We derive exact analytical expressions for the power dissipation (PD) and swimming efficiency (SE) of an active particle enclosed in a droplet in a Brinkman medium. Our analysis reveals that the SE of an encapsulated particle strongly depends on droplet size and environmental factors, including the viscosity ratio and medium porosity. For the active particles considered, the locomotion mode (slip- versus torque-driven) does not affect SE. For biomedical applications such as drug delivery, Lighthill’s SE (ratio of towed rigid particle PD to swimming PD) determines which active particles (self-propelled or field-driven) would be more energetically favorable.

The recently discovered polymer diffusive instability (PDI) in rectilinear flows of an Oldroyd-B fluid has wavelengths of the order of the size of the polymer for realistic polymer diffusivities, raising a question on the applicability of continuum constitutive equations. We show, using the Giesekus model (augmented with stress diffusion), that the PDI is rapidly suppressed as the anisotropy parameter is increased, suggesting that anisotropic diffusion needs to be incorporated in order to obtain physically consistent results, either in stability calculations or in direct numerical simulations.

The stress response of a suspension of nonspherical particles in polymeric fluids is important in many practical applications. This study examines the flow around a single spheroid in a polymeric fluid in the limit of small viscoelasticity, and performs an ensemble average of the stress tensor over all particle configurations to determine the effective long-time viscosity and normal stress coefficients of the suspension in linear flow fields. There are two contributions to the extra stress: one from the force dipole on the particles (stresslet) and another from the fluctuations in the velocity in the bulk fluid (fluid-induced particle stress), both of which are quantified in the paper.

New boundary conditions for the Boltzmann equation proposed recently by the authors based on a kinetic model of gas-surface interactions are applied to three basic problems of a rarefied gas between two parallel plates: the heat-transfer between the plates, plane Couette flow, and plane Poiseuille flow driven by an external force. The results are compared with those based on the conventional Maxwell-type condition including the diffuse reflection. The effects of parameters characterizing gas-surface interactions in the above basic problems are clarified.

Quasi-stable large-scale circulation in turbulent thermal convection intermittently reverses its rotational direction. A fusion of physical insight into turbulent convection and a data-driven method known as reservoir computing enables accurate prediction of these chaotic reversals using only non-intrusive sensing via measurements of shear stresses and temperatures on the sidewalls. The successful prediction using such non-intrusive and sparse sensing opens up possibilities for closed-loop control of turbulent flows and feasibility in industrial applications.

This study investigates steady solutions of two-dimensional Rayleigh-Bénard convection under Navier-slip boundary conditions, bridging the gap between classical no-slip and free-slip models. By systematically varying the slip length, the work reveals a critical range where the heat transport and flow strength are highly sensitive to the boundary slip. The findings uncover universal scaling laws and highlight the pivotal role of slip length in modulating boundary layer structures and optimizing heat-flux configurations, offering new insights into both theoretical fluid dynamics and practical microstructured surface applications.

Vertical convection in the presence of a magnetic field has found wide-ranging applications in metallurgy and astrophysics. In the field of metallurgy, magnetic fields are commonly employed to regulate the stability during material formation, resulting in a more uniform distribution of materials and thereby significantly enhancing the quality of the final products. In this process, the combined regulatory mechanism of buoyancy and Lorentz forces plays a crucial role. Therefore, this paper systematically studies this dynamic mechanism over a wide range of parameters. A deeper understanding of these underlying mechanisms will help further improve the quality of metallurgical products.

A warm, upwelling flow is induced by a floating “thermal blanket”, which locally cuts the heat loss from a fluid body that undergoes thermal convection. The interaction between the flows and the thermal blanket (a freely moving boundary) leads to rich behaviors, and each corresponds to a different potential landscape experienced by the free boundary. When the free boundary is small, it sees a bulged hill and tends to slide away. But when the free boundary is large enough, it is trapped in the middle of the fluid surface, as if it sits in a potential valley. The authors developed a method to reconstruct the potential landscapes through a simple model using their experimental data.

Moist convection — driven by the buoyancy released when moisture condenses — plays a central role in tropospheric dynamics. While often explored through simulations or simplified models, we present here a laboratory analog that captures key features of moist convection. The observed instabilities are interpreted using linear stability analyses.

