Slowly sheared particulate media like sand and suspensions flow heterogeneously as they yield via shear bands, in which most strain accumulates. Understanding shear band localization from microscopics is still a major challenge. One class of so-called nonlocal theories identified that the width of the shearing zone $\xi$ should depend on the stress field, in particular, through the local distance to the yield point of the material. We explicitly test this stress sensitivity picture by using a uniquely stress-tunable suspension while probing its flow behavior in a classic geometry in which shear bands are known to scale nontrivially with local stress: the Split-Bottom Shear Cell. The stress-tunable suspension is composed of mildly polydisperse soft, slippery hydrogel spheres submersed in water. We measure their flow profiles and rheology while controlling the confinement stress via both hydrostatic effects and compression. Unique for these soft particles is that we can probe flow fields under confining normal stresses that reach about 1% of their elastic modulus. We determine the average angular velocity profiles in the quasistatic flow regime using Magnetic Resonance Imaging based particle image velocimetry and discrete element method (DEM) simulations. We explicitly match a pressure-sensitive nonlocal granular fluidity (NGF) model to observed flow behavior. We find that shear bands for this type of suspension become extremely broad under the low confining stresses from the almost density-matched fluid particle mixture, while collapsing to a narrow shear zone under finite, externally imposed compression levels. The DEM and NGF results match the observations qualitatively, confirming the conjectured pressure sensitivity for suspensions and its role in the NGF model. Our results indicate that pressure sensitivity should be part of nonlocal flow rules to describe slow flows of granular media.

The primary breakup mechanism in close-coupled gas atomization (CCGA) remains unclear due to strong gas recirculation and complex interfacial dynamics. We performed three-dimensional VOF-LES simulations with adaptive mesh refinement across Weber numbers ranging from 40.2 to 360, validated against digital inline holography experiments. Results show that liquid filming along the nozzle perimeter occurs at low to intermediate We, but only dominates at $\mathrm{We}=360$, where it leads to a complete disintegration of the liquid jet due to filming. The change in dominant liquid pathways correlates with a change in droplet size distributions from a power law at lower We to log-normal at the highest We. Distributions of normalized droplet velocities were independent of We, indicating that droplet velocities are dictated by drag. Droplet Weber numbers based on the instantaneous slip velocities only exceeded the critical value for secondary breakup at $\mathrm{We}=360$. Findings indicate that CCGA primary breakup is governed by the interplay between gas recirculation and filming behavior, rather than classical Kelvin–Helmholtz or Rayleigh–Taylor instabilities alone.

Using direct numerical simulation of forced isotropic turbulence at ${\text{Re}}_{\lambda }\approx 1300$ and $\approx 433$, together with two independent Markov-in-scale-by-construction null surrogates, we show that the Markov-Einstein coherence length of the turbulent energy cascade is state-dependent. Conditioning the gap-scan test on the local flow state reveals that intermittent regions of the inertial range carry a coherence length $\mathrm{\Delta }r\approx 3–4$, while the quiescent cascade at midinertial scales recovers $\mathrm{\Delta }r\approx 1.0–1.4$, matching the canonical estimate to within one grid step. Near the dissipation range this pattern reverses: the core of the increment distribution carries more memory than the extreme tails, consistent with the spectral bottleneck. As a consequence, the unconditioned coherence length coincides with that of the intermittent component, whose memory is the last to decay as the scale separation grows. It therefore sets the coherence length, giving $\mathrm{\Delta }r\approx 3.2–3.6$ at the inertial-range centers, approximately three times the canonical reference $\mathrm{\Delta }r\approx 1$. An independent Chapman-Kolmogorov test confirms the state dependence, and a subsampling test shows the excess is present already at the $\sim {10}^5$ samples-per-scale regime of the earlier experiments. The pattern is Reynolds-number-independent over ${\text{Re}}_{\lambda }\approx 433–1300$. The Markov approximation underlying the cascade Fokker-Planck equation and fluctuation-theorem analyses is therefore substantially more restrictive for the intermittent component of the cascade than previously assumed.

