Microscale cilia play a vital role in mucociliary clearance (MCC) in the human respiratory airways. In this numerical study, we examine fluid transport driven by the active beating of a single filament immersed in a three-dimensional two-phase flow. The cilium is modeled as an elastic filament actuated by a time-varying basal angle. The two-phase flow is resolved using the Shan-Chen model in a lattice Boltzmann solver, while the two-way coupling between the filament and the fluid is treated by the immersed boundary method. Pathological conditions such as cystic fibrosis and chronic obstructive pulmonary disease are associated with drastic alterations of MCC properties, including changes in periciliary layer (PCL) thickness and the viscosity ratio between the PCL and the mucus layer. Here, we systematically investigate the effects of these parameters along with filament bending stiffness on the beating pattern and fluid transport. Within the parameter ranges investigated, a moderate PCL thickness and viscosity ratio, together with high bending stiffness, tend to yield higher net flow rate and transport efficiency. The underlying hydrodynamic mechanisms are characterized through analyses of the beating pattern, filament dynamics, energy partition, and flow-field evolution. Two competing mechanisms are identified: the drag-elastic force balance and the viscous diffusion of momentum. Furthermore, quantitative relationships are established between flow rate and beating pattern, expressed in terms of tip amplitude and beating asymmetry.

A stratified and rotating, ideal (i.e., inviscid and nondiffusive) fluid, contained in a box subject to meridional differential heating (“forcing”), is described by two state vectors. These represent (1) the three-dimensional center-of-mass (COM) location relative to the basin center and (2) the nonlinearly coupled basin-averaged angular momentum vector, associated with overturning circulations in zonal, meridional, and horizontal directions. Without wind, horizontal circulation (associated with the vertical component of the basin-averaged angular momentum) is absent. The COM displacements can be likened to the motion of a "fluid pendulum." In addition to the two angles characterizing the motion of a spherical pendulum relative to the vertical and zonal directions, a stratified fluid's "pendulum length"—proportional to the fluid's stratification strength—is changing dynamically too. In this ideal fluid setting, in the absence of forcing or rotation, the remaining equations, though nonlinear, are integrable, and circulation and COM motion are periodic. When rotation and forcing (i.e., differential heating in the meridional plane) are both present, assuming the rotation axis to be antiparallel to gravity, direct integration of the governing equations reveals that the dynamics is inconclusive: both periodic and aperiodic state trajectories are observed. This is attributed to the fact that the resulting two-degrees-of-freedom Hamiltonian system is subject to the Kolmogorov-Arnold-Moser (KAM) theorem. The latter predicts that some of the periodic orbits that occur without rotation or forcing are replaced by chaotic orbits. As this Hamiltonian system, including gyroscopic terms, can be rewritten as a forced, complex Duffing equation, these results demonstrate the presence of Hamiltonian chaos in this type of Duffing equation.

This study investigates the ideal two-fluid plasma Richtmyer-Meshkov instability under the influence of initially uniform magnetic fields. Two magnetic-field orientations are investigated, in the plane of the two-dimensional interface perturbations aligned with the mean interface location ($y$magnetic field) and out of plane ($z$ magnetic field). Results are presented for ion plasma skin depths ranging from 0.1 to 10 perturbation wavelengths and a magnetic interaction parameter of $\beta =0.1$. The simulation results are compared with the unmagnetized and hydrodynamic reference cases. Our analysis demonstrates that an initial magnetic field parallel to the interface suppresses the growth of initial primary and secondary interface instabilities, depending on the plasma length scale. We attribute the suppression of the instability to transport parallel with the interface, leading to high localized vorticity but reduced residual interface out-of-plane vorticity that drives perturbation growth. In contrast, the out-of-plane initial magnetic field prevents the Lorentz transfer of vorticity away from the interface, resulting in perturbation growth rates equivalent to the unmagnetized case but breaking the symmetry of the primary mode.

