We present a direct numerical simulation (DNS) data set for a statistically axisymmetric turbulent jet, plume, and forced plume in a domain of size $40r_0\times 40r_0\times 60r_0$, where $r_0$ is the source diameter. The data set supports the validity of the Priestley-Ball entrainment model in unstratified environments (excluding the region near the source) [Priestley and Ball, Q. J. R. Meteor. Soc. 81, 144 (1955)], which is corroborated further by the Wang-Law and Ezzamel et al. experimental data sets [Wang and Law, J. Fluid Mech. 459, 397 (2002); Ezzamel et al., J. Fluid Mech. 765, 576 (2015)], the latter being corrected for a small but influential coflow that affected the statistics. We show that the second-order turbulence statistics in the core region of the jet and the plume are practically indistinguishable from each other, although there are significant differences near the plume edge. The DNS data indicate that the turbulent Prandtl number is about 0.7 for both jets and plumes. For plumes, this value is a result of the difference in the ratio of the radial turbulent transport of radial momentum and buoyancy. For jets, however, the value originates from a different spread of the buoyancy and velocity profiles, in spite of the fact that the ratio of radial turbulent transport terms is approximately unity. The DNS data do not show any evidence of similarity drift associated with gradual variations in the ratio of buoyancy profile to velocity profile widths.

Superhydrophobic surfaces offer many industrial advantages such as drag reduction and self-cleaning behavior as long as the liquid remains suspended above the composite solid/gas interface (Cassie state). These advantages are hindered when liquid penetrates the gas cavities (Wenzel state), and this is commonly referred to as impalement. Current efforts to drive impaled liquid out of, or dewet, the cavities—such as boiling or mechanical vibrations—are locally disruptive to the flow. In this work, we reveal that passive dewetting is possible during droplet impingement on micropillar substrates under the right thermodynamical conditions. Exploration included substrates with pillar-to-pillar spacing of 8 and $16\mu \mathrm{m}$, pillar diameters of 3 and $6\mu \mathrm{m}$, and pillar heights of 4 to $8\mu \mathrm{m}$ and 8 to $18\mu \mathrm{m}$, respectively. The substrate temperature range considered was $23<T_s<96{}^{\circ }\mathrm{C}$. Results revealed that dewetting increases with increasing pillar height and increasing substrate temperature. Two hypotheses for the driving mechanism are formulated based on evaporation and surface energy. First-order models are consequently constructed, revealing that dewetting does not occur due to evaporation, but is caused by surface energy gradients at the interface. Dissipation in the flow is taken into account due to hydrodynamic and nonhydrodynamic mechanisms; the latter is found to dominate resistance.

Immiscible fluid displacement with average front velocities in the capillary-dominated regime is studied in a transparent Hele-Shaw cell with cylindrical posts. Employing various combinations of fluids and wall materials allows us to cover a range of advancing contact angles ${46}^{\circ }\le {\theta }_a\le {180}^{\circ }$ of the invading fluid in our experiments. In parallel, we study the displacement process in particle-based simulations that account for wall wettability. Considering the same arrangement of posts in experiments and simulation, we find a consistent crossover between stable interfacial displacement at ${\theta }_a\lesssim {80}^{\circ }$ and capillary fingering at high contact angles ${\theta }_a\gtrsim {120}^{\circ }$. The position of the crossover is quantified through the evolution of the interface length and the final saturation of the displaced fluid. A statistical analysis of the local displacement processes demonstrates that the shape evolution of the fluid front is governed by local instabilities as proposed by Cieplak and Robbins for a quasistatic interfacial displacement [Cieplak and Robbins, Phys. Rev. Lett. 60, 2042 (1988)]. The regime of stable front advances coincides with a corresponding region of contact angles where cooperative interfacial instabilities prevail. Capillary fingering, however, is observed only for large ${\theta }_a$, where noncooperative instabilities dominate the invasion process.