We put forward a formulation of the vortex gas model of turbulent circulation statistics to address the challenging case of nonplanar circulation contours. Relying upon a field-theoretical description, statistical moments of the circulation turn out to be functionally dependent on specific optimal surfaces bounded by the circulation loops. Circulation is modeled in the optimal curved spaces with the help of scalar vertex operators that represent the multifractal density fluctuations of Gaussian-correlated vortex structures. We show that minimal surfaces are optimal within the inertial range, but subdominant deviations are expected to become significant for contours with linear dimensions close to the Kolmogorov dissipation length. As a case study, we demonstrate the model's applicability through a Monte Carlo evaluation of the circulation probability distribution function for nonplanar contours, which is in excellent agreement with results from extensive direct numerical simulations.

Biomicrofluidics research such as single-cell analysis, cell-sorting, and droplet-based microchemical reactors often involves isolating a single cell or drop in a bioreactor chamber and exposing it to controlled flow of nutrient-rich solution. We use three-dimensional moving-frame boundary-integral simulations along with macroscopic flow-cell experiments to study the motion of a deformable droplet under gravity into and out of a well with nearly sharp corners in the Stokes flow regime. The dynamics of the droplet is influenced by the drop-to-bulk fluid viscosity ratio, capillary number, Archimedes number, and the chamber length. Increasing the Archimedes number (ratio of gravity and viscous forces) causes the drop to settle toward the bottom of the chamber, while a smaller Archimedes number allows the drop to escape without any hook or tail. An intermediate Archimedes number may lead to droplet breakup, with the parent drop either becoming trapped or escaping after forming a thin neck near the corner. Higher capillary numbers lead to large, wormlike drop elongation, with the tail becoming trapped and the head elongating out of the channel.

Many turbulence applications require instantaneous spatiotemporal realizations, not only mean statistics. Eddy-resolving simulations produce such information at high cost, while measurements are often sparse, noisy, or indirect. This article argues that transport-based generative models, including diffusion models and flow matching, should be viewed as reusable probabilistic priors for turbulence. Once trained, such priors can be queried conditionally without retraining, providing a unified framework for flow reconstruction, data assimilation, super-resolution, data restoration, and solver-constrained inference. We review this framework through three capabilities: forward generation, inverse conditioning, and scalable composition. Diffusion and flow-matching priors can synthesize temporally coherent turbulent realizations, condition samples on sparse or indirect information, and compose local patchwise priors for large domains beyond training. The goal is to generate an ensemble of plausible turbulent states consistent with data and physical constraints. We close by discussing validation criteria for generative turbulence priors, including distributional fidelity, nonmemorization, data consistency, posterior calibration, physical admissibility, and large-domain coherence. Looking forward, such priors may serve as a statistical backbone for turbulence foundation models which are conditionable and uncertainty-aware, supporting predictive CFD, data assimilation, and decision-making workflows.

The conversion of kinetic energy into internal energy in high-speed boundary layers creates nonuniform density and viscosity fields, which invalidate many foundational theoretical models of wall-bounded turbulence flow, most notably the incompressible log-law for the mean velocity profile. Modeling and prediction of compressible turbulent boundary layers therefore requires a theoretical means of accounting for fluid property variations, the most famous of which is the so-called “Van Driest transformation” that originated in 1951. This paper sets up the general problem and describes our current theoretical understanding of it, with a focus on developments during the last decade. It also describes applications of the theory to engineering friction estimation methods and the development of wall models for large eddy simulations.