The Kármán-Howarth-Monin-Hill equation has been used by various authors to quantify and understand the small-scale turbulent energy cascade without assumptions and therefore even in the case of nonhomogeneous turbulence. A complementary equation was introduced by Germano [Germano et al., Phys. Fluids 19, 038102 (2007)] to describe the large-scale dynamics of the flow. In this paper, the links between the Germano equation and large-eddy simulation (LES) are examined and an approximation of an exact equation is used to design a new LES model which captures the physical energy transfer between filtered scales and residual subfilter scales. This new model, based on simple simplifications of exact equations, is tested both a priori and a posteriori in a Taylor-Green flow. The model is found to better represent the local energy transfers compared to a similar model introduced by Brun [Brun et al., Theor. Comput. Fluid Dyn. 20, 1 (2006)], especially for both extreme forward and backscatter events. The Bardina et al. scale similarity model [Bardina et al., AIAA 80, 1357 (1980)] overperforms our model in the a priori analysis, meaning that refining the mathematical approximations used for the derivation of our model could be useful, but our model's performance is comparable to, if not even better than, the scale similarity model in a mixed configuration, including a turbulent viscosity model. Therefore, our model, derived with simple simplifications of the exact two-point equations, already performs similarly to the LES models classically used for simulations. This paper provides a proof of concept that two-point equations can be used to develop new LES models and it may be the right direction to develop more efficient models derived from the Navier-Stokes equations.

At supercritical pressures, intermolecular forces and molecular packing effects strongly influence fluid behavior, leading to thermodynamic and transport properties that differ significantly from those at subcritical pressures. At these conditions, the resulting high-pressure thermodynamic state space can be divided into liquidlike and gaslike regimes, separated by the pseudoboiling region, where thermophysical properties change rapidly. In this regard, the effects of real-fluid properties and pseudoboiling phenomena on turbulence at ${\text{Re}}_{\lambda }=30$ and ${\text{Ma}}_t=0.1$ are investigated through direct numerical simulations of isotropic turbulence in five thermodynamic states of ${\mathrm{CO}}_2$: one liquidlike, one gaslike, and three pseudoboiling conditions. The thermophysical operating conditions result in Prandtl numbers greater than one, leading to the generation of sub-Kolmogorov thermal scales. Turbulence statistics are, thus, assessed through spectra, probability density functions, and higher-order moments. Temperature-related quantities are particularly sensitive to supercritical fluid effects, showing increased intermittency in the temperature variance dissipation rate and reduced production of mean-square temperature gradients, particularly in strong pseudoboiling conditions. Finally, local flow topology is analyzed using joint probability density functions of the velocity gradient invariants, conditioned on regions with intense pseudoboiling activity. These regions are found to suppress strain-dominated structures while enhancing vortical motions.

Linear temporal stability analysis of a viscous liquid jet in ambient gas under a thermal field is performed, considering both axisymmetric and nonaxisymmetric disturbances. The basic temperature profile is analytically derived from the thermal conduction equation. The thermal field influences the jet instability characteristics through thermal-capillary and Marangoni effects by changing the stress at the jet surface. Two unstable modes are stimulated under the thermal field, including varicose and helical modes. The energy budget analysis reveals that the helical mode is induced by the azimuthal Marangoni instability. The influences of Marangoni effect and thermal diffusivity on the nonisothermal jet instability are studied systematically. The enhancement of the Marangoni effect (increasing the Ma) or the suppression of the thermal diffusivity effect (increasing the Pr) will promote the helical mode and make it dominate the jet instability. As the dominant mode changes from varicose mode to helical mode, the dominant instability mechanism changes from the Rayleigh-Plateau instability to the azimuthal Marangoni instability synchronously. Phase diagrams of different dominant modes and instability mechanisms are represented in the $(\mathrm{Pr},\mathrm{Ma})$ plane with varying inertial stress. The enhancement of the inertial effect will decrease the critical Ma and Pr for the transition from varicose mode to helical mode, which encourages the helical mode to dominate the jet instability.

