Red blood cells under shear flow present a specific swinging motion superimposed to a fluidlike tank-treading motion. Swinging is hypothesized to originate from periodic storage of shear energy in the cell membrane. Here we designed giant unilamellar vesicles with two lipid phases separated by a contact line, which swing and tank-tread like red cells. We propose a model that quantitatively fits our data, finds the value of the contact-line tension, and shows that swinging is due to the storage of elastic energy associated with the periodic modulation of the contact-line length during tank-treading.

When a drop impinges on a superheated surface, a Leidenfrost vapor layer forms between the drop and the surface. Transient dynamics of the layer can play a critical role for cooling in power plants but is not fully understood. Here we successfully visualize transient dynamics of the layer using ultrafast x-ray imaging. We reveal that a vapor disk with a homogeneous thickness, developed during drop impact, grows in thickness following the Fourier law. At a certain thickness (12 ± 2 μm in this study) of the vapor disk, ripples generate at its periphery due to capillary waves, resulting in significant enhancement of drop vaporization.

We present a study of buoyancy-driven variable-density homogeneous turbulence, using a two-point spectral closure model. We compute the time-evolution of the spectral distribution in wave number $k$ of the correlation of density and specific volume $b\left(k\right)$, the velocity associated with the turbulent mass flux $\mathit{a}\left(k\right)$, and the turbulent kinetic energy $E\left(k\right)$, using a set of coupled equations. Under the modeling assumptions, each dynamical variable has two coefficients governing spectral transfer among modes. In addition, the velocity $\mathit{a}\left(k\right)$ has two coefficients governing the drag between the two fluids. Using a prescribed initial condition for $b\left(k\right)$ and starting from a quiescent flow, we first evaluate the relative importance of the different coefficients used to model this system and their impact on the statistical quantities. We next assess the accuracy of the model, relative to direct numerical simulation of the complete hydrodynamical equations, using $b,\mathit{a}$, and $E$ as metrics. We show that the model is able to capture the spectral distribution and global means of all three statistical quantities at both low and high Atwood number for a set of optimized coefficients. The optimization procedure also permits us to discern a minimal set of four coefficients which are sufficient to yield reasonable results while pointing to the mechanisms that dominate the mixing process in this problem.

Between streamwise distances $4d$ and at least $10d$ in the planar turbulent wake of a square prism of side length $d$, the turbulent fluctuating velocities are highly non-Gaussian, the turbulent energy spectrum has a close to $-5/3$ power law range, and the turbulence dissipation rate obeys the nonequilibrium dissipation scaling if the energy of the coherent structures is not included in the scaling. In this same range of streamwise distances, the coherent structure dissipation rate decays proportionally to the stochastic turbulence dissipation rate and there is a strong tendency of alignment or antialignment between fluctuating velocities and fluctuating vorticities which appears to coincide with the presence of coherent structures.

The transition from Tayor vortex flow to wavy-vortex flow is revisited. The self-sustaining process (SSP) of Waleffe [Phys. Fluids 9, 883 (1997)] proposes that a key ingredient in transition to turbulence in wall-bounded shear flows is a three-step process involving rolls advecting streamwise velocity, leading to streaks which become unstable to a wavy perturbation whose nonlinear interaction with itself feeds the rolls. We investigate this process in Taylor-Couette flow. The instability of Taylor-vortex flow to wavy-vortex flow, a process which is the inspiration for the second phase of the SSP, is shown to be caused by the streaks, with the rolls playing a negligible role, as predicted by Jones [J. Fluid Mech. 157, 135 (1985)] and demonstrated by Martinand et al. [Phys. Fluids 26, 094102 (2014)]. In the third phase of the SSP, the nonlinear interaction of the waves with themselves reinforces the rolls. We show this both quantitatively and qualitatively, identifying physical regions in which this reinforcement is strongest, and also demonstrate that this nonlinear interaction depletes the streaks.

