The anisotropy and structure of turbulence simulated by large-eddy simulations with and without Stokes-drift forcing are analyzed, with an emphasis on the linkage between the distinctive structure of Langmuir turbulence near the surface where cellular vortices aligned with the wind and wave propagation direction are apparent and the Langmuir-enhanced mixed layer entrainment at the base of the ocean surface boundary layer (OSBL) where turbulent structures differ. The tensor invariants of the Reynolds stresses, the variance of vertical velocity and buoyancy, and the velocity gradient statistics are used to categorize turbulence structures as a function of depth, including an extension of the barycentric map to show the direction as well as the magnitude of turbulence anisotropy and a vector-invariant extension of the Okubo-Weiss parameter. The extended anisotropic barycentric map and the velocity gradient statistics are demonstrated to be useful, providing compact information of the anisotropy, orientation, and structure of turbulent flows. It is found that the distinctive anisotropy and structures of Langmuir turbulence are quickly lost below regions where Stokes drift shear is significant and vortices are apparent, consistent with past observations and model results. As a result, the turbulent structures near the base of the OSBL are not significantly affected by the presence of Stokes drift above but are instead dominated by local Eulerian shear, except in one important manner. Langmuir turbulence does affect the mixed layer entrainment by providing extra available turbulent kinetic energy (TKE) via enhanced near-surface TKE production and higher vertical TKE transport energizing the turbulent structures near the base of the OSBL. The additional TKE is utilized by structures similar to those that exist without Stokes drift forcing in terms of anisotropy of their Reynolds stresses, but they are more energetic because of the Langmuir turbulence. Thus, parametrizing the major aspects of Langmuir turbulence on entrainment at the base of the OSBL can be incorporated through enhancing available energy without other modifications.

During evaporation in porous media, two types of corner films are distinguished. A continuous corner film is connected to the bulk liquid, while a discontinuous one is not. To disclose their effects on evaporation in porous media, a pore network model with both continuous and discontinuous corner films is developed, which considers the capillary and viscous forces as well as the effects of corner films on the threshold pressures of pores. The capillary valve effect induced by the sudden geometrical expansion between the small and large pores is also taken into account in the model. The developed pore network model agrees well with the evaporation experiment with a quasi-two-dimensional micromodel porous medium, in terms of not only the variation of the liquid saturation in each pore but also the variation of the total evaporation rate. The pore network models that neglect the corner films or the liquid viscosity are also compared with the experiment so as to shed light on the roles of the corner films. The continuous corner films, which contribute to sustain the high evaporation rate, can be interrupted to be the discontinuous ones not only by the gas invasion into pores but also by the capillary scissors effect due to the local convex topology of the solid matrix.

Using mixtures of soap, water, and long-chain polymers, free-floating soap bubbles can be formed with volumes approaching $100{\mathrm{m}}^3$. Here we investigate how such thin films are created and maintained over time. We show how the extensional rheology is the most important factor in creating the bubble and how polydispersity in molecular weight of the solvated polymers leads to better performance at lower concentrations. Additionally, using IR absorption, we measure soap film thickness profiles and film lifetimes. Although the initial thickness mostly depends on the choice of detergent, polymers can dramatically increase film lifetime at high molecular weights and high concentrations, although such high concentrations can inhibit the initial film formation. Thus, the ideal concentration of polymer additives for making giant bubbles requires a robust viscoelastic rheology during extension and is aided by long film lifetimes during gravitational drainage and evaporation.

We consider a drop of constant density and uniform interfacial tension rising in a linearly density stratified fluid. In the limits of weak inertia and stratification effects, we calculate the drag acting on the drop, the flow fields inside and outside the drop, the drop deformation, and the drift volume induced by the drop using the method of matched asymptotic expansions. Stratification or inertia increase the drag, and this enhanced drag acting on a drop is equal to ${\left(\frac{3\lambda +2}{3\left(\lambda +1\right)}\right)}^2$ times the enhanced drag acting on a rigid sphere, where $\lambda$ is the viscosity ratio. This relation between the enhanced drags of a drop and a rigid sphere holds even in the presence of both of these effects (stratification and inertia). On the other hand, stratification does not result in any deformation of the drop up to the first order of approximation. At zero inertia and small advective transport rate of density, the drift volume induced by the drop rising in a stratified fluid is finite (but large compared to the drop's volume), unlike the drift volume in a homogeneous fluid, which is infinite.

