Due to the inherent nonlinearity of fluid dynamics, a large class of oscillating flows gives rise to rectified effects of steady motion. It has recently been shown that particle transport in such flows leads to differential displacement and efficient sorting of microparticles. Here we present a model that generalizes a Maxey-Riley-like equation for particle motion, incorporating important viscous and inviscid effects near oscillating interfaces and efficiently bridging the acoustofluidic and microfluidic approaches. Resulting in direct predictions for particle motion on slower timescales, the model predicts a richer and qualitatively different behavior from that expected from simplified radiation-force formalisms: depending on experimental control parameters, the net effect of interfacial oscillation can be either an attraction to or a repulsion from the interface, and particles can be captured at a fixed distance or released. These results are verified in comparison with experiments.

We consider freely decaying homogeneous anisotropic turbulence whose energy spectrum $E\left(k\right)$ at $k\to 0$ is given by $E\left(k\right)=C{k}^2+o\left(k^2\right)$ at an initial instant, where $k$ is the wave number and $C$ is a $k$-independent positive number. An argument is given to show that there are an infinite number of invariants characterizing the large-scale structure of the turbulence. This is a generalization of Saffman's argument, which shows the existence of a finite number of invariants [P. G. Saffman, J. Fluid Mech. 27, 581 (1967)]. By applying a similar argument to homogeneous anisotropic passive scalar turbulence without any scalar source, we show that there are an infinite number of invariants characterizing the large-scale structure of passive scalar fields. Theoretical analysis based on the invariance and a self-similarity assumption for the large-scale evolution shows that the anisotropy of the velocity and passive scalar fields is persistent at large scales. The decay laws of the velocity and passive scalar fields are derived by a simple dimensional analysis.

High-resolution three-dimensional large-eddy simulations are used to investigate the effects of internal solitary waves (ISWs) breaking over a sloping boundary. The lock release method is applied in a two-layer stratified fluid system to generate three different breaking mechanisms (i.e., plunging, collapsing, and surging breakers). The different breaking types are investigated in terms of their effects on the dynamics of the ISW and the interaction of the ISW with the sloping boundary. During each breaking event, the pycnocline region entrains fresher water from the upper layer and saltier water from the lower one. The associated increase of the intermediate density layer also induces changes of the pycnocline water density. This process occurs with a velocity that can be evaluated using the bulk entrainment parameter. We show how the intermediate layer features depend on the ISW shoaling and breaking dynamics and we discuss entrainment in breaking ISWs. The instabilities induced by boundary layer separation allow entrainment of saltier water, while the run-up of the gravity current causes the decrease of the intermediate layer mean density. Simultaneously, the entrained water mixes into the pycnocline region. For all cases, the temporal evolution of the instantaneous mixing efficiency is discussed. The plunging breaker case shows the largest amount of mixing, which is mostly induced by rear-edge overturning in the onshore direction. The largest entrainment is observed in the surging breaker case in response to the large gravity current flowing upslope. The paper discusses how the different turbulent instabilities induced by the ISWs breaking affect the time delay between the times when entrainment of patches of salty and fresh water from the neighboring layers occurs and the time the density of the intermediate layers becomes fairly uniform via mixing. We finally point out that the entrainment parameter and the mixing efficiency describe two different effects of the turbulent instabilities occurring in a stratified fluid in terms of changes of the bulk density profile.

We characterize the local concentration dependence of segregation velocity and segregation flux in both size and density bidisperse gravity-driven free-surface granular flows as a function of the particle size ratio and density ratio, respectively, using discrete element method simulations. For a range of particle size ratios and inlet volume flow rates in size-bidisperse flows, the maximum segregation flux occurs at a small particle concentration less than 0.5, which decreases with increasing particle size ratio. The segregation flux increases up to a size ratio of 2.4 but plateaus from there to a size ratio of 3. In density bidisperse flows, the segregation flux is greatest at a heavy particle concentration less than 0.5, which decreases with increasing particle density ratio. The segregation flux increases with increasing density ratio for the extent of density ratios studied, up to 10. We further demonstrate that the simulation results for size-driven segregation are in accord with the predictions of the kinetic sieving segregation model of Savage and Lun [J. Fluid Mech. 189, 311 (1988)].