We investigate electroconvection and its impact on ion transport in a model system comprised of an ion-selective membrane, an aqueous electrolyte, and an external electric field applied normal to the membrane. We develop a direct numerical simulation code to solve the governing Poisson-Nernst-Planck and Navier-Stokes equations in three dimensions using a specialized parallel numerical algorithm and sufficient resolution to capture the high frequency and high wavenumber physics. We show a comprehensive statistical analysis of the transport phenomena in the highly chaotic regime. Qualitative and quantitative comparisons of two-dimensional (2D) and 3D simulations include prediction of the mean concentration fields as well as the spectra of concentration, charge density, and velocity signals. Our analyses reveal a significant quantitative difference between 2D and 3D electroconvection. Furthermore, we show that high-intensity yet short-lived current density hot spots appear randomly on the membrane surface, contributing significantly to the mean current density. By examining cross correlations between current density on the membrane and other field quantities we explore the physical mechanisms leading to current hot spots. We also present analysis of transport fluxes in the context of ensemble-averaged equations. Our analysis reveals that in the highly chaotic regime the mixing layer (ML), which spans the majority of the domain extent, is governed by advective fluctuations. Furthermore, we show that in the ML the mean electromigration fluxes cancel out for positive and negative ions, indicating that the mean transport of total salt content within the ML can be represented via the electroneutral approximation. Finally, we present an assessment of the importance of different length scales in enhancing transport by computing the cross covariance of concentration and velocity fluctuations in the wavenumber space. Our analysis indicates that in the majority of the domain the large scales contribute most significantly to transport, while the effects of small scales become more appreciable in regions very near the membrane.

Relative flow between granular material and gas can create phenomena in which particles behave like a liquid with bubbles rising through them. In this paper, magnetic resonance imaging is used to measure the velocities of the gas and solid phases in a bubbling fluidized bed. Comparison with theory shows that the average velocity of gas through the interstices between particles is predicted correctly by classic analytical theory. Experiments were also used to validate predictions from computer simulations of gas and solid motion. The experiments show a wide distribution of gas velocities in both bubbling and emulsion regions, providing a different direction for computational and analytical theory.

Particle image velocimetry is conducted in the near field of two distinct wall-mounted trips for the artificial generation of a high Reynolds number turbulent boundary layer. The first of these trips consists of high aspect ratio obstacles, which are supposed to minimize the influence of their wakes on the near-wall region, contrasting with low aspect ratio trips, which would enhance this influence. A comprehensive study involving flow description, turbulent-nonturbulent interface detection, a low-order model description of the flow and an exploration of the influence of the wake in the near-wall region is conducted and two different mechanisms are clearly identified and described. First, high aspect ratio trips generate a wall-driven mechanism whose characteristics are a thinner, sharper, and less tortuous turbulent-nonturbulent interface and a reduced influence of the trips' wake in the near-wall region. Second, low aspect ratio trips generate a wake-driven mechanisms in which their turbulent-nonturbulent interface is thicker, less sharply defined, and with a higher tortuosity and the detached wake of the obstacles presents a significant influence on the near-wall region. Study of the low-order modeling of the flow field suggests that these two mechanisms may not be exclusive to the particular geometries tested in the present study but, on the contrary, can be explained based on the predominant flow features. In particular, the distinction of these two mechanisms can explain some of the trends that have appeared in the literature in the past decades.

It is now well established that nearby beating pairs of eukaryotic flagella or cilia typically synchronize in phase. A substantial body of evidence supports the hypothesis that hydrodynamic coupling between the active filaments, combined with waveform compliance, provides a robust mechanism for synchrony. This elastohydrodynamic mechanism has been incorporated into bead-spring models in which the beating flagella are represented by microspheres tethered by radial springs as they are driven about orbits by internal forces. While these low-dimensional models reproduce the phenomenon of synchrony, their parameters are not readily relatable to those of the filaments they represent. More realistic models, which reflect the underlying elasticity of the axonemes and the active force generation, take the form of fourth-order nonlinear partial differential equations (PDEs). While computational studies have shown the occurrence of synchrony, the effects of hydrodynamic coupling between nearby filaments governed by such continuum models have been examined theoretically only in the regime of interflagellar distances $d$ large compared to flagellar length $L$. Yet in many biological situations $d/L\ll 1$. Here we present an asymptotic analysis of the hydrodynamic coupling between two extended filaments in the regime $d/L\ll 1$ and find that the form of the coupling is independent of the microscopic details of the internal forces that govern the motion of the individual filaments. The analysis is analogous to that yielding the localized induction approximation for vortex filament motion, extended to the case of mutual induction. In order to understand how the elastohydrodynamic coupling mechanism leads to synchrony of extended objects, we introduce a heuristic model of flagellar beating. The model takes the form of a single fourth-order nonlinear PDE whose form is derived from symmetry considerations, the physics of elasticity, and the overdamped nature of the dynamics. Analytical and numerical studies of this model illustrate how synchrony between a pair of filaments is achieved through the asymptotic coupling.