We consider the gravity-driven flow of a perfect dielectric, viscous, thin liquid film, wetting a flat substrate inclined at a nonzero angle to the horizontal. The dynamics of the thin film is influenced by an electric field which is set up parallel to the substrate surface—this nonlocal physical mechanism has a linearly stabilizing effect on the interfacial dynamics. Our particular interest is in fluid films that are hanging from the underside of the substrate; these films may drip depending on physical parameters, and we investigate whether a sufficiently strong electric field can suppress such nonlinear phenomena. For a non-electrified flow, it was observed by Brun et al. [Phys. Fluids 27, 084107 (2015)] that the thresholds of linear absolute instability and dripping are reasonably close. In the present study, we incorporate an electric field and analyze the absolute and convective instabilities of a hierarchy of reduced-order models to predict the dripping limit in parameter space. The spatial stability results for the reduced-order models are verified by performing an impulse-response analysis with direct numerical simulations (DNS) of the Navier–Stokes equations coupled to the appropriate electrical equations. Guided by the results of the linear theory, we perform DNS on extended domains with inflow and outflow conditions (mimicking an experimental setup) to investigate the dripping limit for both non-electrified and electrified liquid films. For the latter, we find that the absolute instability threshold provides an order-of-magnitude estimate for the electric-field strength required to suppress dripping; the linear theory may thus be used to determine the feasibility of dripping suppression given a set of geometrical, fluid, and electrical parameters.

The motion of isolated heavy particles on the bottom wall of a turbulent shear flow is investigated experimentally (using high-frequency particle tracking) and correlated to that of the fluid (from high-resolution LDV measurements). Numerous particle diameters, particle densities, and flow velocities are considered, where the particles remain within the viscous sublayer (particle Reynolds number lower than 10). It is shown that fluid flow fluctuations within the viscous sublayer (varying Couette flow) induce particle velocity fluctuations of the same magnitude, slightly smaller. The mean particle velocity, standard deviation, and Lagrangian correlation time are found to scale with the viscous scales. Particles roll and slide without takeoff, unlike what happens in viscous laminar flow where the lift force may overcome the immersed particle weight. Arguments are given for this difference. Probability density functions for the streamwise and spanwise velocity are found to follow Gamma and Gaussian laws, respectively, which also scale with the viscous scales.

We study the mixing of a passive scalar in homogeneous turbulent flow with and without anisotropic external force. It is assumed that no scalar source exists and the scalar spectrum at an initial time instant $t_0$ is given by the form $C{k}^2+o\left(k^2\right)$ at the wave number $k\to 0$, where $C$ is independent of $k$. We have performed direct numerical simulations (DNSs) of the mixing, in which the initial integral length scales of the scalar field are comparable to those of the velocity field and the Schmidt number is unity. The DNSs show that even though the large-scale anisotropy of the velocity field grows with time owing to the external force, its scalar field counterpart remains almost unchanged, i.e., frozen with respect to time, in a state where the scalar field evolves in a self-similar manner. The degree of the anisotropy of each of the velocity and scalar fields is measured by the ratios of the integral length scales in different Cartesian directions. The DNSs also suggest that the scalar spectrum keeps the form $C{k}^2+o\left(k^2\right)$ at small $k$ for time $t(\ge t_0)$, and that $C$ is time independent.

We use numerical simulations to study the dynamics of three-dimensional (3D) vesicles in unconfined and confined Poiseuille flow. Previous numerical studies have shown that when the fluid viscosity inside and outside the vesicle is the same (no viscosity contrast), a transition from asymmetric slippers to symmetric parachutes takes place as viscous forcing or capillary number is increased. At higher viscosity contrast, an outward migration tendency has also been observed in unconfined flow simulations. In this paper, we study how the presence of viscosity contrast and confining walls affect the dynamics of vesicles and present phase diagrams for confined Poiseuille flow with and without viscosity contrast. To our knowledge, this is the first study that provides a phase diagram for 3D vesicles with viscosity contrast in confined Poiseuille flow. The confining walls push the vesicle towards the center while the viscosity contrast has the opposite effect. This interplay leads to important differences in the dynamics, such as bistability, at high capillary numbers.

