In this study, a partially submerged vertical cylinder is moved at constant velocity through water, which is initially at rest. During the motion, the wake behind the cylinder induces free-surface deformation. Eleven cylinders, with diameters from $D=1.4$ to 16 cm, were tested under two different conditions: (i) constant immersed height $h$ and (ii) constant $h/D$. The range of translation velocities and diameters are in the regime of turbulent wake with experiments carried out for $4500<\mathrm{Re}<240000$ and $0.2<\mathrm{Fr}<2.4$, where Re and Fr are the Reynolds and Froude numbers based on $D$. The focus here is on drag-force measurements and relatively strong free-surface deformation up to air-entrainment. Specifically, two modes of air-entraiment have been uncovered: (i) in the cavity along the cylinder wall and (ii) in the wake of the cylinder. A scaling for the critical velocity for air-entrainment in the cavity has been observed in agreement with a simple model. Furthermore, for $\mathrm{Fr}>1.2$, the drag force varies linearly with Fr.

In this work, we study the effect of sphere rotation on the drag coefficient experienced by a sphere sedimenting through a nearly constant viscosity and elastic Boger fluid, using experiments, numerical simulations, and an asymptotic theory. For the purely sedimenting (nonrotating) sphere, we find that the drag coefficient is larger in the Boger fluid than in the Newtonian case, in accordance with previous studies. In the Boger fluid, rotation of the sphere (around the axis aligned with translation) causes a reduction in the drag coefficient compared to the purely sedimenting case; this trend is observed in the experiments, numerical simulations, and theory. The numerical results indicate that the decrease in the drag due to sphere rotation results from modifications in the pressure contribution to the drag.

Yield stress fluid (YSF) flows through porous materials are fundamental to biological, industrial, and geophysical processes, from blood and mucus transport to enhanced oil recovery. Despite their widely recognized importance across scales, the emergent transport properties of YSFs in porous environments remain poorly understood due to the nonlinear interplay between complex fluid rheology and pore microstructure. Here, we combine microfluidic experiments and nonlinear network theory to uncover an anomalous, hierarchical yielding process in the fluidization transition of a generic YSF flowing through a random medium. Percolation of a single fluidized filament gives way to pathways that branch and merge to form a complex flow network within the saturated porous medium. The evolution of the fluidized network with the flowing fraction of YSF results in a highly nonlinear flow conductivity and reveals a novel dispersion mechanism, resulting from the rerouting of fluid streamlines. The identified flow percolation phenomenon has broad implications for YSF transport in natural and engineered systems, and provides a tractable archetype for a diverse class of breakdown phenomena.

We investigate the collapse of a cloud composed of $12500$ gas bubbles in a liquid through large-scale simulations. The gas bubbles are discretized by a diffuse interface method, and a finite volume scheme is used to solve on a structured Cartesian grid the Euler equations. We investigate the propagation of the collapse wave front through the cloud and provide comparisons to existing models such as Mørch's ordinary differential equations and a homogeneous mixture approach. We analyze the flow field to examine the evolution of individual gas bubbles and in particular their associated microjet. We find that the velocity magnitude of the microjets depends on the local strength of the collapse wave and hence on the radial position of the bubbles in the cloud. At the same time, the direction of the microjets is influenced by the distribution of the bubbles in its vicinity. We envision that the present, state-of-the-art, large-scale simulations will serve the further development of low-order models for bubble collapse.

The effects of different initial perturbations on the evolution of stratified shear flows that are subject to Kelvin-Helmholtz instability and vortex pairing have been investigated through direct numerical simulation. The effects of purely random perturbations of the background flow are sensitive to the phase of the subharmonic component of the perturbation that has a wavelength double that of the Kelvin-Helmholtz instability. If the phase relationship between the Kelvin-Helmholtz mode and its subharmonic mode is optimal, or close to it, then vortex pairing occurs. Vortex pairing is delayed when there is a phase difference, and this delay increases with increasing phase difference. In three-dimensional simulations vortex pairing is suppressed if the phase difference is sufficiently large, reducing the amount of mixing and mixing efficiency. For a given phase difference close enough to the optimal phase, the response of the flow to eigenfunctions perturbations is very similar to the response to random perturbations. The phase difference has a more significant effect on vortex pairing compared to the initial perturbation amplitude ratio between the KH and the subharmonic modes. In addition to traditional diagnostics, we show quantitatively that a nonmodal Fourier component in a random perturbation quickly evolves to be modal and describe the process of vortex pairing using Lagrangian trajectories.