In this paper we investigate experimentally the waves produced by a parabolically shaped wave maker partially immersed into a water-filled basin and oscillating in the vertical direction. The main motivation of our study is to follow the analogy between light waves that focus on caustics, creating zones of intense light concentration, and surface waves in liquids. Similarly to light focusing, the surface waves undergo spatial focusing leading to the growth of their amplitudes till they reach a cusp singularity. We detect three regimes. In the first one, which corresponds to small forcing amplitudes, the wave field agrees well with geometrical optics and with Pearcey diffraction theory near the caustics. In the second regime, weak nonlinearities are detected. However, waves still focus as predicted. In the third regime, at large forcing amplitude, a large-scale mean flow is generated. This flow is concentrated in two symmetric jets emerging from the wave maker front wall and producing two counter-rotating eddies because of the finite size of the basin. This large-scale flow modifies the shape of the wave fronts and leads to a displacement of the cusp towards the wave maker, modifying the analogy between light and surface waves.

Direct numerical simulations of incompressible homogeneous-isotropic turbulence laden with a dilute suspension of inertial point particles are performed in conjunction with a wavelet multiresolution analysis of the results. The use of spatially localized wavelet basis functions enables the simultaneous consideration of physical and scale spaces in the spectral characterization of the flow field of the carrier phase and the concentration field of the dispersed phase. The multiresolution analysis of the dispersed phase provides statistical information about the spatial variabilities of a scale-dependent coarse-grained number density field and the local energy spectra of its fluctuations, characterizing the sensitivities of those quantities to variations in scale and Stokes number. In particular, the spatial variabilities of the wavelet energy spectrum of the particle concentration fluctuations are observed to be maximum in regimes where the particles preferentially concentrate. The results highlight the scale-dependent inhomogeneities of the structures in the concentration field generated by preferential concentration, and the existence of characteristic scales of interaction between the dispersed and carrier phases. Additionally, an interphase multiresolution analysis is performed that indicates the occurrence of a spatial anticorrelation between the enstrophy and kinetic-energy spectra of the carrier phase and the particle concentration at small scales in regimes where preferential concentration is important. This anticorrelation vanishes as the scale is increased and is largely suppressed when the preferential-concentration effect is negligible.

The physalis method for resolved numerical simulation of particulate flows, recently extended to include particles-fluid heat transfer, is applied to the turbulent flow past a planar particle array perpendicular to the incoming mean flow. The array consists of nine equal spheres. Periodicity boundary conditions are imposed on the boundaries of the computational domain parallel to the mean flow. The Reynolds number based on the particle diameter and mean incident flow is 120, the Taylor-scale Reynolds number is close to 30, and the ratio of particle radius to the Kolmogorov length is about 10. A detailed characterization of the flow and heat transfer is given including probability distribution functions of temperature and streamwise velocity, contour maps of the temperature fluctuations, diagonal Reynolds stresses, turbulent heat flux, and the various contributions to the energy budget. Turbulence moderately increases the heat transfer and considerably shortens the thermal wake of the particles. Temperature and streamwise velocity develop very differently downstream of the spheres in spite of the fact that the Prandtl number equals 1, because of the blockage by the spheres, which has no counterpart for the temperature.

When an elastic object is dragged through a viscous fluid tangent to a rigid boundary, it experiences a lift force perpendicular to its direction of motion. An analogous lift occurs when a rigid symmetric object translates parallel to an elastic interface or a soft substrate. The induced lift force is attributed to an elastohydrodynamic coupling that arises from the breaking of the flow reversal symmetry produced by the elastic deformation of the translating object or the interface. Here we derive explicit analytical expressions for the quasi-steady-state lift force exerted on a rigid spherical particle translating parallel to a finite-sized membrane exhibiting a resistance toward both shear and bending. Our analytical approach applies the Lorentz reciprocal theorem so as to obtain the solution of the flow problem using a perturbation technique for small deformations of the membrane. We find that the shear-related contribution to the normal force leads to an attractive interaction between the particle and the membrane. This emerging attractive force decreases quadratically with the system size to eventually vanish in the limit of an infinitely extended membrane. In contrast, membrane bending leads to a repulsive interaction whose effect becomes more pronounced upon increasing the system size, where the lift force is found to diverge logarithmically for an infinitely large membrane. The unphysical divergence of the bending-induced lift force can be rendered finite by regularizing the solution with a cutoff length beyond which the bending forces become subdominant to an external body force.