Quantum mechanics places significant restrictions on the hydrodynamics of superfluid flows. Despite this it has been observed that turbulence in superfluids can, in a statistical sense, share many of the properties of its classical brethren; coherent bundles of superfluid vortices are often invoked as an important feature leading to this quasiclassical behavior. A recent experimental study [E. Rusaouen, B. Rousset, and P.-E. Roche, Europhys. Lett. 118, 14005, (2017)] inferred the presence of these bundles through intermittency in the pressure field; however, direct visualization of the quantized vortices to corroborate this finding was not possible. In this work, we performed detailed numerical simulations of superfluid turbulence at the level of individual quantized vortices through the vortex filament model. Through course graining of the turbulent fields, we find compelling evidence supporting these conclusions at low temperature. Moreover, elementary simulations of an isolated bundle show that the number of vortices inside a bundle can be directly inferred from the magnitude of the pressure dip, with good theoretical agreement derived from the Hall-Vinen-Bekarevich-Khalatnikov (HVBK) equations. Full simulations of superfluid turbulence show strong spatial correlations between course-grained vorticity and low-pressure regions, with intermittent vortex bundles appearing as deviations from the underlying Maxwellian (vorticity) and Gaussian (pressure) distributions. Finally, simulations of a decaying random tangle in an ultraquantum regime show a unique fingerprint in the evolution of the pressure distribution, which we argue can be fully understood using the HVBK framework.

This paper reports a breakup regime of bubbles and droplets that is caused by a sudden channel expansion in a microfluidic device. In this regime, bubbles or droplets generated at a flow-focusing geometry periodically breakup into smaller bubbles or droplets, respectively, upon entering an expansion. In addition to Capillary number $Ca$, which is previously shown to govern the dispersion breakup in such geometries, we find that, at a high-inertia regime, the Weber number $We$ also plays a significant role in specifying the transition from non-breakup to breakup regimes. Furthermore, we identify different periodic breakup modes, for example, symmetric and asymmetric breakup, which are dictated by the Ohnesorge number. A power law of $f^{0.5}\propto W{e}^{0.1}C{a}^{0.2}$, where $f$ denotes the frequency at which the dispersions arrive at the expansion region, governs when the droplets and bubbles breakup. This power law highlights the importance of inertia to the dispersion breakup in an expansion-mediated geometry. Our results demonstrate that, without modifying the geometry and by only tuning several dimensionless parameters related to the fluid flow, a microchannel expansion region can produce mono-, bi-, or tri-disperse bubble or droplet populations. These discoveries may find utility in the design of multi-disperse bubble or droplet populations using microfluidics.

We investigate impact of a sphere onto a floating elastic sheet and the resulting formation and evolution of wrinkles in the sheet. Following impact, we observe a radially propagating wave, beyond which the sheet remains approximately planar but is decorated by a series of radial wrinkles whose wavelength grows in time. We develop a mathematical model to describe these phenomena by exploiting the asymptotic limit in which the bending stiffness is small compared to stresses in the sheet. The results of this analysis show that, at a time $t$ after impact, the transverse wave is located at a radial distance $r\sim t^{1/2}$ from the impactor, in contrast to the classic $r\sim t^{2/3}$ scaling observed for capillary–inertia ripples produced by dropping a stone into a pond. We describe the shape of this wave, starting from the simplest case of a point impactor, but subsequently addressing a finite-radius spherical impactor, contrasting this case with the classic Wagner theory of impact. We show also that the coarsening of wrinkles in the flat portion of the sheet is controlled by the inertia of the underlying liquid: short-wavelength, small-amplitude wrinkles form at early times since they accommodate the geometrically imposed compression without significantly displacing the underlying liquid. As time progresses, the liquid accelerates and the wrinkles grow larger and coarsen. We explain this coarsening quantitatively using numerical simulations and scaling arguments, and we compare our predictions with experimental data.

The hydrodynamic viscous fingering instability can be influenced by a simple viscosity-changing chemical reaction of type $A+B\to C$, when a solution of reactant $A$ is injected into a solution of $B$ and a product $C$ of different viscosity is formed by reaction. We investigate here numerically such reactive viscous fingering in the case of a reaction decreasing the viscosity to define the optimal conditions on the chemical and hydrodynamic parameters for controlling fingering. In particular, we analyze the influence of the Péclet number, $\mathrm{Pe}$, on the efficiency of the chemical control of fingering. We show that the viscosity-decreasing reaction has an increased stabilizing effect when $\mathrm{Pe}$ is decreased. On the contrary, fingering is more intense and the system more unstable when $\mathrm{Pe}$ is increased. The related reactive fingering patterns cover then respectively a smaller (larger) area than in the nonreactive equivalent. Depending on the value of the Péclet number, a given chemical reaction may thus either enhance or suppress a fingering instability. This stabilization and destabilization at low and high $\mathrm{Pe}$ are shown to be related to the $\mathrm{Pe}$-dependent characteristics of a minimum in the viscosity profile that develops around the miscible interface thanks to the effect of the chemical reaction.