We study how the dynamics of a drying front propagating through a porous medium are affected by small-scale correlations in material properties. For this, we first present drying experiments in microfluidic micromodels of porous media. Here, the fluid pressures develop more intermittent dynamics as local correlations are added to the structure of the pore spaces. We also consider this problem numerically, using a model of invasion percolation with trapping, and find that there is a crossover in invasion behavior associated with the length scale of the disorder in the system. The critical exponents that describe large enough events are similar to the classic invasion percolation problem, while the addition of a finite correlation length significantly affects the exponent values of avalanches and bursts, up to some characteristic size. We find that even a weak local structure can interfere with the universality of invasion percolation phenomena. This has implications for a variety of multiphase flow problems, such as drying, drainage, and fluid invasion.

Understanding rare events in turbulence provides a basis for the science of extreme weather, for which the atmosphere is modeled by Navier-Stokes equations (NSEs). In solutions of NSEs for isotropic fluids, various quantities, such as fluid velocities, roughly follow Gaussian distributions, where extreme events are prominent only in small-scale quantities associated with the dissipation-dominating length scale or anomalous scaling regime. Using numerical simulations, this study reveals another universal promotion mechanism at much larger scales if three-dimensional fluids accompany strong two-dimensional anisotropies, as is the case in the atmosphere. The dimensional crossover between two and three dimensions generates prominent fat-tailed non-Gaussian distributions with intermittency accompanied by colossal chainlike structures with densely populated self-organized vortices (serpentinely organized vortices). The promotion is caused by a sudden increase of the available phase space at the crossover length scale. Since the discovered intermittency can involve much larger energies than those in the conventional intermittency in small spatial scales, it governs extreme events and chaotic unpredictability in the synoptic weather system.

Detonation initiation has been extensively investigated in the past several decades. In the literature, there are many studies on detonation initiation using a large amount of blast energy and obstacles to respectively achieve direct detonation initiation or deflagration to detonation transition (DDT). However, there are few studies on detonation initiation with a nonuniform initiation zone. In this work, two-dimensional numerical simulations considering detailed chemistry and transport are conducted to investigate the effects of disturbance on detonation initiation in a stoichiometric ${\mathrm{H}}_2/{\mathrm{O}}_2/{\mathrm{N}}_2$ mixture. The high-pressure and high-temperature detonation initiation regime is imposed by a sinusoidal disturbance. Introduction of such disturbance is found to promote the onset of detonation and to reduce time and distance for detonation formation. This is mainly because such disturbance can induce shock-wave interaction, which generates transverse waves. The reflected transverse waves result in local autoignition and explosion. The coherent coupling between local autoignition and pressure wave resulting from a large amount of heat release eventually leads to the detonation development. It is found that the distance and duration for detonation initiation become shorter when a disturbance with smaller wavelength or larger amplitude is enforced. When the ratio between the wavelength and amplitude of disturbance is fixed, the change in wavelength and amplitude has little influence on detonation initiation. Therefore, disturbance with either small wavelength or large amplitude can be used to promote detonation initiation.

We develop a theory of spatial distribution of fine bubbles in turbulence and confirm it numerically. The bubbles are a few hundred microns in size and the considered value of the turbulence's strength is typical for oceans. The fluid applies a lift force on bubbles that causes bubble clustering by acting in a direction perpendicular to the rise velocity and the horizontal vorticity. We demonstrate that the centripetal attraction of bubbles to the cores of vortices is negligible compared with this effect. The combined action of the lift and the turbulence creates a continuum flow of bubbles distinct from the flow of the fluid and identical to the Peddley-Kessler (PK) model of swimming phytoplankton cells in the limit of strong gravitaxis. This allows one to derive a whole array of results by applying the theory of this model, which is well developed in the limit. The similarity explains the patchiness and clustering of bubbles in regions of downwelling flow; these properties are understood for motile phytoplankton. The bubble clustering decreases the average rise velocity, prolonging the time until the bubble's rupture at the surface. We demonstrate that bubbles form columnar structures characterized by a multifractal distribution with the dimension deficit increasing as the eighth power of the radius. Fractal dimensions are derived from the information dimension given by the Kaplan-Yorke formula. We also provide some results for the shape-dependent PK model. We confirm the theory by direct numerical simulations of the bubbles' motion in Navier-Stokes turbulence.