During heavy rainstorms, how can pathogenic spores at the surface of plant leaves travel upward and contaminate other leaves above? The spores are released in the sessile drops left on the leaves by previous raindrops. In this manuscript, we show that upon impact of a large raindrop, a leaf may strongly vibrate. The subsequent inertial forces may be sufficient to expel water from its surface. We describe this droplet ejection mechanism as a function of both leaf and raindrop properties. The droplets inherit from the leaf velocity, so some of them can be shot upward. This ejection mechanism likely induces a significant upward flux of biological material during rainstorms.

We present a predictive model for transient spray cooling of a heated flat substrate under a single nozzle, capturing the transition through film, transitional, and nucleate boiling regimes. Heat transfer from individual droplet impacts is evaluated using regime-specific theoretical correlations from literature, combined through a superposition approach. The evolution of the temperature of the substrate is computed via finite difference-based conjugate heat transfer simulation. Validated against experimental data, the model is further used to explore how spray parameters influence cooling effectiveness.

The problem of a long gas bubble transported in a capillary channel by a wetting liquid is traditionally studied under the assumption of steady-state flow. However, the flow becomes unsteady when the Reynolds number (Re) is above a threshold dependent on the capillary number (Ca${}_I$). This work shows that the instability is triggered by the build-up of dynamic pressure of the flow impinging the rear meniscus of the bubble. The stability curve, which can be predicted based on a modified version of the Weber number, divides the Re-Ca${}_I$ map into stable and unstable regimes.

This study presents a numerical model of foam confined in granular media. It shows that, permeability decreases as the bubble-to-grain size ratio increases, due to the redistribution of liquid from the pore core to the grain-grain contacts and grain walls. It improves on previous analytical models and matches experimental data, highlighting the important role of geometrical confinement and wall plateau edges in liquid flow. The work also compares gas-liquid interfacial models and shows that a Navier slip condition - with a slip length ~2% of the bubble size - accurately accounts for the liquid permeability of bulk foam, providing an alternative to the Lemlich interfacial viscosity approach.

Breath figures (BF) form when water vapor condenses into drops on a surface. While most studies focus on the substrate influence, the allocation of vapors between the growth of existing drops and the nucleation of new ones remains unresolved, affecting BF polydispersity. We present a many-droplet theory accounting for interactions mediated by vapor diffusion using asymptotic matching. We show that after nucleation, drop count stabilizes due to collective effects, resulting in nearly monodisperse BFs on defect-free substrates under diffusion control. Our model explains sub-diffusive growth, nucleation arrest, drop density selection, and coarsening as observed in joint experiments.

An unconstrained evaporating Leidenfrost droplet trampolines intermittently at specific radii. We show that the reemergence of trampolining is triggered by parametric resonance between the droplet’s Rayleigh frequency and the oscillation frequency of the vapor layer beneath it. The parametric resonance arises from temporal variations in the contact area of the levitating droplet leading to time dependent lubrication force. We demonstrate that the phenomenon of resonance-driven bouncing dynamics in the Leidenfrost droplets is universal irrespective of the liquid, initial droplet volume, substrate, and substrate temperature.

The influence of vertical surface motion on droplet spreading and retraction dynamics upon impact on elastic substrates remains poorly understood. To address this, we derive a universal linear law for early-stage spreading. During retraction, the retraction speed is observed to oscillate with substrate vibrations. We identify the underlying mechanism driving this behavior and develop a predictive model for retraction on moving surfaces. This work offers new insights into droplet dynamics on elastic substrates.

Micro-electrohydrodynamic (EHD) conduction pumping has become a promising actuator in two-phase heat transport systems. Here we present, for the first time, a unified numerical framework that simultaneously resolves three distinct charge structures: the electric double layer (EDL) at an insulated substrate, the heterocharge layer near electrodes, and the interface charge layer at a free liquid-film surface. The effects of three charge layers on the pumping performance of dielectric liquid film are quantitatively investigated. The volume-of-fluid (VOF) method is employed to track electric-field-induced gas-liquid interface deformation.

We study the evolution of an initially uniform magnetic field in vortical flows at high magnetic Reynolds numbers. By including the magnetic field’s back-reaction on the flow, we extend the kinematic theory of flux expulsion into the dynamical regime. Using an incompressible two-dimensional magnetohydrodynamic model with various vortex configurations and magnetic field strengths, we identify four distinct dynamical regimes. Our results suggest that even a very weak magnetic field can influence flow dynamics, indicating that purely hydrodynamic models may be inadequate for some astrophysical systems.