We study fully three-dimensional droplets that slide down an incline by employing a thin-film equation that accounts for capillarity, wettability, and a lateral driving force in small-gradient (or long-wave) approximation. In particular, we focus on qualitative changes in the morphology and behavior of stationary sliding drops. We employ the inclination angle of the substrate as control parameter and use continuation techniques to analyze for several fixed droplet sizes the bifurcation diagram of stationary droplets, their linear stability, and relevant eigenmodes. The obtained predictions on existence ranges and instabilities are tested via direct numerical simulations that are also used to investigate a branch of time-periodic behavior (corresponding to repeated breakup-coalescence cycles, where the breakup is also denoted as pearling) which emerges at a global instability, the related hysteresis in behavior, and a period-doubling cascade. The nontrivial oscillatory behavior close to a Hopf bifurcation of drops with a finite-length tail is also studied. Finally, it is shown that the main features of the bifurcation diagram follow scaling laws over several decades of the droplet size.

Miscible viscous fingering is studied experimentally in the presence of a nonmonotonic viscosity profile due to nonideal mixing properties in a porous medium consisting in a micropillar array column used for chromatographic applications. In this setup, a mobile phase composed of an aqueous solution of methanol displaces a miscible finite-size sample containing mainly water. Due to a local buildup by nonideal mixing of maxima in the viscosity profile, fingering is observed at both the frontal and rear miscible interfaces of the sample phase, however with different spatial extents. The influence on the fingering dynamics of the pressure in the column and of the viscosity of the mobile or sample phases is analyzed.

Buoyant spheres released below the free surface can rise well above the surface in a phenomenon known as pop-up. Contrary to intuition, increasing the release depth sometimes results in a lower pop-up height. We present the pop-up height of rising buoyant spheres over a range of release depths (1–12.5 diameters) and Reynolds numbers $(4\times {10}^4$ to $6\times {10}^5)$. While the dynamics of rising buoyant spheres and bubbles has been thoroughly investigated for Reynolds numbers below ${10}^4$, pop-up in these larger-Reynolds-number regimes has not been studied. Yet the underwater motions of the sphere for the Reynolds numbers we study are the key to understanding the pop-up height. Two major regimes are apparent: vertical and oscillatory. The vertical regime exhibits a nearly vertical underwater trajectory and results in the largest pop-up heights. The oscillatory regime exhibits an underwater trajectory with periodic lateral motions and results in lower pop-up heights; this periodic lateral motion is modulated by unsteady vortex shedding in the wake of the sphere. Despite these complex fluid structure interactions, the experiments presented herein yield extremely repeatable results.

Confinement-guided coalescence of drops in microfluidic devices is an effective means to manipulate the composition of individual droplets. Recently, Sun et al. [Lab Chip 11, 3949 (2011)] have shown that coalescence between a long moving plug and an array of parked droplets in a microfluidic network can be used to flexibly manipulate the composition of the static droplet arrays. However, the transport mechanisms underlying this complex dilution process have not been elucidated. In this study, we develop phenomenological models and perform particle-based numerical simulations to identify the key mass transfer mechanisms influencing the concentration profiles of drops during coalescence-induced drop dilution. Motivated by experimental observations, in the simulations we consider (i) advection within the moving plug, (ii) diffusion in the moving plug and parked droplets, (iii) fluid advection due to initiation of coalescence, and (iv) advection in the coalesced plug due to the continuous phase flowing through the gutters in noncircular microchannels. We find that the dilution process is dominated by diffusion, recirculation in the moving plug, and gutter-flow-induced advection, but is only weakly affected by coalescence-induced advection. We show that the control parameters regulating dilution can be divided into those influencing the duration of mass transfer (e.g., plug length and velocity) and those affecting the rate of mass transfer (e.g., diffusion and gutter-flow-induced advection). Finally, we demonstrate that our simulations are able to predict droplet concentration profiles in experiments. The results from this study will allow better design of drop dilution microfluidic devices. Furthermore, the identification of gutter-flow-induced advection as an alternative mass transfer mechanism in two-phase flows could potentially lead to more efficient means of oil recovery from droplets trapped in porous media.

We propose a recipe to calculate accurately the Nusselt number $\text{Nu}$ in turbulent Rayleigh-Bénard convection, using the measured total heat flux $q$ and known parameters of the fluid and convection cell. More precisely, we present a method to compute the conductive heat flux $\widehat{q}$, which is a normalization of $q$ in the definition of $\text{Nu}$, for conditions where the fluid parameters may vary strongly across the fluid layer. We show that in the Oberbeck-Boussinesq approximation and also when the thermal conductivity depends exclusively on the temperature, the value of $\widehat{q}$ is determined by simple explicit formulas. For a general non-Oberbeck-Boussinesq (NOB) case we propose an iterative procedure to compute $\widehat{q}$. Using our procedure, we critically analyze some already conducted and some hypothetical experiments and show how $\widehat{q}$ is influenced by the NOB effects.