We use lubricated-flow discrete-element-method simulations to examine how contact-network organization shapes particle motion in dense shear-thickening suspensions. The primary system studied is a two-dimensional bidisperse monolayer where rigid clusters are identified by the (3,3) pebble game; three-dimensional simulations are shown to have qualitatively similar rotational velocity statistics. Across the stress–solid-fraction state diagram, frictional contact number, $k\ge 3$ percolation, and rigid-cluster fluctuations all strengthen in the same region where translational velocity correlations grow, consistent with coherent translation within rigid clusters and a state-dependent contrast in relative motion between particles inside and outside them. Rotational motion provides a complementary view: nonaffine angular-velocity distributions broaden, near-contact nonaffine rotational fluctuations become increasingly anticorrelated, and particles inside and outside rigid clusters carry distinct statistics. Connectivity, rigidity, and velocity correlations are related but distinct signatures of the constrained collective motion that accompanies shear thickening and the approach to shear jamming.

Detonation initiation by shock focusing is a promising approach for detonation engines; however, the role of viscous effects remains insufficiently understood because most previous studies relied on inviscid models. In this work, two-dimensional viscous simulations with detailed hydrogen–air chemistry are performed to investigate how reflected shock–boundary layer interactions govern ignition and detonation initiation in shock-focusing systems across a wide range of incident shock Mach numbers and reflector angles. Five distinct initiation modes are identified: ignition failure, nondetonative autoignition on the reflector wall, detonation initiated by autoignition on the reflector wall, detonation initiated by autoignition on the side wall, and shock-focusing-induced detonation. For the latter three modes, reflected shock–boundary layer interaction plays a decisive role by inducing boundary-layer separation, where intense viscous dissipation and prolonged fluid residence time generate localized heating that triggers mixture autoignition and subsequent detonation development. Quantitative assessment of boundary layer effects on the critical Mach number is conducted through comparison with inviscid simulations. Results demonstrate that neglecting boundary layer effects leads to qualitatively incorrect predictions of both ignition mode and critical Mach number. A striking nonmonotonic dependence of critical Mach number on boundary layer effects is observed as the reflector angle varies: boundary layer effects reduce the critical Mach number for θ = 100°, 110°, and 150° by facilitating detonation initiation while producing negligible effects for θ = 90°, 120°, and 125°. This nonmonotonic behavior arises from two competing mechanisms. Increasing reflector angle elevates the critical Mach number and postshock temperature, thereby favoring detonation development; simultaneously, it reduces boundary layer thickness and weakens reflected shock–boundary layer interaction above the reflector wall, suppressing autoignition on the reflector wall. This interplay causes a transition of detonation initiation from the reflector wall to the side wall across reflector angles, resulting in the nonmonotonic variation of boundary layer influence on the critical Mach number. These findings underscore the essential role of shock–boundary layer interactions in governing detonation initiation behavior in shock-focusing systems.

It is well known that the Coriolis force due to Earth's rotation can induce wind veer in the mean flow velocity of an atmospheric boundary layer, but much less is known about its effects on turbulent coherent structures. In this work, large-eddy simulation is employed to investigate the effects of the Coriolis force on the characteristics of turbulent coherent structures in the conventionally neutral atmospheric boundary layers. Variation of the Coriolis force is realized by changing latitude or geostrophic wind speed. We found that the Coriolis force causes distinct deflection of coherent velocity structures to the geostrophic wind direction, which is not aligned with the direction of either the mean wind or the mean shear. When a relative structure deflection angle is plotted against a relative local wind veer angle, a universal relationship between them can be established regardless of latitude or geostrophic wind speed. Moreover, we also studied the effect of the Coriolis force on the inclination of large-scale turbulent structures. It is found that the inclination angle in the surface layer varies under different conditions, which is probably due to the deflection of turbulent structures caused by the Coriolis force.

We present a combined theoretical and experimental study of gravity-capillary waves generated by a disk oscillating vertically about the horizontal water surface. The theory predicts the radial propagation and decay of surface waves by incorporating fluid viscosity and surface elasticity. Laboratory experiments were conducted to measure the surface elevation using the synthetic Schlieren method and separately using a confocal displacement sensor. The results show that viscosity and elasticity have a minor impact on the wavelength of radiating waves and a major impact on the amplitude of the decaying waves in the far field. Viscosity dampens the waves to decay exponentially at a rate that depends sensitively on the surface elasticity. The findings may serve as a foundation for studying the range of perception and communication by various organisms on the water surface.