We investigated the transport of model firebrands in a canopy-plume system to explore which physical parameters influenced their landing positions. Broad landing distributions motivated a division of particle populations based on landing distance. Particles that travelled further spent more time in the plume and remained higher in the water column. We found that common assumptions in wildfire literature, such as ballistic transport of firebrands, did not capture the dynamics we observed. Stochastic simulations suggested that spatiotemporal coherence in the flow field is an important reason why this ballistic assumption fails.

Canonical Ekman layer theory offers a prediction for the transport that takes place in the oceanic bottom boundary layer, relying only on the local bottom stress and Coriolis parameter. In this study, we use idealized Large Eddy Simulations to illustrate that the presence of small-scale topography can introduce large deviations from the theoretical predictions made by canonical Ekman layer theory. In particular, we show that topography can magnify the transport by as much as 30% in the presence of strong flow separation.

The Wegener-Bergeron-Findeisen (WBF) process is one pathway to cloud glaciation, during which ice grows at the expense of liquid droplets. Earth-system models tend to overestimate the WBF process, limiting our ability to forecast weather and predict climate. An oversimplified representation of turbulence and cloud microphysics in such models has long been suggested to cause this behavior. We developed a statistical model to investigate small-scale turbulence effects on the WBF process. While turbulence slightly broadens droplet-size distributions, it minimally affects glaciation on submeter scales. Larger-scale turbulence may have a stronger effect, motivating future model developments.

Motivated by the need to improve fundamental understanding of multilayer coating on discrete objects, we consider a model problem involving the flow of bilayer thin liquid films on rotating cylinders. A parametric study reveals that the critical rotation rate required to cause motion of liquid lobes that form due to gravitational drainage is lowered for a more viscous and thicker inner film due to an increase in viscous forces. These properties of the inner layer also lead to a reduction in the amplitude of temporal oscillations in the film thickness. In addition to advancing fundamental understanding, we suggest strategies for improving the uniformity of coatings on discrete objects.

For over 150 years, the presence of a thin water layer on ice surfaces has been debated. While at low temperatures, droplet pinning is attributed to crystallization, near the melting point, crystallization is too slow to account for the observed contact angles. Our experiments reveal a persistent contact angle plateau of 12 degrees, showing that surface energy balances govern wetting near the melting temperature. This challenges the existence of liquid-like behavior at the outermost crystalline layer of ice.

Oscillatory flow near deformable boundaries arises in a variety of biological and engineered contexts. In this study, peristaltically driven flow is quantified as a function of a passive boundary’s elasticity for transverse and longitudinal driving waves. Compliance of the elastic half-space generally leads to a decrease in flow rate. However, under longitudinal loading and sufficient confinement, flow can increase. Lagrangian velocities quantify reflux, supporting claims longitudinal waves reduce reflux near the peristaltic wave. We show our analysis agrees with experimental data for pulsatile cerebrospinal fluid flow in the brain.

Most existing propulsion systems rely on pressure for thrust generation, with shear stress being a major source of drag associated with skin friction. In this study, we propose a novel thrust-generation system using shear stress for thrust production. It features a barrel-shaped body whose outer membrane circulates in a tank-treading manner. Through numerical simulations, the feasibility of this design has been confirmed. The underlying physics and the potential performance have also been explored.

This paper presents a systematic investigation of vortex-induced vibration (VIV) of a D-section prism at subcritical Re. It is found that the response is persistently VIV typed, which can be excited and sustained by the viscous and/or pressure lift coefficient. Galloping is found to be absent because it requires an unstable structural mode with a frequency close to the prism natural frequency and flow mode with the natural vortex shedding frequency.

In Hele-Shaw cells, pressure-driven viscous fluid motion between two closely-spaced plates gives rise to a two-dimensional potential flow with zero circulation. Here, we show how the introduction of electromagnetic effects enables the realization of potential flows with circulation. We present canonical Hele-Shaw experiments with circulation prescribed by the electromagnetic configuration, and rationalize the observed flows theoretically. We also draw an analogy between this new class of circulatory potential flows and a class of electrostatic systems.

Multiphase displacement is important in oil recovery, microfluidics, and CO${}_2$ capture. We study viscous oil trapping in microfluidic devices with sinusoidal pockets during water invasion. Varying capillary number (Ca), viscosity ratios, and pore geometries reveals that higher oil viscosity and water velocities increase oil trapping due to transition from meniscus displacement to viscous fingering. We find that trapping dynamics at high Ca are geometry independent. Our three-dimensional model based on the long-wave approximation predicts some experimental observations, such as increased oil retention at higher Ca and viscosity ratios, and the characteristic interfacial shape of trapped oil.