Polyelectrolyte microgels find many uses as rheological modifiers and stimulus-responsive materials. Understanding their swelling and collapse dynamics therefore holds broad importance in science and technology. We report remarkably simple experiments, requiring little sophistication, that reveal the subtle physics of microgel collapse. Millimeter-scale bubbles, sugar grains, and other small particles remain suspended and supported by the yield stress of household hand sanitizer, which arises due to a jammed suspension of swollen microgels. By contrast, salt grains with almost identical physical properties sediment through the material, leaving milky “comet tails” behind. Remarkably, the settling speed of a salt crystal remains constant as it dissolves—completely independent of its size or shape until it completely dissolves. Because the settling speed does depend on the type of salt that sediments, we hypothesize that salt grains effectively bore holes through hand sanitizer, with a velocity that is limited by the salt-induced dynamic collapse of the individual microgel particles. A simple convection-diffusion-collapse model successfully relates sedimentation velocities to microgel collapse dynamics for various salts. This model and its predictions are consistent with other observations and with complementary microfluidic experiments.

The method of regularized Stokeslets, based on the divergence-free exact solution to the equations of highly viscous flow due to a spatially smoothed concentrated force, is widely employed in biological fluid mechanics. Many problems of interest are axisymmetric, motivating the study of the azimuthally integrated form of the Stokeslet which physically corresponds to a ring of smoothed forces. The regularized fundamental solution for the velocity (single-layer potential) and stress (double-layer potential) due to an axisymmetric ring of smoothed point forces, the regularized ringlet, is derived in terms of complete elliptic integrals of the first and second kind. The relative errors in the total drag and surrounding fluid velocity for the resistance problem on the translating, rotating unit sphere, as well as the condition number of the underlying resistance matrix, are calculated; the regularized method is also compared to three-dimensional regularized Stokeslets and the singular method of fundamental solutions. The velocity of Purcell's toroidal swimmer is calculated; regularized ringlets enable accurate evaluation of surface forces and propulsion speeds for nonslender tori. The benefits of regularization are illustrated by a model of the internal cytosolic fluid velocity profile in the rapidly growing pollen tube. Actomyosin transport of vesicles in the tube is modeled using forces immersed in the fluid, from which it is found that transport along the central actin bundle is essential for experimentally observed flow speeds to be attained. The effect of tube growth speed on the internal cytosolic velocity is also considered. For axisymmetric problems, the regularized ringlet method exhibits a comparable accuracy to the method of fundamental solutions while also allowing for the placement of forces inside of the fluid domain and having more satisfactory convergence properties.

Coherent turbulent wave-packet structures in a jet at Reynolds number $460000$ and Mach number 0.4 are extracted from experimental measurements and are modeled as linear fluctuations around the mean flow. The linear model is based on harmonic optimal forcing structures and their associated flow response at individual Strouhal numbers, obtained from analysis of the global linear resolvent operator. These forcing-response wave packets (“resolvent modes”) are first discussed with regard to relevant physical mechanisms that provide energy gain of flow perturbations in the jet. Modal shear instability and the nonmodal Orr mechanism are identified as dominant elements, cleanly separated between the optimal and suboptimal forcing-response pairs. A theoretical development in the framework of spectral covariance dynamics then explicates the link between linear harmonic forcing-response structures and the cross-spectral density (CSD) of stochastic turbulent fluctuations. A low-rank model of the CSD at given Strouhal number is formulated from a truncated set of linear resolvent modes. Corresponding experimental CSD matrices are constructed from extensive two-point velocity measurements. Their eigenmodes (spectral proper orthogonal or SPOD modes) represent coherent wave-packet structures, and these are compared to their counterparts obtained from the linear model. Close agreement is demonstrated in the range of “preferred mode” Strouhal numbers, around a value of 0.4, between the leading coherent wave-packet structures as educed from the experiment and from the linear resolvent-based model.