This paper presents a detailed experimental study of the evolution of a sediment bed under the action of the boundary layers formed under a spin-down flow in a rotating fluid-filled cylindrical tank. Both complete and partial spin-down are considered, i.e., with the tank coming to a complete stop or being only partially decelerated. Two nondimensional numbers, the Reynolds (Re) and Rossby (Ro) numbers, govern the flow. During the spin-down, the bed morphology changes, exhibiting distinct characteristic patterns. The changes are measured using a light attenuation technique (LAT). Background rotation suppresses the emergence of instabilities and turbulence, making the patterns more regular and smoother. In spite of the differences and complexity in the patterns, radially inward transport is explained by the total radial force exerted by the flow as computed using classical expressions for the structure of laminar boundary layers.

A parametric study of the magnetic dipole behavior in resistive incompressible magnetohydrodynamics inside a rotating sphere is performed, using direct numerical simulations and considering Reynolds and Ekman numbers as controlling parameters. The tendency is to obtain geodynamolike magnetic dipole reversal regimes for sufficiently small Ekman and large Reynolds numbers. The typical dipole latitude obtained in the reversal regime is around ${40}^{\circ }$ (with respect to the rotation axis of the sphere). A statistical analysis of waiting times between dipole reversals is also performed, obtaining a non-Poissonian distribution of waiting times, indicating long-term memory effects. We also report the presence of a $1/f$ frequency power spectrum in the magnetic dipole time series, which also shows a tendency to grow toward lower frequencies as the Ekman number is decreased.

When a small sphere is passing through an oil-water interface without dewetting, an oil film will be coated on the sphere's surface. Here a nominal Bond number is defined to classify different behaviors of the sphere crossing the oil-water interface with an initial velocity of zero, according to the radius of the spheres and the density difference between the spheres and the liquid. The critical value of the nominal Bond number for the small sphere to pass through the interface is derived to be 1.5, and the thickness of the coating film on the spheres can be well-predicted when the nominal Bond number is in the range of 1.5–7.5. It is demonstrated that this predictable coating film can be used as a potential coating technology to form thick and even coating film on small spheres.

A granular layer can form standing-wave patterns, such as squares, stripes, and hexagons, when it is fluidized with a pulsed gas flow. These patterns resemble the well-known patterns formed in vertically vibrated granular layers, but are governed by different dimensionless numbers. Recent research [de Martín et al., Phys. Rev. Fluids 3, 034303 (2018)] reveals that the onset to pattern formation in shallow pulsed beds can be understood in terms of the dimensionless number ${\mathrm{\Gamma }}_p=u_a/u_t\overline{\varphi }$, where $u_a$ is the amplitude of the gas velocity, $u_t$ is the terminal velocity of the particles, and $\overline{\varphi }$ is the average solids volume fraction. In contrast, pattern formation in vertically vibrated granular layers in vacuo is governed by the dimensionless number ${\mathrm{\Gamma }}_v=4{\pi }^2{f}^{2}d/g$, where $f$ and $d$ are the frequency and displacement of the vibrated plate, respectively, and $g$ is the gravitational acceleration. In addition, the threshold for pattern formation in pulsed beds exhibits a strong dependence with the frequency of the excitation that is not observed in the threshold for pattern formation in vibrated systems. This work explores the origin of these differences by simulating the dynamics of a one-dimensional pulsed array of particles. Simulations reproduce well the experimental stability curves, and reveal that the criterion for instability in shallow pulsed and vibrated systems is actually the same; the layer flight time must be equal to $1/f$. In pulsed beds, this criterion is determined by the traveling time of the kinematic wave that forms in each flow pulse. These results provide a theoretical basis to the recent experimental observations and highlights commonalities between the mechanisms behind pattern formation in thin vibrated granular layers and shallow pulsed fluidized beds.