The effect of different definitions of the momentum flux on the properties of the coherent structures of the logarithmic region of wall-bounded turbulence is investigated by comparing the structures of intense tangential Reynolds stress with those of the alternative flux proposed in [Jiménez, J. Fluid Mech. 809, 585 (2016)]. Despite the fairly different statistical properties of the two flux definitions, it is found that their intense structures show many similarities, such as the dominance of “wall-attached” objects, and geometric self-similarity. The new structures are wider, but not taller, than the classical ones, and include both high- and low-momentum regions within the same object. It is concluded that they represent the same phenomenon as the classical groups of a sweep, an ejection, and a roller, suggesting that these groups should be considered the fundamental coherent structures of the momentum flux. The present results show that the properties of these composite momentum structures are robust with respect to the definition of the fluxes.

A fluid droplet suspended in an extensional flow of moderate intensity may break into pieces, depending on the amplitude of the initial droplet deformation. In subcritical uniaxial extensional flow the nonbreaking base state is linearly stable, implying that only a finite-amplitude perturbation can trigger breakup. Consequently, the stable base solution is surrounded by its finite basin of attraction. The basin boundary, which separates initial droplet shapes returning to the nonbreaking base state from those becoming unstable and breaking up, is characterized using edge tracking techniques. We numerically construct the edge state, a dynamically unstable equilibrium whose stable manifold forms the basin boundary. The edge state equilibrium controls if the droplet breaks and selects a unique path towards breakup. This path physically corresponds to the well-known end-pinching mechanism. Our results thereby rationalize the dynamics observed experimentally [H. A. Stone and L. G. Leal, J. Fluid Mech. 206, 223 (1989)].

We study the fronts that appear when a shear-thickening suspension is submitted to a sudden driving force at a boundary. Using a quasi-one-dimensional experimental geometry, we extract the front shape and the propagation speed from the suspension flow field and map out their dependence on applied shear. We find that the relation between stress and velocity is quadratic, as is generally true for inertial effects in liquids, but with a prefactor that can be much larger than the material density. We show that these experimental findings can be explained by an extension of a phenomenological model originally developed to describe steady-state shear thickening. This is achieved by introducing a sole additional parameter: the characteristic strain scale that controls the crossover from startup response to steady-state behavior. The theoretical framework we obtain points out a linkage between transient and steady-state properties of shear-thickening materials.

We analyze the resolvent operator in three flows around a nominal NACA-0012 airfoil at ${\text{Re}}_C=50,000$ and $5^{\circ }$ angle of attack. In particular, we study two naturally developing flows (around the airfoil with straight and blunt trailing edges) and one tripped flow. The naturally developing flows exhibit laminar separation, transition and turbulent reattachment, while the tripped flow remains attached in the suction side. For all cases, the time-averaged flow fields are computed from separate DNS simulations. The resolvent analysis can identify the areas of maximum receptivity of the flow field as well as the most amplified modes (optimal response). The former was located close to the leading edge, and in the case of naturally developing flows, also in the free-stream. The spatial distribution of optimal forcing was dominated by structures tilted against the mean flow, in agreement with other studies of boundary layer flows. The optimal response of the two naturally developing flows were different. For the NACA-0012 airfoil with straight trailing edge, the response was maximized at the natural frequency of the separating shear layer, and the shape matched closely with the corresponding DMD mode obtained from processing the DNS results. For the blunt airfoil, the receptivity of the separating shear layer was suppressed in the region of natural frequency, while it was maximized at the frequency of vortex shedding from the trailing edge. This is attributed to the lock-in mechanism between the shedding and the separating shear layer observed in the DNS simulations; the lock-in makes the separating shear layer less sensitive to forcing. In the tripped flow, the amplification of the perturbations is significantly diminished, and only by restricting the resolvent analysis to a region close to the suction side can we get a dominant frequency that matches with DNS at that region. The dominant resolvent modes were used to get estimations of the velocity spectra based only on the mean flow and the signal of one velocity component at discrete calibration points. Very good approximation is observed with only one or two points (depending on the flow examined), provided that they are located in energetic regions of the flow that contain sufficient spectral content at the relevant frequencies.