We present an experimental study of the gravitational instability triggered by dissolution of carbon dioxide through a water-gas interface. We restrict the study to vertical parallelepipedic Hele-Shaw geometries, for which the thickness is smaller than the other dimensions. The partial pressure of carbon dioxide is quickly increased, leading to a denser layer of ${\mathrm{CO}}_2$-enriched water underneath the surface. This initially one-dimensional diffusive layer destabilizes through a convection-diffusion process. The concentration field of carbon dioxide, which is visualized by means of a pH-sensitive dye, shows a fingering pattern whose characteristics (wavelength and amplitude growth rate) are functions of the Rayleigh ($\text{Ra}$) and the Darcy ($\text{Da}$) numbers. At low Rayleigh numbers, the growth rate and the wave numbers are independent of the Rayleigh number and in excellent agreement with the classical results obtained numerically and theoretically in the Darcy regime. However, above a threshold of $\text{Ra}\sqrt{\text{Da}}$ of the order of 10, the growth rate and the wave number strongly decrease due to the Brinkman term associated with the viscous diffusion in the vertical and longitudinal directions. In this Darcy-Brinkman regime, the growth rate and the wave number depend only on the thickness-based Rayleigh number $\text{Ra}\sqrt{\text{Da}}$. The classical Rayleigh-Taylor theory including the Brinkman term has been extended to this diffusive gravitational instability and gives an excellent prediction of the growth rate over four decades of Rayleigh numbers. However, the Brinkman regime seems to be valid only until $\text{Ra}\sqrt{\text{Da}}=1000$. Above this threshold, the transverse velocity profile is no longer parabolic, which leads to an overestimation of the wave number by the theory.

We investigate the anisotropy in turbulent convection in a three-dimensional (3D) box using direct numerical simulation. We compute the anisotropic parameter $A=u_{\perp }^2/\left(2u_{\parallel }^2\right)$, where $u_{\perp }$ and $u_{\parallel }$ are the components of velocity perpendicular and parallel to the buoyancy direction, the shell and ring spectra, and shell-to-shell energy transfers. We observe that the flow is nearly isotropic for the Prandtl number $\mathrm{Pr}\approx 1$, but the anisotropy increases with the Prandtl number. For $\mathrm{Pr}=\infty ,A\approx 0.3$, anisotropy is not very significant even in extreme cases. We also observe that $u_{\parallel }$ feeds energy to $u_{\perp }$ via pressure. The computation of shell-to-shell energy transfers reveals that the energy transfer in turbulent convection is local and forward, similar to hydrodynamic turbulence. These results are consistent with the Kolmogorov's spectrum observed by Kumar et al. [Phys. Rev. E 90, 023016 (2014)] for turbulent convection.

We study the decay of high-Reynolds-number Taylor-Couette turbulence, i.e., the turbulent flow between two coaxial rotating cylinders. To do so, the rotation of the inner cylinder (${Re}_i=2\times {10}^6$, the outer cylinder is at rest) is stopped within 12 s, thus fully removing the energy input to the system. Using a combination of laser Doppler anemometry and particle image velocimetry measurements, six decay decades of the kinetic energy could be captured. First, in the absence of cylinder rotation, the flow-velocity during the decay does not develop any height dependence in contrast to the well-known Taylor vortex state. Second, the radial profile of the azimuthal velocity is found to be self-similar. Nonetheless, the decay of this wall-bounded inhomogeneous turbulent flow does not follow a strict power law as for decaying turbulent homogeneous isotropic flows, but it is faster, due to the strong viscous drag applied by the bounding walls. We theoretically describe the decay in a quantitative way by taking the effects of additional friction at the walls into account.

We present an experimental study of nonhomogeneous turbulence using a Rayleigh-Bénard convection cell. The fluid motion is forced by a temperature difference between two horizontal plates. Using Lagrangian tracking on a large volume we can capture part of the large-scale circulation. The velocity statistics are strongly affected by the inhomogeneous mean flow, but we recover the typical homogeneous isotropic turbulence statistics by removing the local average. We discuss and explain a Lagrangian unsteadiness which persists because of the large-scale circulation oscillations. Our Lagrangian approach is a way to study specificities of the convective roll motions in turbulent thermal convection. We propose a model based on the convolution between the large-scale circulation oscillations and the turbulent fluctuations to explain the shape of the velocity PDFs. However, the acceleration statistics are not affected by the mean flow.