The drag on pairs of square obstacles (of side D) in open channel flow is measured in experiments using a laboratory flume. The depth is uniform across the obstacles and the conditions in the flume are subcritical, with Froude number $\mathrm{Fr}<0.59$, Reynolds number Re = 4800 to 21900, and turbulence intensity $I_T\sim 8$ to 10%. The drag coefficient for an isolated square obstacle is found to be $C_D=2.11$, in agreement with previous studies, and independent of Re (for the range covered here). The root-mean-square variation in the drag coefficient for the single obstacle decreased monotonically with Re, defined in terms of hydraulic radius, and approached 0.241 at high Re in agreement with previous research. For two obstacles, standard tandem and side-by-side arrangements are studied first, followed by a full range of relative positions covering $-5\le s_x/D\le 20$ in the downstream direction and $0\le s_y/D\le 7.0$ in the cross-stream direction. The lowest drag coefficients are observed when the downstream obstacle is shielded directly behind the upstream obstacle (tandem arrangement) when negative drag coefficients are found. The largest drag coefficients are observed for nearly side-by-side arrangements, with the peak values found to be for the slightly upstream obstacle of a pair $(s_x/D=-1)$. The blockage ratio (D/B, the relative size of the obstacle compared to the channel width) is found to be an important factor. For D/B = 12.7% the largest drag coefficient is $C_D=3.82$, while for D/B = 6.3% the largest value is $C_D=2.85$. For tandem obstacles, the drag on one obstacle can largely be accounted for by the change in flow speed induced by the other obstacle, except at small separations $\left(\right|s_x/D|<3)$. The results will be useful in any applications where the force on multiple obstacles is required, such as the design of marine or riverine structures, or flood flows past buildings and vegetation.

We report on the shape relaxation of two-dimensional (2D) droplets, formed right after the spontaneous pinch-off of a capillary bridge droplet confined within a Hele-Shaw cell. An array of bridge droplets confined within a microchip device first undergoes neck thinning due to the evaporation-driven volume change. Subsequently, an abrupt topological change transforms each bridge droplet into a small central satellite droplet and the twin droplets pinned at the edges of the cell. We monitor the shape relaxation with high-temporal-resolution optical microscopy. Capillary action drives the 2D shape relaxation, while the viscous dissipation in the film retards it. As a result, the tip of the twin droplets exhibits a self-similar parabolic shape evolution. Based on these observations, the lubrication-approximation model accurately predicts the internal pressure evolution and the droplet tip displacement. The geometrical confinement substantially slows down the dynamics, facilitating visualization of the capillary-viscous regime, even for low-viscosity liquids. The characteristic relaxation timescale shows an explicit dependence on the confinement ratio (width/gap) and the capillary velocity of liquid. We verify the broad applicability of the model using different liquids.

Motivated by the potential use of self-rewetting fluids (i.e., fluids that exhibit a nonmonotonic variation of surface tension with temperature) in various heat-transfer applications, in the present work we formulate and analyze a theoretical model for the unsteady motion of a long bubble or droplet in a self-rewetting system in a nonuniformly heated tube due to a combination of Marangoni effects due to the variation of surface tension with temperature, gravitational effects due to the density difference between the two fluids, and an imposed background flow along the tube. We find that the evolution of the shape (but not of the position) of the bubble or droplet is driven entirely by Marangoni effects and depends on the initial value of its radius in relation to a critical value. In the case in which Marangoni effects are absent, the bubble or droplet always moves with constant velocity without changing shape. In the case in which only Marangoni effects are present, the bubble or droplet either always moves away from or always moves towards the position of minimum surface tension; in the latter case it ultimately fills the entire cross section of the tube at a final stationary position which is closer to the position of minimum surface tension than its original position. In the cases in which either only Marangoni effects and gravitational effects or only Marangoni effects and background-flow effects are present the competition between the two effects can lead to a nonmonotonic evolution of the position of the center of mass of the bubble or droplet. The behavior of a self-rewetting system described in the present work is qualitatively different from that for ordinary fluids, in which case the bubble or droplet always moves with constant velocity without changing shape.