Inertial migration in microfluidic channels enables label-free sorting of particles and cells, yet the role of particle rotation has remained unclear. Using large-scale simulations, we show that rotation dramatically alters particle focusing positions in both circular and square ducts. We find that rotation induces a substantial lateral lift force, a simple phenomenological explanation extending existing theories is presented, that agrees well with our findings. Our findings suggest new design strategies for rotation-controlled particle sorting in microfluidic devices.

Modelling ultrathin platelike particles in viscous flow is notoriously difficult due to the influence of their edges. This work introduces a two-dimensional slender body theory that bypasses these complexities by systematically excluding edge effects. Derived from the boundary integral formulation of Stokes flow, the theory reduces the problem to a nonlocal line integral along the particle’s centerline. The resulting model accurately captures the flow and rheology of passive and active particles across a range of conditions.

Aerosol dispersal in indoor spaces is a two-point, two-time stochastic process, defined by a mean behavior and uncertainties from turbulent fluctuations and spatial inhomogeneity. While existing models capture the mean accurately, few address the associated variances. We develop a theoretical model to quantify the turbulence-related uncertainty. Euler–Lagrange large-eddy simulations (LES) coupled with a novel statistical overloading technique are employed to construct a data-driven model capable of predicting the mean aerosol concentration and the total variance. The proposed model is compared against experimental data.

Microfluidic systems have traditionally relied on external hardware or compliant structures to generate flow rate oscillations. Here, we demonstrate that persistent oscillations and even chaotic behavior can spontaneously emerge without external modulation, deformable structures, or fluid compressibility. Through a combination of numerical simulations and a reduced model, we uncover a mechanism governed by fluid inertia that drives this behavior at moderate Reynolds numbers. These findings expand the design space for on-chip flow control and reveal new opportunities for microfluidic timing, precision control, and chaos-based applications.

Oceanic eddies are dynamic swirling formations that vary in size from about a few kilometers at mid-latitudes to hundreds of kilometers near the tropics. These eddies can persist for days to months and play a crucial role in regulating the climate by transporting heat, salt, and marine life over long distances. Through complex networks, we have discovered both local and nonlocal interactions between these eddies. We have also examined their connectivity and resilience to evaluate the ecosystem’s capacity to withstand disturbances.

The evolution of plumes presented in this study highlights the relative importance of permeability, injection rate, and density difference on the development of plume morphology. Considering these factors in the form of non-dimensional parameters results in semi-empirical correlations for length and entrained volume that describe plume evolution. We propose two separate flow regimes to highlight the difference in early and late-time plume behavior.

This study presents a simplified model for shear flows developed to capture essential features of turbulence using a sparse representation based on intense structures called vortons. These dynamically regularized quasi-singularities interact with large-scale shear and give rise to two distinct flow regimes: a laminar regime governed by large-scale dissipation and a turbulent regime driven by vorton activity. Remarkably, the model reproduces power-law scaling behaviors consistent with classical turbulence, offering a compact yet insightful tool for investigating energy transfer and dissipation in complex flows.

High-Reynolds number turbulence presents an enormous computational challenge due to its large scale separation. We explore a reduced dimensional approach to compute forced Homogeneous Isotropic Turbulence (HIT) up to a Taylor-scale Reynold’s number of 5428. The developed formulation based on one-dimensional turbulence captures many quantitative characteristics of HIT including energy spectra, normalized dissipation rate, skewness, energy flux, high-order structure functions and intermittency, along with an insight into occurrence of extreme events.

We relate the concept of multiscaling in the inertial range of turbulence to a hidden scaling symmetry. We deduce that the anomalous exponents of scaling laws are determined solely by the degree of time-scale homogeneity of the observed quantities. This yields a universal rule that includes the usual structure functions and Kolmogorov multipliers, and extends further to multi-time correlations and other multi-time properties of turbulent statistics.

Accurately predicting thermal response for fire-engulfed objects subjected to crosswind requires a multiphysics, turbulent reacting flow model suite that leverages large-eddy simulation (LES). Structural uncertainty assessment for isothermal, elevated cylinder configurations showcase excellent predictivity and mesh convergence when using dynamic coefficient LES with nonlocal wall model velocity sampling. This model suite is deployed to a liquid hydrocarbon fire validation study (elevated mock fuselage exposed to low- and high-crosswind) where replication of windward-to-leeward migration of peak heat fluxes and flame attachment characteristics are noted, while revealing novel fire dynamics.