The displacement of a viscous fluid by an air bubble in the narrow gap between two parallel plates can readily drive complex interfacial pattern formation known as viscous fingering. We focus on a modified system suggested recently by Zheng et al. [Phys. Rev. Lett. 115, 174501 (2015)], in which the onset of the fingering instability is delayed by introducing a time-dependent (power-law) plate separation. We perform a complete linear stability analysis of a depth-averaged theoretical model to show that the plate separation delays the onset of nonaxisymmetric instabilities, in qualitative agreement with the predictions obtained from a simplified analysis by Zheng et al. We then employ direct numerical simulations to show that in the parameter regime where the axisymmetrically expanding air bubble is unstable to nonaxisymmetric perturbations, the interface can evolve in a self-similar fashion such that the interface shape at a given time is simply a rescaled version of the shape at an earlier time. These novel, self-similar solutions are linearly stable but they only develop if the initially circular interface is subjected to unimodal perturbations. Conversely, the application of nonunimodal perturbations (e.g., via the superposition of multiple linearly unstable modes) leads to the development of complex, constantly evolving finger patterns similar to those that are typically observed in constant-width Hele-Shaw cells.

We investigate through direct numerical simulations (DNSs) the statistical properties of turbulent flows in the inertial subrange for non-Newtonian power-law fluids. The structural invariance found for the vortex size distribution is achieved through a self-organized mechanism at the microscopic scale of the turbulent motion that adjusts, according to the rheological properties of the fluid, the ratio between the viscous dissipations inside and outside the vortices. Moreover, the deviations from the K41 theory of the structure functions' exponents reveal that the anomalous scaling exhibits a systematic nonuniversal behavior with respect to the rheological properties of the fluids.

Lagrangian statistics and pair dispersion induced by an isolated pulse of a small jellyfish, Aurelia aurita, were quantified and characterized using 3D particle tracking velocimetry (3D-PTV). Probability density functions (PDF) of the Lagrangian velocity components indicated more intense mixing in the radial direction and revealed three stages dominated by flow acceleration, mixing, and dissipation. Time evolution of the Lagrangian acceleration variance further illustrates each phase. During the mixing phase, the flow shares characteristics of homogeneous isotropic turbulence. In addition, we show that a single pulse may induce rich wake dynamics characterized by pair dispersion with a super-diffusive $t^3$ regime due to large-scale flow inhomogeneity, followed by a coherent $t^2$-Batchelor scaling and then $t^1$-Brownian motions. The first trend occurred in the accelerated flow, whereas the second dynamic was observed in the mixed wake and depended on the initial separation. The Brownian motion was present in the late stage dominated by flow dissipation. Kolmogorov microscales during the fully mixed phase were obtained with three distinct approaches, namely, Heisenberg-Yaglom relation of the Lagrangian acceleration variance, the fluctuating rate of the strain tensor in the Eulerian frame of reference as well as the Batchelor scaling in pair dispersion, which showed good agreement.

An advanced leukocyte model based on a lattice-Boltzmann lattice-spring model (LLM) and an adhesive dynamics (AD) is presented. In principle, the model can deal with not only extensional and compressional but also bending deformation of microvilli of of leukocytes. In this work, the model is applied to investigate how different flow shear rates affect bending deformation of the microvilli and related physical properties. It is demonstrated that at each given flexural stiffness, adhesive bond force, rolling velocity, contact area, number of bonds, and bending deformation increase as the shear rate increases. At each given shear rate, the bending angles of microvilli increase as the flexural stiffness decreases. Therefore, the adhesive bond force, contact area, and number of bonds increase and result in a decrease in cell rolling velocity. The degree of the decrease depends on both shear rate and flexural stiffness. In addition, a bonding and debonding process for individual microvilli is observed and explored from a bending angular point of view.