Microorganisms navigating through narrow spaces encounter significant hydrodynamic challenges. To overcome these constraints and sustain efficient motion, they employ adaptive strategies, including adaptive oscillatory body deformations. While artificial microdroplets can traverse channels narrower than their diameter, studies of their locomotion have thus far been largely restricted to steady-shape regimes. In this work, we demonstrate a transition from steady shape to dynamic interfacial undulations in 5CB (4-cyano-$4^{\prime }$-pentylbiphenyl) droplets within aqueous tetradecyltrimethylammonium bromide (TTAB) solutions. We show that while droplets in dilute, additive-free solutions maintain a steady shape, the introduction of solutes or higher surfactant concentrations triggers pronounced interfacial undulations. Notably, both steady and undulating droplets exhibit a comparable velocity dependence on the confinement ratio—characterized by an initial deceleration followed by saturation—governed by the competition between hydrodynamic resistance and phoretic flow within the lubrication film. Furthermore, we find that increased surfactant concentration increases the Capillary number, resulting in a thicker lubrication layer that facilitates a symmetry-breaking transition. Upon varying confinement, the droplet interface shifts from bilateral undulations to being localized on one side, traveling-wave mode strongly coupled to flow field fluctuations at the droplet's anterior. Linear stability analysis identifies the Yih-Marangoni instability as the underlying mechanism for these oscillations, revealing a previously unrecognized mode of adaptive locomotion in confined active matter.

The electroosmosis of multivalent electrolytes through hydrophobic channels are commonly modeled through a mean-field-based approach and imposing the Navier-slip condition at the charged surface. However, the surface charge at the hydrophobic interface are laterally mobile, creating frictional force as well as electric force to the adjacent fluid and, thus, modify the slip condition and influence the ion transport. The slip velocity condition at the interface is developed based on the balance of hydrodynamic and electric forces on the surface ions. Electrokinetics involving multivalent counterions manifest the strong coupling among ions, ceasing the validity of the mean-field-based ion transport. The ion-ion correlations among the finite-sized ions are modeled based on the nonlocal electrostatic consideration. The governing equations are solved numerically to elucidate the interactions of surface charge with its hydrophobicity as well as the short-range effects on ion transport. A simplified model is also developed under the assumption of a small Debye length-to-channel height ratio, which is further solved analytically based on a linearized approximation. At the nondilute situation the short-range effects, such as ion steric interactions and ion-ion correlations manifest. Our results show that the ionic correlations induced counterion condensed layer can overscreen the surface charge and creates a inversion in charge density, leading to a reversal in the electroosmosis. This counterion condensed layer diffuses at a higher ionic concentration when surface charge density becomes sufficiently large. The occurrence of velocity slip at the wall defers the charge density inversion and, consequently, electroosmotic flow reversal, by enhancing momentum transfer to the fluid. The intensity of the slip attenuates when the surface charge is considered to be laterally mobile.