Jet drops ejected from bursting bubbles are ubiquitous, transporting aromatics from sparkling beverages, pathogens from contaminated water sources, and sea salts and organic species from the ocean surface to the atmosphere. In all of these processes, the smallest drops are noteworthy because their slow settling velocities allow them to persist longer and travel further than large drops, provided they escape the viscous sublayer. Yet it is unclear what sets the limit to how small these jet drops can become. Here we directly observe microscale jet drop formation and demonstrate that the smallest jet drops are not produced by the smallest jet drop-producing bubbles, as predicted numerically by Duchemin et al. [Duchemin et al., Phys. Fluids 14, 3000 (2002)]. Through a combination of high-speed imaging and numerical simulation, we show that the minimum jet drop size is set by an interplay of viscous and inertial-capillary forces both prior and subsequent to the jet formation. Based on the observation of self-similar jet growth, the jet drop size is decomposed into a shape factor and a jet growth time to rationalize the nonmonotonic relationship of drop size to bubble size. These findings provide constraints on submicron aerosol production from jet drops in the ocean.

Numerical simulations are performed to study the effect of particle size and density on dust dispersion behind a moving shock. The numerical model used in this paper takes into account multiple particle types with a binning approach, and each bin of particles has its own characteristic uniform particle size and density. The model solves one set of governing equations for the gas phase and $M$ sets of governing equations for the $M$ particle types. Equations for each bin of particles are coupled with the gas flow as well as all other particle types. The specific conditions simulate a Mach-1.4 shock passing over a dust layer containing two uniformly mixed particle types. The background gas condition is at 67 kPa and 295 K. The dust layer is 1.27 cm thick and consists of spherical particles with selected sizes and densities. Preliminary one-dimensional computations of a shock passing through a dilute particle curtain containing different particle types suggest that particles with different sizes or densities behave differently and can separate into different clouds. Particles with larger inertia require a longer relaxation time to the postshock condition. The two-dimensional calculations show that larger particles are lifted to a higher level than smaller particles. In regions near the shock front, larger particles experience a smaller drag force, pushing the particles into the dust layer, and a larger lifting force, pulling the particles into the air. In addition, lighter particles are lifted higher than heavier particles due to a smaller inertia. Particle size plays a significant role on dust dispersion, while particle density has only a minor effect.

As computing power has grown and turbulent flows at increasing Reynolds numbers are being computed by direct numerical simulations, conventional assumptions on adequate spatial and temporal resolutions are being continually challenged. We perform a systematic study of the resolution effects via numerical simulations at various spatial and temporal resolutions to clarify the proper scaling of dissipation and enstrophy (vorticity squared). Results show that inadequate resolution in space and/or time leads to overestimation of the likelihood and intensity of extreme fluctuations in dissipation and enstrophy. In order to capture rare events accurately, for instance, one needs to have not only grid resolutions that are increasingly smaller fractions of the Kolmogorov scale as the Reynolds number increases but also the Courant number that becomes increasingly smaller than that assumed to be adequate previously. Some comparisons are made with results obtained from an alternative approach where a stricter criterion for truncation in wave-number space allows aliasing errors to be removed completely. In contrast to prior work, the present data do not support the notion that dissipation and enstrophy probability density functions (PDFs) approach each other in the far tails at high Reynolds number. However the two PDFs are remarkably similar in form, being well described by stretched exponentials.