In this work, we studied experimentally and numerically the pressure–flow rate relationship for yield stress fluids in porous media. We developed and validated 3D numerical simulations of the velocity field via a lattice Boltzmann method based on the TRT scheme, and a specific experimental setup allowing yield stress fluids to flow in a closed-loop system to obtain stable rheological properties over a wide range of flow rates (4 decades). The porous medium studied experimentally is a sandstone. The flow properties were also simulated on a regular sphere packing and a random sphere packing as well as on a 3D geometry of a sandstone obtained by x-ray tomography. These different geometries allow highlighting the role of the heterogeneity of the pore structure on the flow properties. All results are expressed as the flow rate $\tilde{Q}$ versus the difference of the pressure gradient to the critical pressure $(\mathrm{\Delta }\tilde{P}-\mathrm{\Delta }{\tilde{P}}_c)$; $P_c$ defines the pressure below which there is no flow. We observed both numerically and experimentally three specific scaling regimes, already identified by Talon and Bauer [Eur. Phys. J. E 36, 139 (2013)] for a Bingham fluid in 2D porous media. We also evidenced the existence of two critical pressures: the “true” critical pressure ${\tilde{P}}_c$ defined as the pressure below which there is no flow and the “pseudo” critical pressure threshold ${\tilde{P}}_c^{\infty }$ determined by fitting the data in the high-flow-rate regime. We show that the “true” critical pressure is always lower than the “pseudo” one in heterogeneous porous media and can be equal only in the case of regular porous structures. We explain these observations using an energy minimization principle.

A two-phase flow model is developed to study the small deformation of a poroelastic drop under linear flows. Inside the drop a deformable porous network characterized by an elastic modulus is fully immersed in a viscous fluid. When the viscous dissipation of the interior fluid phase is negligible (compared to the friction between the fluid and the skeleton), the two-phase flow is reduced to a poroelastic Darcy flow with a deformable porous network. At the interface between the poroelastic drop and the exterior viscous Stokes flow, a set of boundary conditions are derived by the free-energy-dissipation principle. Both interfacial slip and permeability are taken into account and the permeating flow induces dissipation that depends on the elastic stress of the interior solid. Assuming that the porous network has a large elastic modulus, a small-deformation analysis is conducted. A steady equilibrium is computed for two linear applied flows: a uniaxial extensional flow and a planar shear flow. By exploring the interfacial slip, permeability, and network elasticity, various flow patterns about these slightly deformed poroelastic drops are found at equilibrium. The linear dynamics of the small-amplitude deviation of the poroelastic drop from the spherical shape is governed by a nonlinear eigenvalue problem, and the eigenvalues are determined.

We propose a methodology for generating time-dependent turbulent inflow data with the aid of machine learning (ML), which has the possibility to replace conventional driver simulations or synthetic turbulent inflow generators. As for the ML model, we use an autoencoder-type convolutional neural network with a multilayer perceptron. For the test case, we study a fully developed turbulent channel flow at the friction Reynolds number of ${\mathrm{Re}}_{\tau }=180$ for easiness of assessment. The ML models are trained using a time series of instantaneous velocity fields in a single cross section obtained by direct numerical simulation (DNS) so as to output the cross-sectional velocity field at a specified future time instant. From the a priori test in which the output from the trained ML model are recycled to the input, the spatiotemporal evolution of cross-sectional structure is found to be reasonably well reproduced by the proposed method. The turbulence statistics obtained in the a priori test are also, in general, in reasonable agreement with the DNS data, although some deviation in the flow rate was found. It is also found that the present machine-learned inflow generator is free from the spurious periodicity, unlike the conventional driver DNS in a periodic domain. As an a posteriori test, we perform DNS of inflow-outflow turbulent channel flow with the trained ML model used as a machine-learned turbulent inflow generator (MLTG) at the inlet. It is shown that the present MLTG can maintain the turbulent channel flow for a long time period sufficient to accumulate turbulent statistics, with much lower computational cost than the corresponding driver simulation. It is also demonstrated that we can obtain accurate turbulent statistics by properly correcting the deviation in the flow rate.