Turbulence in two dimensions tends to order the flow into large-scale vortices via the inverse cascade. In between 2D and 3D, quasi-2D flows show rich behavior: both the direction of the turbulent cascade and the large-scale condensation of turbulent energy display critical behavior in the dependence on flow parameters. In this work, we experimentally study the transition to turbulence in quasi-2D nanofluidic channels using superfluid helium. We find a cascade of metastable coexisting states (pictured is the large-scale dissipation as a function of flow velocity), whose exact origin remains uncertain. The transitions between states follow scaling of certain nonequilibrium phase transitions.

Complex network analysis has been used previously in turbulence fluid mechanics to characterize dynamics in a discrete manner. In this work, rather than defining nodes based on physical coordinates, we use the invariants of the velocity gradient tensor. The image shows the joint probability distribution of the second (Q) and third (R) invariants, divided into six regions. In each, the area of the symbol is proportional to exchanges between nodes in a region and the width of the arrows is proportional to exchanges between adjacent regions. The results in red are from a direct numerical simulation and differ somewhat to those in blue for the enhanced Gaussian closure model.

Homogeneous and isotropic turbulence in a viscoelastic fluid is examined theoretically with the role of small parameter played by either the fluid relaxation time or the Weissenberg number. A Martin-Siggia-Rose framework is used to obtain a formal expression for the velocity correlation function of the non-Newtonian flow, and expanded to linear order in the relaxation time. The expansion coefficients are correlation functions of the base Newtonian flow. These correlations are not derived, but replaced by their values according to K41 theory. While substantial work will be necessary to validate the model against numerical and experimental data, preliminary results are encouraging.

In rotating turbulence, the energy spectrum with -2 exponent was initially proposed under the assumption of isotropy (Zeman 1994; Zhou 1995). However, rotation inevitably induces anisotropy. To fill the gap between theoretical assumptions and realizability, we study the turbulence of inertial waves in an idealized two-dimensional isotropic rotating turbulence system by introducing an artificial horizontal rotation. In the limit of a small Rossby number, we asymptotically derive a nonlinear amplitude equation for inertial waves which gives the energy spectrum with -2 exponent using a strong turbulence argument. This scaling is justified by numerical simulations.

We propose a scale-decomposition method for the Lagrangian velocity that relates the hierarchy of coherent vortices to the Lagrangian properties of turbulence. Our scale-decomposition analysis reveals how vortices at different scales form the power spectral density of the Lagrangian velocity: small-scale vortices in the inertial range contribute to the spectra in a self-similar manner, whereas the contribution from the largest-scale flows exhibits non-universal behavior and can contaminate the Kolmogorov scaling.

When analyzing leading-edge vortex growth, there are several different ways that researchers have normalized relevant quantities. In order to better compare between different motions and conditions, a normalization grounded in the fundamental equations is necessary. To achieve that, this paper derives a non-dimensionalization of circulation and time from an integral analysis of the vorticity equation and tests the efficacy of this non-dimensionalization on data from surging, rotating, and pitching wings.

Accurate simulation of offshore wind farm performance requires realistic modeling of sea-surface interactions. A comparison was performed between the wave-phase-aware and wave-phase-averaged boundary conditions in large-eddy simulations of a utility-scale offshore wind farm. The wave-phase-aware approach, informed by high-order wave modeling, yields faster wake recovery and improved agreement with supervisory control and data acquisition (SCADA) measurements, highlighting the importance of resolving wave kinematics in high-fidelity wind farm modeling.

This study presents a theoretical model for gravity wave attenuation in a multilayered fluid system, incorporating the dynamics of fluidized mud, water, oil, and air. By solving the dispersion relation, it examines how attenuation rates vary with fluid properties, layer depths, and wave frequencies. Results highlight the dominant role of air dynamics, which become particularly significant for deep-water, low-frequency waves. Maximum attenuation rates arise from strong velocity gradients in fluid layers and can be understood through variations in group velocity and penetration depth, the latter being related to the rotational part of the velocity field.

Synthetic inflow turbulence generation is a critical bottleneck for high-fidelity, eddy-resolving simulations due to limitations in realism, generalizability, and computational cost. This study introduces CoNFiLD-inlet, a parametric inflow generator that couples conditional neural fields with latent diffusion models to synthesize high-fidelity inflow turbulence with Reynolds number (Re) awareness. Unlike autoregressive or deterministic methods, CoNFiLD-inlet enables mesh-independent, stochastic generation of temporally coherent velocity fields with generalization across unseen Re. Comprehensive validations in DNS and WMLES confirm robustness, scalability, and superior statistical fidelity.