The far-field contribution to vortex stretching at a high-vorticity point can be bounded by an unsigned Calderón-Zygmund singular-integral estimate. We separate this bound into the quantity it bounds and the quantity it uses to bound it, and measure both by direct summation of the contracted Biot-Savart stretching integral on direct numerical simulation data, as functions of the outer integration radius $R$. Across forced isotropic turbulence at Taylor-scale Reynolds numbers ${\mathrm{Re}}_{\lambda }\approx 433$, 611, and 1300, the unsigned capacity—the magnitude the estimate permits—grows approximately logarithmically in $R$, whereas the realized signed magnitude—what the same integral actually delivers—grows with only $10–19\%$ of the capacity slope. The empirical tightness $C_{\mathrm{far}}=\left|{\sigma }_{\mathrm{far}}\right|/{\sigma }_{\mathrm{far}}^{\mathrm{abs}}$ therefore decreases by $21–39\%$ over $R/\eta =25-60$, with block-bootstrap confidence intervals excluding zero at both median and extreme-vorticity targets. This decline is robust: it is unchanged when target classes are defined by a threshold pooled across all sampled cutouts rather than locally, it survives a sixth-order finite-difference recomputation of the full pipeline, and it is insensitive to the inner cutoff. The looseness of the bound is thus a radius-dependent margin, not a fixed factor. Expressed as the dimensionless tightness rather than the dimensional capacity, the curves nearly collapse across the threefold range in ${\mathrm{Re}}_{\lambda }$. The realized far field is dynamically substantial: the magnitude ratio $|{\sigma }_{\mathrm{far}}|/|{\sigma }_{\mathrm{total}}|$ reaches 0.50 at median targets and 0.44–0.48 in the extreme-vorticity tail at $R/\eta =60$, so by the triangle inequality the contribution complementary to the measured far-field band has a magnitude at least approximately half of the total at the median and at least $52–56\%$ at the most intense events, with the far field a near-equal partner at the largest measured radius. Cancellation is systematically weaker at extreme-vorticity targets than at the median: the tail-to-median tightness ratio is 1.2–1.7 and grows with radius, so the sign organization that suppresses the far field weakens precisely at the events most relevant to amplification. A per-shell cancellation diagnostic shows that the looseness is already present within individual radial shells and strengthens with radius in both intensity classes.

We examine experimentally the boundary layer beneath a Rankine vortex, which consists of a central vortex tube surrounded by an irrotational free vortex. We do this by setting up a tornado-like vortex in a large water tank, and then we examine the resulting boundary layer using particle image velocimetry. The boundary layer beneath a Rankine vortex has attracted considerable attention in the past, as it is thought to play an important role in the dynamics of a tornado R. Rotunno [Annu. Rev. Fluid. Mech. 45, 59 (2013)]. In particular, Burggraf [Phys. Fluids 14, 1821 (1971)] have performed an approximate asymptotic analysis of the steady, laminar boundary layer beneath a free vortex, predicting a complex, two-layer structure for the boundary layer. Their predictions have been found to be in qualitative agreement with experiments on the flow surrounding a tornado-like vortex, but to date there is no detailed, quantitative comparison. We provide such a comparison here. We find that the analysis of Burggraf et al. is in good agreement with our measurements when the boundary layer is steady, but discrepancies start to arise as the Reynolds number increases and the flow becomes unsteady.

Reliable prediction of hypersonic aerothermodynamics depends critically on the accuracy of thermochemical nonequilibrium kinetics models, yet their experimental validation remains expensive and diagnostically constrained. This work develops a Bayesian experimental design framework to identify experimental conditions that are maximally informative for calibrating the modified Marrone-Treanor air-chemistry model. Informativeness is quantified through expected information gain using information-theoretic utilities that incorporate prior parameter uncertainty and measurement noise. To render the required repeated utility evaluations tractable for field-valued observables, we construct reduced-order surrogates via a Karhunen-Loève expansion with Gaussian process regression of the modal coefficients. The framework is demonstrated on an adiabatic zero-dimensional reactor and on hypersonic flow over a two-dimensional cylinder, producing full and marginal utility maps over design variables and measurement locations. Synthetic Bayesian inference studies confirm that designs selected from high-utility regions yield substantially tighter posteriors than designs from low-utility regions, providing a practical pathway for targeted, resource-efficient validation of nonequilibrium kinetics in hypersonic flows.