Understanding the re-energization of wind turbine wakes is crucial for the design and control of wind farms. Close to the rotor, this process is determined by the dynamics of the tip vortices. Here, we experimentally investigate the downstream evolution of the tip vortices for different inflow conditions. The experiments were performed in the Variable Density Turbulence Tunnel at the Max Planck Institute for Dynamics and Self-Organization, which uses pressurized ${\mathrm{SF}}_6$ as the working fluid to achieve a turbine diameter-based Reynolds number of ${\mathrm{Re}}_D=2.9\times {10}^6$. An active turbulence grid was used to generate atmospheric inflow conditions with varying levels of mean shear and turbulence intensity. Hot wire measurements of the streamwise velocity component were conducted in the inflow and the wake of a model wind turbine MoWiTO 0.6 for various tip speed ratios and are used to investigate the scaling of tip vortex breakdown in the near wake. Three different scaling regimes can be identified, which we link to an initial advection phase, the vortex breakdown, and a decaying turbulence regime. While the scaling in the vortex breakdown regime is only weakly affected by variations in mean velocity shear and turbulence intensity, higher tip speed ratios lead to faster breakdown.

Polar sea ice is crucial to Earth's climate system. Its dynamics also affect coastal communities, wildlife, and global shipping. Sea ice is typically modeled as a continuum fluid using a model proposed almost 50 years ago, which is moderately accurate for packed ice, but loses its predictive accuracy outside of the central ice pack. Discrete element methods (DEMs), which are commonly used for modeling granular media, offer an alternative by resolving the behavior of individual ice floes, including collisions, frictional contact, fracture, and ridging. However, DEMs are generally too costly for large-scale simulations. To address this, we present a framework for inferring rheological behavior from DEM velocity data. We characterize isotropic constitutive laws as scalar functions of the principal invariants of the strain-rate tensor. These functions are parameterized by neural networks trained on DEM data. By combining machine learning and finite element methods, we incorporate the governing partial differential equation (PDE) into the training, requiring to solve a PDE-constrained optimization problem for the network parameters. We focus on unidirectional parallel shear flows, which allow us to infer the effective shear viscosity. We find that, over a wide range of ice concentrations, the velocity fields observed in a complex sea ice DEM can be captured by a nonlinear rheology. Depending on the ice concentration, a shear-thinning or a shear-thickening behavior is observed. Moreover, the effective shear viscosity is found to increase by several orders of magnitude with changes as small as 5% in the sea ice concentration. We show that the learned rheology generalizes to different forcing scenarios, time-dependent problems, and settings in which compressibility is not a dominant factor. For these reasons, our framework represents a major step toward developing non-Newtonian models that accurately reproduce observed sea ice dynamics.

The influence of initial shape imperfections on the post-buckling and translational behavior of encapsulated microbubbles is investigated subject to acoustic excitation in an unbounded flow. Bifurcation analysis reveals that imperfections lower the critical overpressure for buckling, guiding the bubble along stable branches with transitions influenced by the nature of the imperfections. The resulting branches emerge as unfoldings of bifurcation diagrams and closely resemble solution families emanating from the standard bifurcation diagram of a perfect sphere. Dynamic simulations for fixed forcing frequency demonstrate that the microbubble buckles at the defective pole and at maximum compression adopts the shape corresponding to the buckled shape that emerges in the static bifurcation diagram for the same pressure disturbance. Simulations further reveal that the deformed microbubble exhibits translational motion in the direction of concavity, driven by the balance between pressure and viscous drag, both aligned with this motion as a result of the deformed shape acquired by the microbubble. The translational speed is highly dependent on the shell stretching and bending elasticities and forcing frequency, with an optimal speed achieved when the forcing frequency equals the difference between the resonance frequencies of the initial shape and the compressed static shape corresponding to the imposed sound amplitude. Higher sound amplitude or lower bending resistance leads to more pronounced deformations that enhance translational motion. The impact of this dynamic response pattern on the recently reported translational motion of properly engineered coated microbubbles to act as microswimmers in modern drug delivery modalities under ultrasound excitation is highlighted.

