We perform direct numerical simulations of three-dimensional Rayleigh-Taylor turbulence with a nonuniform singular initial temperature background. In such conditions, the mixing layer evolves under the driving of a varying effective Atwood number; the long-time growth is still self-similar, but no longer proportional to $t^2$ and depends on the singularity exponent $c$ of the initial profile $\mathrm{\Delta }T\propto z^c$. We show that universality is recovered when looking at the efficiency, defined as the ratio of the variation rates of the kinetic energy over the heat flux. A closure model is proposed that is able to reproduce analytically the time evolution of the mean temperature profiles, in excellent agreement with the numerical results. Finally, we reinterpret our findings in the light of spontaneous stochasticity where the growth of the mixing layer is mapped into the propagation of a wave of turbulent fluctuations on a rough background.

We investigate the collisions of a regular stream of drops with a continuous immiscible liquid jet. By varying the jet and drop diameters, their velocities, and relative orientation, we observe a broad variety of liquid structures, some of which have a high applicability for capsule and advanced fiber production. First, these structures are described and classified into four regimes that account for potential liquid fragmentation and the resulting liquid distribution. Fragmentation mechanisms are proposed based on a physical analysis accounting for the problem geometry, the system inertia, and the system's surface energy. Corresponding dimensionless numbers are built, which are used to draw two-dimensional regime maps that can very well distinguish the experimental outcomes. Finally, the effects of viscosity, qualitatively evidenced by employing various liquid pairs, are discussed.

The force and torque on a Janus sphere moving in a rarefied gas with a thermal gradient are calculated. The regime of large Knudsen number is considered, with the momenta of impinging gas molecules either obtained from a Chapman-Enskog distribution or from a binary Maxwellian distribution between two opposing parallel plates at different temperature. The reflection properties at the surface of the Janus particle are characterized by accommodation coefficients having constant but dissimilar values on each hemisphere. It is shown that the Janus particle preferentially orients such that the hemisphere with a larger accommodation coefficient points toward the lower temperature. The thermophoretic velocity of the particle is computed, and the influence of the thermophoretic motion on the magnitude of the torque responsible for the particle orientation is studied. The analytical calculations are supported by direct simulation Monte Carlo results, extending the scope of the study toward smaller Knudsen numbers. The results shed light on the efficiency of oriented deposition of nanoparticles from the gas phase onto a cold surface.

The spatial and orientation distributions of fibers in suspension were measured during oscillatory flow within a circular pipe. The fibers were rigid and non-colloidal, and two aspect ratios (length $L$ to diameter $d$ ratios) of $L/d=11$ and 23 were tested; the suspending fluid was viscous, Newtonian, and density matched to the particles. As with shear-induced migration of spheres in parabolic flows, fibers in the concentrated suspensions migrated toward the center of the pipe. The migration was similar for the fibers, irrespective of the aspect ratio, at the same dimensionless number density $n_0{L}^{2}d$ ($n_0$ is the number of fibers per unit volume of the bulk suspension), rather than at the same volume fraction. The extent of migration was maximum at $n_0{L}^{2}d=0.84$ for both aspect ratios. The orientation distribution of the fibers was spatially dependent. Fibers near the center of the channel aligned closely with the flow direction, while fibers near the pipe wall had an enhanced probability of aligning in the vorticity direction.

In this Rapid Communication, we study with the Stuart-Landau (SL) amplitude equation, a wake flow control scenario using experimental data from a cylinder wake forced by plasma actuators. Given the formal framework recently discussed by Gallaire et al. [Fluid Dyn. Res. 48, 061401 (2016)] on pushing amplitude equations far from threshold, we analyze experimental data of a forced wake in order to test the SL reduced order model. Linear stability theory and global mode concepts are used to determine the SL parameters. The extension to forced wakes of the SL model had been proposed by Thira and Wesfreid [J. Fluid Mech. 579, 137 (2007)] in the context of their study on stability properties, but its employment still remained an open question. Here, we show that a forced wake at a Reynolds number far from the first threshold can also attain the critical behavior described by the SL model.

While a theoretical limit has long been established for the performance of a single turbine, no corresponding upper bound exists for the power output from a large wind farm, making it difficult to evaluate the available potential for further performance gains. Recent work involving vertical-axis turbines has achieved large increases in power density relative to traditional wind farms [J. O. Dabiri, J. Renewable Sustainable Energy 3, 043104 (2011)], thereby adding motivation to the search for an upper bound. Here, we build a model describing the essential features of a large array of turbines with arbitrary design and layout, by considering a fully-developed wind farm whose upper edge is bounded by a self-similar boundary layer. The exchanges between the wind farm, the overlaying boundary layer, and the outer flow are parametrized by means of the classical entrainment hypothesis. We obtain a concise expression for the wind farm's power density (corresponding to power output per unit planform area), as a function of three coefficients, which represent the array thrust and the turbulent exchanges at each of the two interfaces. Before seeking an upper bound on farm performance, we assess the performance of our simple model by comparing the predicted power density to field data, laboratory measurements, and large-eddy simulations for the fully-developed regions of wind farms, finding good agreement. Furthermore, we extend our model to include the effect of atmospheric stability on power output, by using a parametrization (which had been previously developed in the context of geophysical fluid dynamics) relating entrainment coefficients to local Froude numbers. Our predictions for power variation with atmospheric stability are in agreement with field measurements and large-eddy simulations. Finally, we consider an ideal limit for array operation, whereby turbines are designed to maximize momentum exchange with the overlying boundary layer. This enables us to obtain an upper bound for the performance of large wind farms, which we determine to be an order of magnitude larger than the output of contemporary turbine arrays.

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)].