Dynamics and rheology of red blood cell (RBC) suspensions in confined Poiseuille flows are studied numerically using simplified vesicle and capsule models. By using periodic boundary conditions along flow direction, the RBC and its images are forced to align to the same lateral position, showing a single file with equal interdistance. Lateral migration of RBC is analyzed by increasing RBC concentration $\varphi$ (defined as the area or volume fraction occupied by RBCs). A scaling law for the migration velocity as a function of RBC concentration is proposed. The intrinsic viscosity $\left[\eta \right]$ (the contribution of each RBC on effective viscosity) shows a nontrivial property with the increase of RBC concentration $\varphi$, due to the spatial organization of RBCs. We find that the overall behavior of the periodic suspension shares the same features as those obtained for a suspension for which the periodicity along the flow line is relaxed. For the periodic suspension the computational time is greatly reduced as compared to a situation without imposing periodicity. This study offers an interesting perspective for the study of concentrated suspension, not only for a single file but also for more complex structures, where in each periodicity more than a single RBC is considered. These findings can help understanding the behaviors of blood flow in microcirculation with a highly reduced computational cost.

This study investigates miscible Rayleigh-Taylor (RT) turbulence subjected to gravity removal or reversal at different stages of its development, using high-resolution numerical simulations and Lagrangian passive-particle tracking. The state of the mixing layer at the switching time, particularly its thickness and turbulent intensity, is shown to control the subsequent evolution. Gravity reversal transforms the unstable RT layer into a weakly turbulent, stably stratified flow with a thick mixed region. The vertical mass flux and kinetic-energy anisotropy exhibit decaying oscillations whose characteristic period increases with the mixing-layer thickness at reversal and is described by the Brunt-Väisälä frequency. In contrast, gravity removal eliminates further buoyancy production without imposing a restoring force, allowing the mixing layer to continue broadening through inertial coasting while retaining the large-scale structure inherited from the preceding RT stage. The Lagrangian analysis distinguishes absolute material transport from relative turbulent stirring. After gravity removal, the vertical velocity correlation remains positive over a comparatively long interval, sustaining both single-particle displacement and particle-pair separation. Gravity reversal instead drives the correlation through zero and induces particle oscillations consistent with the Brunt-Väisälä timescale, thereby suppressing both absolute transport and the relative stretching of initially neighboring particles. These results show that the postswitch dynamics are governed jointly by the flow state at the switching time and by whether the modified forcing preserves or actively destroys vertical velocity memory.

Low Reynolds number flow near a poroelastic interface can be found across scales in biological and engineered systems. We develop a two-dimensional model of peristaltic flow confined under a poroelastic solid. In this geometry, the lower boundary is an infinite train of traveling waves which pump fluid along a channel. The upper boundary of the flow is a poroelastic half-space. The flow and deformation are solved analytically by an asymptotic expansion in the peristaltic amplitude and depend nonlinearly on dimensionless poroelastic stiffness, permeability, and interfacial slip. We quantify the effect of material properties on the poroelastic fluid-structure interaction. Peristaltic flow through the channel is inhibited by poroelastic confinement owing to increased viscous dissipation across the interface and energy loss in deforming the elastic solid. Permeability and slip interact with the material stiffness to produce material dependent regimes of forward or backward interstitial flow within the poroelastic domain. The maximum Darcy flow is found to occur at permeability values that optimize the elastic matrix interaction.

We investigate the lift and drag corrections acting on a particle suspended in a planar viscoelastic shear flow when the particle is tuned to translate relative to the flow by an external mechanism. A cross-stream lift force arises when particle is driven in streamwise direction; we find that the nature of the driving mechanism dictates the lift direction: force-bearing mechanisms (such as gravity acting on non-neutrally buoyant particles) and force-free mechanisms (such as electrophoresis) generate lift forces of opposite sign. By explicitly deriving the first-order fields and stresses, we demonstrate that this reversal originates from distinct hydrodynamic disturbances induced by each mechanism, which produce qualitatively different polymeric stress distributions. This analytical result is further verified through an independent derivation using the reciprocal theorem. Further, we find that driving the particle in the gradient direction gives rise to a streamwise drag correction that is of the same sign for both mechanisms. Beyond microfluidic particle manipulation, these results have broader implications for understanding the locomotion of microswimmers in viscoelastic shear flows, where distinct force-free propulsion mechanisms are expected to generate unique force and torque modifications.