This study presents a numerical investigation of electro-thermo-convection (ETC) turbulence resulting from unipolar charge injection under microgravity conditions. Both strong and moderate unipolar injection ETC in a cavity are considered. In the turbulent state, convection driven by electric field forces can effectively mix the flow. The mode decomposition reveals that the flow field exhibits several main modes, whereas the temperature and charge fields are only dominated by a specific mode. Moreover, the flow demonstrates self-similarity under a range of parameters. It is shown that both moderate and strong charge injection conditions can realize effective heat transfer enhancement. The Nusselt number increases with the increase of the electric Rayleigh number and the decrease of the dimensionless mobility. This study also demonstrates that the ETC turbulence can enhance heat transfer by two orders of magnitude compared to the pure conduction state. This enhancement is comparable to the intensity of thermal convection achieved at a Rayleigh number of ${10}^9$. This study extends prior research on electrohydrodynamics by investigating ETC turbulence. The findings provide valuable reference for experiments and thermal management applications under microgravity conditions.

Fluid displacement in porous media is a key process in many industrial and environmental applications. When a less viscous fluid displaces a more viscous one in porous media or Hele-Shaw cells, a finger-like interfacial pattern known as the Saffman-Taylor instability typically occurs. Recently, partially miscible systems have attracted attention because they exhibit multiple droplet formations instead of conventional fingering. While the effects of Hele-Shaw-cell gap width on hydrodynamic instability have been well established in fully miscible and immiscible systems, where narrower gaps produce thinner and more numerous fingers, the influence of gap confinement in partially miscible systems remains unclear. In this study, we experimentally investigated the effect of gap width on fluid displacement dynamics in a partially miscible $\mathrm{PEG}\text{−}{\mathrm{Na}}_2{\mathrm{SO}}_4$-water system. The droplet size decreased and the number of the droplets increased as the gap became smaller, indicating that confinement intensified droplet formation. The total interfacial length was successfully scaled using the flow rate, flow velocity, and gap width, collapsing onto a universal curve when expressed as a function of flow-rate-to-gap ratio. The derived empirical exponent was consistent with a force balance between inertial and capillary stresses, suggesting a transitional “inertia-modified capillary” regime. This scaling framework provides predictive insights into the interfacial morphology of partially miscible systems, bridging thermodynamic interfacial forces and hydrodynamic flow.

We investigate the structure of damped two-dimensional perturbations in unstable plane-parallel shear flows with an inflection point. In inviscid flows within the stable wave number region $k$, no regular eigenmodes exist – the frequency spectrum $\omega$ consists of a continuous set of singular van Kampen modes with real frequencies. Nevertheless, initial perturbations of the total vorticity integrated across the flow decay exponentially, resembling the behavior of an eigenmode with complex eigenfrequency $\mathrm{Im}\omega <0$ (Landau damping). However, the vorticity itself does not decay but becomes increasingly corrugated across the flow. We demonstrate that accounting for arbitrarily small viscosity transforms this exponentially decaying perturbation into a true eigenmode in which the vorticity preserves its spatial form. We numerically trace the transformation of the vorticity structure of this mode and its disappearance as viscosity approaches zero. We discuss similarities and differences between the behavior of damped perturbations in the transition from inviscid to nearly inviscid flows in hydrodynamics and their behavior in plasma and homogeneous stellar systems during the analogous transition from collisionless to very weakly collisional systems.