At high Reynolds numbers, the logarithmic range in wall-bounded flows spans many scales. An important conceptual modeling framework of the logarithmic range is Townsend's attached eddy hypothesis [The Structure of Turbulent Shear Flow (Cambridge University Press, Cambridge, 1976)], where high Reynolds number wall-bounded flows are modeled as assemblies of space-filling, self-similar, and wall-attached eddies. Recently, Yang et al. [Phys. Rev. Fluids 1, 024402 (2016)] reinterpreted this hypothesis and developed the “hierarchical random additive process” model (HRAP), which provides further insights into the scaling implications of the attached eddies. For example, in a recent study [Yang et al., Phys. Rev. Fluids 2, 064602 (2017)], the HRAP model was used for making scaling predictions of the second-order structure function $〈[u_i^{\prime }\left(\mathbf{x}\right)-u_i^{\prime }\left({\mathbf{x}}^{\prime }\right)][u_j^{\prime }\left(\mathbf{x}\right)-u_j^{\prime }\left({\mathbf{x}}^{\prime }\right)]〉$ in the logarithmic range, where $u_i$'s are the velocity fluctuations in the $i\mathrm{th}$ Cartesian direction. Here, we provide empirical support for this HRAP model using high-fidelity experimental data of all three components of velocity in a high Reynolds number boundary layer flow. We show that the spanwise velocity fluctuation can be modeled as a random additive process, and that the wall-normal velocity fluctuation is dominated by the closest neighboring wall-attached eddy. By accounting for all the three velocities in all the three Cartesian directions, the HRAP model is formally a well rounded model for the momentum-carrying scales in wall-bounded flows at high Reynolds numbers.

When vortex rings collide head-on at high enough Reynolds numbers, they ultimately annihilate through a violent interaction which breaks down their cores into a turbulent cloud. We experimentally show that this very strong interaction, which leads to the production of fluid motion at very fine scales, uncovers direct evidence of an iterative cascade of instabilities in a bulk fluid. When the coherent vortex cores approach each other, they deform into tentlike structures and the mutual strain causes them to locally flatten into extremely thin vortex sheets. These sheets then break down into smaller secondary vortex filaments, which themselves rapidly flatten and break down into even smaller tertiary filaments. By performing numerical simulations of the full Navier-Stokes equations, we also resolve one iteration of this instability and highlight the subtle role that viscosity must play in the rupturing of a vortex sheet. The concurrence of this observed iterative cascade of instabilities over various scales with those of recent theoretical predictions could provide a mechanistic framework in which the evolution of turbulent flows can be examined in real time as a series of discrete dynamic instabilities.

We discuss the impact of viscosity on nonlinear propagation of surface waves at the interface of air and a fluid of large depth. After a survey of the available approximations of the dispersion relation, we propose to modify the hydrodynamic boundary conditions to model both short and long waves. From them, we derive a nonlinear Schrödinger equation where both linear and nonlinear parts are modified by dissipation and show that the former plays the main role in both gravity and capillary-gravity waves while, in most situations, the latter represents only small corrections. This provides a justification of the conventional approaches to damped propagation found in the literature.

The motion of a liquid above textured surfaces, impregnated with either a gas or a lubricant oil, is considered by homogenizing the microscopic near-wall flow to obtain protrusion heights (or Navier slip lengths), which can then be used in (macroscopic) direct numerical simulations of turbulence. The microstructure of the wall consists in longitudinally aligned ridges; this renders the small-scale Stokes problem amenable to decoupling into two problems, solved by the boundary element method with full account of the deformation of the liquid-lubricant interface, finally yielding two different protrusion heights, a longitudinal and a transverse one, respectively $h_{\left|\right|}$ and $h_{\perp }$. Such heights are then employed in direct numerical simulations of the turbulent flow in a channel bounded by superhydrophobic or lubricant-impregnated walls, demonstrating the reduction in skin-friction drag which can be achieved with the rise in protrusion height difference, $\mathrm{\Delta }h=h_{\left|\right|}-h_{\perp }$. The results are in good agreement with an analytical approximation, provided $\mathrm{\Delta }{h}^{+}$ ($\mathrm{\Delta }h$ scaled in wall units) remains below 2 and the protrusion heights small in magnitude.