Liquid-infused surfaces (LISs) make drops remarkably mobile. However, the dynamics of those drops proved to be subtle, due to the numerous phases at stake (lubricating liquid, drop, solid texture, and air). In this article, we highlight the role played by a feature specific to LISs, namely, the “foot” of oil surrounding the drops and drawn by their surface tension. Consequently, viscous dissipation can be localized in four distinct regions, which we tune independently through various experimental setups. Despite this complexity, we evidence a universal scaling for the friction law and reconcile recent results produced on this topic.

This study investigates the Reynolds-number dependence of shock-induced flow through stationary particle clouds at 10% volume fraction, using ensemble-averaged results from three-dimensional particle-resolved large eddy simulations. The advantage of using large eddy simulations to study this problem is that they capture the strong velocity shears and flow separation caused by the no-slip condition at the particle surfaces. The shock particle cloud interaction produces a reflected shock wave, whose strength increases with decreasing particle Reynolds number. This results in important changes to the flow field that enters the particle cloud. The results show an approximate proportionality between the mean flow velocity and the flow fluctuation magnitudes. Maximum particle drag forces are in excellent agreement with previous inviscid studies, and we complement these results with statistics of time-averaged particle forces as well as the variation of temporal oscillations. The results of this work provide a basis for development of improved simplified dispersed flow models.

The dynamics of perturbed aircraft wake models is investigated in the two-dimensional limit by means of a linear stability analysis. The base flow, computed by a direct numerical simulation of the incompressible Navier-Stokes equations, is a viscous counter-rotating vortex dipole obtained from an initial condition which is either a superposition of two Lamb-Oseen vortices or a vorticity sheet with elliptical vorticity distribution. The former, referred to as the Lamb-Oseen dipole (LOD), is a model for the far field of the wake and gives rise to a family of quasisteady dipoles parametrized by their aspect ratio only. The later approaches the near-field wake of a wing during the rolling phase which eventually converges towards the LOD model at later times. First, a modal stability analysis of the LOD under the assumption of a frozen base flow is performed for aspect ratios $a/b$ ranging from 0.05 to 0.36 at various Reynolds numbers. Several families of unstable antisymmetric and symmetric modes are observed. The maximal growth rates are reached at low Reynolds numbers. The results are consistent with those obtained by Brion et al. [Phys. Fluids 26, 064103 (2014)] for the higher aspect ratio inviscid Lamb-Chaplygin dipole (LCD). However, the a posteriori verification of the validity of the frozen base flow assumption shows that, except for a few modes occurring at the highest aspect ratios and large Reynolds numbers, these two-dimensional instabilities do not survive the base flow unsteadiness due to viscous diffusion. They are thus not likely to develop in the flow. Second, we focus on the transient dynamics of the dipoles by looking for the optimal perturbations through a nonmodal stability analysis based on a direct-adjoint approach. The observed energy gains are substantial and indicate the potential of transient mechanisms. In the short time dynamics, the optimal perturbation consists of intertwined vorticity layers located within each vortex core and leading to a $m=2$ deformation Kelvin wave excited by the Orr mechanism. For moderate to large horizon times, the optimal perturbation takes the form of vorticity layers localized outside the vortex core which eventually give rise to the two-dimensional unstable mode unveiled by the modal analysis through a combination of Orr mechanism and velocity induction. The robustness of these modes is examined by considering the initial stage of the development of aircraft wakes. The optimal perturbations developing on an elliptic and a double-elliptic vorticity sheet present a similar structure and rely on the same mechanisms as the ones observed for the LOD but come with lower energy gains. It is concluded that the rolling-up of the vorticity sheet in the near-field of the wake does not influence significantly the linear development of these two-dimensional perturbations.