Turbulent mixers have been widely used in industrial settings for chemical production and increasingly for therapeutic nanoparticle formulation by antisolvent precipitation. The quality of the product is closely related to the fluid and mixing dynamics inside the mixers. Due to the rapid timescales and small sizes of many turbulent mixing geometries, computational fluid dynamics simulations have been the primary tool used to predict and understand fluid behavior within these mixers. In this study, we used the residual-based variational multiscale finite element method to perform high-fidelity turbulent simulations on two commonly used turbulent mixers: the multi-inlet vortex mixer (MIVM) and the confined impinging jets mixer (CIJM). We simulated two geometric variations, two inlets and four inlets, of the MIVM and two different inflow ratios of the CIJM. Through detailed turbulence results, we identify differences in turbulence onset, total energy, and mixing performance of the two MIVM configurations. With the CIJM results, we demonstrate the effect of the flow rate ratio on the impingement behavior, and as a result, on the mixing performance and turbulence. The cross-comparison between the two mixers shows key differences in turbulence and mixing behaviors, such as the turbulence onset, the energy decay, and the output mixing index. This study demonstrates the importance of a high-accuracy numerical scheme in simulating the turbulent mixers and understanding the similarities and differences among mixers. Furthermore, the results show a potential for optimizing the operating conditions to achieve the best mixing performance.

The effects of axial boundaries or endcaps are of fundamental interest in many Taylor-Couette (TC) flow experiments. A main challenge in those experiments has been to minimize these effects, which can substantially alter the flow structure compared to the axially unbounded idealized case. Therefore, understanding and disentangling the influence of endcaps on the TC flow dynamics is essential for the unambiguous interpretation of experimental results, particularly when other dynamical processes (instabilities) in TC flows are involved. In this paper, we study the hydrodynamic evolution of a quasi-Keplerian TC flow in the presence of split endcaps for experimentally relevant high Reynolds numbers, $\text{Re}$, up to $2\times {10}^5$, which are larger than those considered in related previous studies. At these $\text{Re}$, the flow deviates from the ideal TC flow profile without endcaps, resulting in about $15\%$ deviation in angular velocity at the midheight of the cylinder. Aside from turbulent fluctuations caused by shearing instability near the endcaps, the bulk flow remains nearly axially independent and exhibits overall Rayleigh stability. We characterize the scalings of the Ekman and Stewartson layer sizes with $\text{Re}$ as well as examine the effect of the ratio of the outer to inner cylinders' angular velocities on the flow. The implications of these findings for ongoing magnetorotational instability (MRI) experiments based on the similar axially bounded TC setup are also discussed. Specifically, it is shown that when imposing a constant axial magnetic field in all the considered configurations, the flow profile modified by the endcaps lowers the critical threshold for the onset of MRI that in turn can facilitate its emergence and detection in those experiments.

We introduce a framework for assimilating planar PIV experimental data using a variational approach to enhance the predictions of the Spalart-Allmaras Reynolds-averaged Navier-Stokes turbulence model. Our method applies three-dimensional constraints to the assimilation of mean velocity data, incorporating a corrective forcing term in the momentum equations. The advantages of this approach are highlighted through a direct comparison with traditional two-dimensional assimilation using the same experimental dataset. We demonstrate its efficacy by assimilating the deep stall flow over a NACA0012 airfoil at a ${15}^{\circ }$ angle of attack and a chord-based Reynolds number of ${\text{Re}}_c\approx 7.5\times {10}^4$. We find that in two-dimensional assimilation, the corrective forcing term compensates not only for physical modeling errors but also for the lack of divergence in the experimental data. This conflation makes it difficult to isolate the effects of measurement inconsistencies from deficiencies in the turbulence model. In contrast, three-dimensional assimilation allows the corrective forcing term to primarily address experimental setup errors while enabling the turbulence model to more accurately capture the flow physics. We establish the benefits of three-dimensional assimilation through its ability to account for the inherent three-dimensionality of the flow, thereby enabling more physically consistent reconstructions of key quantities such as pressure, lift force, and eddy viscosity.