Stability and pattern formation of a two-layer liquid system with large aspect ratio subjected to vertical harmonic oscillations is studied by means of an integrated boundary layer model. The lower layer rests on an oscillating solid substrate, the upper layer is separated by a deformable interface from the lower layer and bounded at the top with a second, free interface to the ambient passive air. The model is derived from the Navier-Stokes equations in long-wave approximation, including inertial terms. Applying a Floquet analysis, linear stability charts and dispersion relations are computed and compared with results from the full linearized Navier-Stokes equations and the long-wave approximation. Nonlinear Faraday patterns simultaneously occurring at the interface and at the film surface are studied by numerically solving the integrated boundary layer model in two and three spatial dimensions. For gravitationally stable two-layer films with a lighter fluid on top of the heavier fluid, we find squares, hexagons, quasiperiodic patterns with eightfold symmetry as well as localized states in the form of large scale depletion regions or finite depth holes, occurring at the interface and surface. For a Rayleigh-Taylor unstable combination (heavier fluid above the light one) we show that external vibration increases the lifetime of the film by delaying or completely suppressing the film rupture.

Multilayer film flow down an inclined plane in the presence of an insoluble surfactant is investigated with particular emphasis on determining flow stability and investigating the possibility of traveling-wave solutions. The investigation is conducted for two or three layers under conditions of Stokes flow and, separately, on the basis of a long-wave assumption. A normal mode linear stability analysis for Stokes flow shows that adding surfactant to one of the film surfaces can destabilize an otherwise stable flow configuration. For the long-wave system, periodic traveling-wave branches are detected and traced, revealing solutions with pulselike solitary waves on each film surface traveling in phase with each other, traveling waves with capillary ridge structures, and solutions with two of the film surfaces almost in contact. Time-periodic traveling-wave solutions are also found. The stability of the traveling waves is determined by solving initial-value problems and by computing eigenvalue spectra. Boundary element simulations for Stokes flow confirm the existence of traveling waves outside the long-wave regime.

In this study, large-eddy simulation combined with a turbine model is used to investigate the effect of vertical wind veer associated with the Coriolis force on the structure and evolution of wind turbine wakes. In order to isolate the Coriolis effect on the wake, two cases are considered. In the first case, atmospheric boundary-layer flow is driven by a geostrophic wind, including the effect of Earth's rotation and the Coriolis force. In the second case, the boundary-layer flow is unidirectional and is forced by an imposed pressure gradient. Both cases have the same mean horizontal velocity and turbulence intensity at the hub height. The simulation results show that the Coriolis force significantly affects the aerodynamics of the wake including the mean velocity deficit, turbulence statistics, and wake-meandering characteristics downwind of the turbine. In particular, when the flow is forced by a geostrophic wind, vertical wind veer causes a skewed spatial structure in the wake. Moreover, the presence of lateral wind shear, in addition to the vertical one, enhances the shear production of turbulent kinetic energy and the turbulent momentum flux. This leads to a larger flow entrainment and, thus, a faster wake recovery compared to the case forced by unidirectional pressure gradient. Consistent with this result, wake meandering is also stronger in both lateral and vertical directions in the case of geostrophic forcing compared to the case with pressure-gradient forcing.

The scale dependence of the statistical alignment tendencies of the eigenvectors of the strain-rate tensor ${\mathit{e}}_i$, with the vorticity vector $\mathbf{\omega }$, is examined in the self-preserving region of a planar turbulent mixing layer. Data from a direct numerical simulation are filtered at various length scales and the probability density functions of the magnitude of the alignment cosines between the two unit vectors $|{\mathit{e}}_i·\widehat{\mathbf{\omega }}|$ are examined. It is observed that the alignment tendencies are insensitive to the concurrent large-scale velocity fluctuations, but are quantitatively affected by the nature of the concurrent large-scale velocity-gradient fluctuations. It is confirmed that the small-scale (local) vorticity vector is preferentially aligned in parallel with the large-scale (background) extensive strain-rate eigenvector ${\mathit{e}}_1$, in contrast to the global tendency for $\mathbf{\omega }$ to be aligned in parallel with the intermediate strain-rate eigenvector [Hamlington et al., Phys. Fluids 20, 111703 (2008)]. When only data from regions of the flow that exhibit strong swirling are included, the so-called high-enstrophy worms, the alignment tendencies are exaggerated with respect to the global picture. These findings support the notion that the production of enstrophy, responsible for a net cascade of turbulent kinetic energy from large scales to small scales, is driven by vorticity stretching due to the preferential parallel alignment between $\mathbf{\omega }$ and nonlocal ${\mathit{e}}_1$ and that the strongly swirling worms are kinematically significant to this process.