The paper is devoted to an experimental study of steady flows excited by an oscillating motion of fluid in a cylinder, the rotation rate of which periodically changes (librations). The rotational oscillations lead to the appearance of a system of averaged toroidal vortices in a viscous Stokes boundary layer close to the cylinder side wall. The number of vortices depends on the frequency of librations, σ. If σ exceeds twice the rotation rate, the steady flow structure has the form of two vortices located close to the cavity ends, i.e., corner flow. If $\sigma <2$ at some libration frequencies, inertial modes—natural modes of rotating fluid oscillations in the closed cavity—are excited. In this case additional averaged vortices arise. The number of vortices is determined by the axial wave number of the inertial mode. With a decrease in the dimensionless frequency of fluid oscillation, the vortices increase in size, which leads to a transformation of the vortex structure. In this case, the flow near the ends is a superposition of the flows excited by inertial mode and corner flow. At the same time, the vortices which are the most distant from the periphery do not feel the corner flow. It is shown that the viscous dissipation of the oscillating motion in the fluid bulk leads to a linear decrease in the velocity of steady circulation with the dimensionless frequency.

In order to provide new insights into the energetics of turbulent boundary layer flows with separation, we compute and characterize energy transport lines, which are defined as the lines tangent to the total mechanical energy transport vector field. Separation is induced in a ${\text{Re}}_{\theta }=490$ turbulent boundary layer by imposing two types of transpiration velocity profiles at the top boundary of the computational domain: one with suction and blowing, and the other with suction only. For both separation bubbles, we find that energy transport lines can exhibit attractors, which are a manifestation of local dissipation in the flow. We identify several attracting sets along the bottom wall and attracting spiral nodes inside the separation bubbles and their corresponding basins of attraction. The size and positions of the energy basins of attraction help us understand where the available total mechanical energy is transported to due to the mean flow, and turbulent Reynolds and viscous stresses, before it is fully dissipated. The suction-and-blowing separation bubble leads to slightly smaller losses of total mechanical energy than those for a reference nonseparated boundary layer, while the suction-only case shows larger losses than the nonseparated boundary layer case.

By combining the momentum exchange method and a unified interpolation bounce-back scheme, a multiple-relaxation-time lattice Boltzmann method is developed to simulate the particle dynamics in a power-law fluid. With this method, the sedimentation of a particle pair in a shear-thinning power-law fluid for the generalized Archimedes number $\left(\mathrm{A}{\mathrm{r}}^{*}\right)$ varying from 100 to 400 is studied. Depending on the value of $\mathrm{A}{\mathrm{r}}^{*}$ and initial geometrical configuration, the particle pair is found to experience several different movement states, namely, the steady oblique doublet, periodic oscillation, period-doubling bifurcation, steady horizontal doublet, and chaos. Distinct from two groups of multiple stable states in the Newtonian system, three groups of multiple stable states are clearly identified in the present shear-thinning system: the steady oblique coexists with the periodic oscillation, the steady horizontal doublet coexists with the period-doubling bifurcation, and the steady horizontal doublet coexists with the chaos state. Moreover, the drafting, kissing, and tumbling (DKT) behavior of a particle pair observed in the Newtonian system is absent in the present shear-thinning system. It is attributed to the high-viscosity region between the particles, which can increase the viscous drag acting on the particle, thus preventing the particles from approaching each other and reducing particle aggregation. In addition, a critical value of the power-law index is obtained, below which the DKT state would not happen regardless of $\mathrm{A}{\mathrm{r}}^{*}$.

Motivated by the observation of sediments being carried by meltwater plumes originating at the base of a marine terminating glacier, laboratory experiments are performed to examine the transport and deposition of particles settling out from a buoyant line-plume rising along a sloping upper boundary. If the plume source has relatively high momentum and is located near the bottom of the domain, then a strong recirculating region develops near the source. Emanating from this region is a particle bearing buoyant plume that moves at near constant speed along the slope. Particles are observed to settle within the plume itself and then descend from the plume toward the tank bottom being drawn back in the direction of the source through a return flow driven by the plume's entrainment of the underlying ambient fluid. A light attenuation technique is employed to measure nonintrusively the depth of the sediment bed after the source is turned off and all the particles settled out. Sediments are found to accumulate near the source over the extent of the recirculating region and then decrease approximately linearly with distance from the source. Conceptual theoretical models suggest that the linearly sloping bed results from a combination of vertical mixing in the plume near the recirculation region and the return flow acting to detrain from the plume particles more effectively near the plume source where the shear between the plume and the return flow is largest. In many aspects the experiments are not representative of a steady glacial meltwater plume due to restrictions of the experimental setup, notably the relatively low Reynolds number of the flow. Nonetheless the experiments are suggestive of the complicated dynamics and sediment deposition patterns that may occur near the base of a marine terminating glacier, with a crude estimate of mean clay deposition at a rate of 6 cm per year over a distance of 2 km from the source.