Using a dynamic surface force apparatus (SFA), we demonstrate that the notion of slip length used to describe the boundary flow of simple liquids is not appropriate for viscoelastic liquids. Rather, the appropriate description lies in the original Navier's partial slip boundary condition, formulated in terms of an interfacial friction coefficient. We establish an exact analytical expression to extract the interfacial friction coefficient from oscillatory drainage forces between a sphere and a plane, suitable for dynamic SFA or atomic force microscopy noncontact measurements. We use this model to investigate the boundary friction of viscoelastic polymer solutions over 5 decades of film thicknesses and 1 decade in frequency. The proper use of the original Navier's condition describes accurately the complex hydrodynamic force up to scales of tens of micrometers, with a simple Newtonian-like friction coefficient that is not frequency dependent and does reflect closely the dynamics of an interfacial depletion layer at the solution-solid interface.

The settling of colloidal particles with short-ranged attractions is investigated via highly resolved immersed boundary simulations. At modest volume fractions, we show that intercolloid attractions lead to clustering that reduces the hinderance to settling imposed by fluid back flow. For sufficient attraction strength, increasing the particle concentration grows the particle clusters, which further increases the mean settling rate in a physical mode termed promoted settling. The immersed boundary simulations are compared to recent experimental measurements of the settling rate in nanoparticle dispersions for which particles are driven to aggregate by short-ranged depletion attractions. The simulations are able to quantitatively reproduce the experimental results. We show that a simple, empirical model for the settling rate of adhesive hard-sphere dispersions can be derived from a combination of the experimental and computational data as well as analytical results valid in certain asymptotic limits of the concentration and attraction strength. This model naturally extends the Richardson-Zaki formalism used to describe hindered settling of hard, repulsive spheres. Experimental measurements of the collective diffusion coefficient in concentrated solutions of globular proteins are used to illustrate inference of effective interaction parameters for sticky, globular macromolecules using this empirical model. Finally, application of the simulation methods and empirical model to other colloidal systems are discussed.

Nectar-drinking bats and honeybees have tongues covered with hairlike structures, enhancing their ability to take up viscous nectar by dipping. Using a combination of model experiments and theory, we explore the physical mechanisms that govern viscous entrainment in a hairy texture. Hairy surfaces are fabricated using laser cut molds and casting samples with polydimethylsiloxane (PDMS) elastomer. We model the liquid trapped within the texture using a Darcy-Brinkmann-like approach and derive the drainage flow solution. The amount of fluid that is entrained is dependent on the viscosity of the fluid, the density of the hairs, and the withdrawal speed. Both experiments and theory reveal an optimal hair density to maximize fluid uptake.

We present numerical simulations of steady, laminar, axisymmetric convection of a Boussinesq fluid in a shallow, rotating, cylindrical domain. The flow is driven by an imposed vertical heat flux and shaped by the background rotation of the domain. The geometry is inspired by that of tropical cyclones and the global flow pattern consists of a shallow swirling vortex combined with a poloidal flow in the $r\text{−}z$ plane which is predominantly inward near the bottom boundary and outward along the upper surface. Our numerical experiments confirm that, as suggested in our recent work [L. Oruba et al., J. Fluid Mech. 812, 890 (2017)], an eye forms at the center of the vortex which is reminiscent of that seen in a tropical cyclone and is characterized by a local reversal in the direction of the poloidal flow. We establish scaling laws for the flow and map out the conditions under which an eye will, or will not, form. We show that, to leading order, the velocity scales with $V={\left(\alpha g\beta \right)}^{1/2}H$, where $g$ is gravity, $\alpha$ is the expansion coefficient, $\beta$ is the background temperature gradient, and $H$ is the depth of the domain. We also show that the two most important parameters controlling the flow are $\mathrm{Re}=VH/\nu$ and $\mathrm{Ro}=V/\left(\mathrm{\Omega }H\right)$, where $\mathrm{\Omega }$ is the background rotation rate and $\nu$ the viscosity. The Prandtl number and aspect ratio also play an important, if secondary, role. Finally, and most importantly, we establish the criteria required for eye formation. These consist of a lower bound on $\mathrm{Re}$, upper and lower bounds on $\mathrm{Ro}$, and an upper bound on the Ekman number.

This paper is associated with a video winner of a 2016 APS/DFD Milton van Dyke Award for work presented at the DFD Gallery of Fluid Motion. The original video is available from the Gallery of Fluid Motion, https://doi.org/10.1103/APS.DFD.2016.GFM.V0055