Observations performed with $\mathrm{C}{\mathrm{O}}_2$ near its critical point onboard sounding rockets show that periodical patterns (bands) develop in a two-phase, liquid-vapor system under tangential vibrations in microgravity conditions. Fluids are slightly below their liquid-vapor critical point where liquid and vapor densities are close, surface tension is low, and they exhibit a scaled, universal behavior. With the increase of vibration amplitude, an instability can develop on the band pattern, leading to the appearance of Faraday waves. Theoretical and numerical investigations of the Faraday instability onset and development are carried out taking into account the interaction between the bands. The critical parameters for the onset of instability are determined. The comparisons between theoretical analysis, two-dimensional direct numerical simulation, and original experimental data show good agreement.

Geophysical flows are often approximated as being two-dimensional on large scales due to their high aspect ratios. Two-dimensional flows in turn are well known to be prone to producing coherent structures that impact their mixing and transport. However, real geophysical flows are not exactly two-dimensional, in that they typically have nonuniform bathymetry that may also affect mixing. We study the interplay of quasi-two-dimensionality, nonuniform bathymetry, and lateral transport via laboratory experiments in an electromagnetically stirred thin-layer flow that is weakly turbulent. We find that spatial variations in bathymetry lead to laterally coexistent zones with different levels of turbulence, and we investigate the transport across the interface dividing these zones using an approach based on transfer operators. We find that this transport is asymmetric and that fluid elements cross from low turbulence to high turbulence via directed advection but from high to low turbulence via random eddying motion. Our results may have implications for understanding geophysical flows where lateral transport is suppressed, such as ocean dead zones.

Statistical properties of an incompressible passive vector convected by homogeneous isotropic turbulence are studied by comparing to the velocity and passive scalar, in order to explore the physics behind the differences and similarities in the statistical properties between the velocity vector and passive scalar. The passive vector obeys an equation similar to the Navier-Stokes equation, with a pseudopressure to ensure the incompressibility of the vector. The von Kármán–Howarth equation for the passive vector is derived and the average of the velocity increment times the square of the passive vector increments obeys a 4/3 law in the inertial-convective range. We carried out direct numerical simulations (DNSs) of up to ${1024}^3$ grid points. The spectra of the kinetic and pseudokinetic energies and the scalar variance obey a $k^{-5/3}$ power law. The Kolmogorov constants are $C_K=1.57$ for the velocity and $C_K^w=0.99$ for the passive vector, and the Obukhov-Corrsin constant of the passive scalar is $C_{\mathrm{OC}}=0.67$. The spectral bump of the compensated spectrum of the passive vector is slightly larger than that of the velocity, but smaller than the passive scalar. It is found that the behavior of the passive vector fluctuations at large scales is close to that of the velocity due to the nonlocal effects of the pseudo-pressure, while the small-scale fluctuations resemble those of the passive scalar. The nonlinearity of the convective term is key to the differences between the velocity and passive fields at small scales.

Skewness and non-Gaussian behavior are essential features of the distribution of short-scale velocity increments in isotropic turbulent flows. Yet, although the skewness has been generally linked to time-reversal symmetry breaking and vortex stretching, the form of the asymmetric heavy tails remain elusive. Here we describe the emergence of both properties through an exactly solvable stochastic model with a scale hierarchy of energy transfer rates. From a statistical superposition of a local equilibrium distribution weighted by a background density, the increments distribution is given by a novel class of skewed heavy-tailed distributions, written as a generalization of the Meijer $G$-functions. Excellent agreement in the multiscale scenario is found with numerical data of systems with different sizes and Reynolds numbers. Remarkably, the single-scale limit provides poor fits to the background density, highlighting the central role of the multiscale mechanism. Our framework can be also applied to describe the challenging emergence of skewed distributions in complex systems.

In this paper we carry out a theoretical study of the stability of gravity-driven flow of liquid layers doped with a soluble surfactant. We develop a model for the flow that accounts for both the concentration of surfactant adsorbed to the surface and that dissolved into the bulk of the layer. Furthermore, the mass density of the surfactant-laden liquid is assumed to increase with the concentration of surfactant in the bulk. A linear stability analysis is performed on the steady flow of a layer with uniform thickness. A nonlinear reduced dimensionality model is also constructed by means of a weighted-residuals approach and used to study the instability of the equilibrium flow and the development of permanent surface waves that arise from the instability.