angular velocity, and in the fluttering regime, the fluttering frequency scales as the $-1/2$ power of $R_1$, the plate density.

When a floating body is internally or externally vibrated, its self-generated wavefield can lead to steady propulsion along the interface. In this article, we review several related and recently discovered systems that leverage this propulsion mechanism and interact hydrodynamically with one another via these surface waves. Particles with an onboard oscillatory driver may self-propel by virtue of a fore-aft asymmetric wavefield, a phenomenon with demonstrated relevance to biological and artificial systems across scales. Freely floating particles on a vibrated fluid bath can also self-propel along straight paths, but may also rotate in place or move along curved arcs, depending sensitively on the particle asymmetries and driving parameters. Such surfing particles interact at a distance through their mutual capillary wavefield and exhibit a rich array of collective dynamics. Overall, these accessible, tunable, and visually appealing systems motivate future investigations into a number of outstanding questions in fundamental fluid mechanics, while potentially also informing advances in the fields of active matter, hydrodynamic quantum analogs, and robotics.

This paper is a personal overview of the efforts over the past half century to understand fluid turbulence in terms of simpler coherent units. The consequences of chaos and the concept of coherence are first reviewed, using examples from free-shear and wall-bounded shear flows, and including how the simplifications due to coherent structures have been useful in the conceptualization and control of turbulence. It is remarked that, even if this approach has revolutionized our understanding of the flow, most of turbulence cannot yet be described by structures. This includes cascades, both direct and inverse, and possibly junk turbulence, whose role, if any, is currently unknown. This part of the paper is mostly a catalog of questions, some of them answered and others still open. A second part of the paper examines which new techniques can be expected to help in attacking the open questions and which, in the opinion of the author, are the strengths and limitations of current approaches, such as data-driven science and causal inference.

Upon the impact of a flat disk on a boiling liquid, i.e., a liquid that is in thermal equilibrium with its own vapor, a thin vapor layer is entrapped under the disk. Due to the tendency of vapor to undergo phase change under pressure variation upon impact, the dynamics of this entrapped vapor pocket are different from those of a noncondensable air pocket. In this work, we experimentally investigate the dynamics of the entrapped vapor pocket, more specifically its time evolution and its subsequent influence on the hydrodynamic loads at different equilibrium ambient temperatures and impact velocities. We find that the retraction of the vapor pocket at high ambient temperature and small impact velocity is slow, occurring from the disk edge, and driven by the dynamic pressure ${\rho }_L{U}_0^2$. In contrast, at lower ambient temperatures and large impact velocities, after a short initial stage, the vapor pocket will collapse rapidly due to condensation. This scenario is confirmed by conducting experiments where, by heating the disk, the vapor pocket collapse is observed to slow down. We attribute this to the vaporization of liquid near the three-phase contact line region that frustrates the condensation process and reduces the impact pressure on the disk. The violent collapse of the vapor pocket may impart additional instantaneous momentum, but the overall pressure and force impulses are still found to be closely associated with the liquid added mass. Finally, we found that at a high tilt angle of the disk, the three-phase contact line movement over the disk surface may hinder the proper entrapment and compression of the vapor pocket, which results in a lower central impact pressure as rapid condensation at the central disk region does not occur.

Solidification processes at the boundary between the Earth's inner and outer core are the primary source of buoyancy forces that drive convection and Geodynamo in the outer core. This study aims to numerically investigate the impact of different buoyancy sources on convection within the Earth's core and the resulting magnetic field. We analyze three models: thermally driven, chemically driven, and thermochemically driven dynamos. The results confirm that both the magnetic field and the convective velocity field depend on the sources of buoyancy. Additionally, dipole polarity reversals and the super-rotation of the Earth's inner core are influenced by different buoyancy sources. As the Ekman number decreases, this dependence weakens.

Input-output analysis has been widely used to predict the transition to turbulence in wall-bounded shear flows, but it typically does not capture the full nonlinear effects involved. This work employs the small-signal finite-gain (SSFG) ${\mathcal{L}}_p$ stability theorem to assess nonlinear input-output stability. This SSFG ${\mathcal{L}}_p$ stability theorem can predict permissible forcing amplitudes below which a finite nonlinear input-output gain can be maintained. Our analysis employs linear matrix inequalities and sum-of-squares as the primary tools to search for a quadratic Lyapunov function of an unforced nonlinear system. The resulting Lyapunov function can certify the SSFG ${\mathcal{L}}_p$ stability of a nonlinear input-output system. We demonstrate the applicability of the SSFG ${\mathcal{L}}_p$ stability theorem using a nine-mode shear flow model with a random body force. The predicted nonlinear input-output ${\mathcal{L}}_p$ gain (amplification) is consistent with numerical simulations; the ${\mathcal{L}}_p$ norm of the output from numerical simulations remains bounded by the theoretical prediction from the SSFG ${\mathcal{L}}_p$ stability theorem, with the gap between simulated and theoretical bounds narrowing as $p\to \infty$. The input-output gain obtained from the nonlinear SSFG ${\mathcal{L}}_p$ stability theorem is higher than the linear ${\mathcal{L}}_p$ gain, which suggests that nonlinearity can significantly amplify small disturbances. Both nonlinear ${\mathcal{L}}_p$ gain and linear ${\mathcal{L}}_p$ gain are valid for each $p\in [1,\infty ]$, and such generalizability leads to much higher upper bounds on input-output gain than those predicted by linear ${\mathcal{L}}_2$ gain (${\mathcal{H}}_{\infty }$ norm of transfer function). The SSFG ${\mathcal{L}}_p$ stability theorem requires the input forcing to be smaller than a permissible forcing amplitude to maintain finite input-output gain, which is an inherently nonlinear behavior that cannot be predicted by linear input-output analysis. We also identify such permissible forcing amplitude using numerical simulations and bisection search, where below such forcing amplitude, the output norm at any time will be lower than a given threshold value. The permissible forcing amplitude identified from the SSFG ${\mathcal{L}}_p$ stability theorem is conservative but also consistent with that obtained by numerical simulations and bisection search. This study demonstrates that the nonlinear SSFG ${\mathcal{L}}_p$ stability theorem is a powerful tool for analyzing nonlinear input-output systems such as transitional shear flows with external disturbance.