We introduce the magnetohydrodynamic thermal rotating shallow water (MTRSW) model as a framework to study magnetized rotating fluids influenced by thermal gradients and stratification. The model is derived from the full magnetohydrodynamic equations incorporating Coriolis forces, magnetic induction, and thermal effects. To extend its applicability to small-scale magnetic dynamics, Hall MTRSW corrections are included. The proposed MTRSW systems are particularly applicable for thin, magnetized, rotating stratified layers, such as the solar tachocline, neutron star oceans, and accretion disks with shallow vertical extent. Numerical simulations confirm that thermal and magnetic coupling substantially impacts the stability and evolution of vortices, with nontrivial temperature gradients fostering prolonged instabilities.

Dinoflagellates are marine phytoplankton that emit flashes of light in response to flow-induced deformation; they are responsible for illuminating breaking waves, wakes of ships, and other intensely turbulent spots of the upper ocean. Here, we ask how bioluminescence is affected by the fluctuating nature of turbulence—a question motivated by the dependence of emitted flashes on both the extent and rate of deformation. Introducing a light-emitting dumbbell as a minimal model, we study the Lagrangian dynamics of flashing in a homogeneous isotropic turbulent flow and contrast it with that in an extensional flow and a Gaussian random flow. We show that turbulent fluctuations strongly enhance bioluminescence, while introducing a Poisson-like stochasticity in the flashing dynamics. Furthermore, the intermittent fluctuations of the velocity-gradient subjects the dinoflagellate to bursts of extreme straining and produces bright flashes—more intense, though less frequent, than what would result from Gaussian fluctuations. Our results suggest that radiant displays of marine bioluminescence are strongly promoted by turbulence and its dissipation-scale intermittency.

This study investigates the influence of titanium dioxide (${\mathrm{TiO}}_2$) nanoparticles suspended in water on convection cells and heat transfer dynamics. To this end, a Rayleigh-Bénard experimental study was conducted for a water-${\mathrm{TiO}}_2$ nanofluid ($<0.02$% wt) in a cylindrical cavity with a diameter to height aspect ratio of 16. A shadowgraph was used to visualize the spatial and temporal evolution of convection cells in a Rayleigh regime ($<{10}^4$), well suited for observing transitions and stability in flow patterns. The observations show that both colloidal stability and nanoparticle sedimentation strongly affect the evolution of convection patterns and heat transfer. These experiments qualitatively demonstrate that ${\mathrm{TiO}}_2$ nanoparticles can enhance heat transfer under convective conditions, as inferred from the observed changes in convection cell pattern and flow organization. While nanofluids are typically designed to maximize colloidal stability, minimize agglomeration, and prevent sedimentation, our results challenge this paradigm by showing that sedimentation plays a key role in intensifying heat transport.

The hydrodynamic pilot-wave system [Couder et al. Nature (London) 437, 208 (2005)] consists of millimetric drops bouncing on the surface of a vibrating liquid bath. When the droplet's bouncing period is twice that of the vibrational forcing, it achieves resonance with its subharmonic Faraday wave field. The bouncing state may then destabilize into a walking state, in which the droplet self-propels, piloted by its own wave field. Since these Faraday waves are subharmonic with respect to the vibrational driving, there are necessarily two resonant bouncing or walking states, distinguished according to the droplet's impact phase relative to the bath vibration. The interaction between two or more bouncing droplets depends strongly on their relative phase. We here consider a bath driven concurrently by a primary oscillation and a secondary oscillation with half the frequency, and demonstrate that the imposition of the latter allows for controlled switching between the two resonant bouncing states. We demonstrate that when such a switch is applied to a stable lattice of bouncing droplets, the resulting phase changes of the droplets prompt the reconfiguration of the lattice. We further demonstrate that when the pilot wave of a walking droplet is sufficiently large, it may play the role of the secondary bath forcing applied here, prompting switching between the two resonant bouncing states. Our integrated experimental and theoretical study thus informs the behavior of walking droplets in a number of established hydrodynamic quantum analogs.