The effects of mechanical generation of turbulent kinetic energy and buoyancy forces on the statistics of air temperature and velocity increments are experimentally investigated at the crossover from production to inertial range scales. The ratio of an approximated mechanical to buoyant production (or destruction) of turbulent kinetic energy can be used to form a dimensionless stability parameter $\zeta$ that classifies the state of the atmosphere as common in many atmospheric surface layer studies. We assess how $\zeta$ affects the scalewise evolution of the probability of extreme air temperature excursions, their asymmetry, and time directionality. The analysis makes use of high-frequency turbulent velocity and air temperature time-series measurements collected at $z=5\mathrm{m}$ above a grass surface at very large frictional Reynolds numbers ${\text{Re}}_{*}=u_{*}z/\nu >1\times {10}^5$ ($u_{*}$ is the friction velocity and $\nu$ is the kinematic viscosity of air). A multitime measure of the imbalance between forward and backward phase-space trajectories is employed to investigate the time-directional properties of the scalar (temperature) field. Using conventional higher-order structure functions, we find that temperature exhibits larger intermittency and wider multifractality when compared to the longitudinal velocity component, consistent with laboratory studies and simulations conducted at lower ${\text{Re}}_{*}$. We find that the magnitude of $\zeta$, rather than the sign of the heat flux, impacts the distribution of scalar increments at separation scales well within the inertial subrange. Conversely, the direction of the heat flux fingerprints the observed time-directionality properties of the scalar field in the first two decades of inertial subrange scales. These combined findings demonstrate that external boundary conditions, and in particular the magnitude and sign of the sensible heat flux, have a significant impact on temperature advection-diffusion dynamics within the inertial range.

We show that the fluidity, made dimensionless by the square root of the granular temperature, measured in numerical simulations of granular shearing flows of frictionless spheres, may be predicted over a wide range of volume fractions using existing kinetic theories. We also show that the departure of these predictions from the measurements in the limit of random close packing is due to the reduction of the dissipation because of velocity correlations and the contribution of the anisotropy of the second moment of the velocity fluctuations to the shear stress. The former causes the granular temperature to increase without bound, the latter ensures that the pressure and shear stress behave in the same way with temperature. This combination of mechanisms may also be relevant to the shearing of emulsions, dense colloids, and non-Brownian suspensions.

Whereas statistical moments of differences of turbulent quantities measured over a given separation (viz., structure functions) have been extensively studied, statistics of incremental sums (or equivalently averages, e.g., $\mathrm{\Sigma }\theta \equiv \left[\theta \right(x+r)+\theta (x\left)\right]/2$) of the same quantities have only been the subject of recent research. The present work investigates incremental averages of a turbulent passive scalar (temperature), measured in nearly homogeneous, and isotropic (passive and active), grid-generated turbulence, for turbulent Reynolds numbers in the range $94\le R_{\lambda }(\equiv u_{\mathrm{rms}}\lambda /\nu )\le 582$. The scalar field is generated by the action of the turbulent velocity field against an imposed mean temperature gradient. Following the approach of Mouri and Hori [Phys. Fluids 22, 115110 (2010)] for the velocity field, we examine statistics of incremental averages of the passive scalar field as a function of separation (viz., incremental average structure functions) for different Reynolds numbers, comparing them with both the results of Mouri and Hori, as well as the corresponding incremental average structure functions for the velocity field for the flows studied herein. While the statistics of $\mathrm{\Sigma }\theta$ are primarily large-scale quantities, and would therefore be expected to be flow dependent, they exhibit certain similarities to the statistics of incremental averages of velocity ($\mathrm{\Sigma }{u}_{\alpha }$), measured both in the flow under consideration as well as the different classes of flows studied by Mouri and Hori. Finally, we derive a scale-dependent evolution equation for the incremental average of the scalar field fluctuations, $\mathrm{\Sigma }\theta$. We discuss its relationship to Yaglom's four-thirds law for differences in passive scalar fluctuations and compare the results with the experimental data.

Impacts of liquid droplets on other stationary droplets on a surface are ubiquitous in numerous applications such as agricultural sprays, inkjet printing, and rain impact on surfaces. We experimentally study the maximum expansion diameter and retraction rate in drop-on-drop impacts on superhydrophobic surfaces. We identify an inertial-capillary and a viscous regime for the expansion phase and we interpret the results using two distinct models. In the inertial-capillary regime, the first model predicts that the maximum diameter is set by an effective capillary length due to the deceleration upon impact. We introduce an effective diameter, velocity, and Weber number that allow the accurate determination of the maximum diameter in drop-on-drop impacts. We use our model to predict the transition to the viscous regime and rationalize the maximum diameter in this case with an energy balance. In our second model, we use an energy balance in both regimes and accurately predict the maximum diameter with a unified expression. We finally show that the retraction phase is a no-memory phenomenon and only depends on the volume of the coalesced droplet. We identify capillary and viscous regimes for the retraction and accurately model the retraction rate in each regime. Our approach provides a framework to characterize the dynamics of multiple-drop impacts.

We present a novel reaction analogy (RA) based forcing method for generating statistically stationary scalar fields in incompressible turbulence. The new method can produce more general scalar probability density functions (PDFs), for example, quasi-double-$\delta$ PDF, than current methods, while ensuring that scalar fields remain bounded, unlike existent forcing methodologies that can potentially violate naturally existing bounds. Such features are useful for generating initial fields in nonpremixed combustion, inlet conditions for spatially developing flows, or for studying non-Gaussian scalar turbulence. The RA method mathematically models hypothetical chemical reactions that convert reactants in a mixed state back into its pure unmixed components. Various types of chemical reactions are formulated and the corresponding mathematical expressions derived such that the reaction term is smooth in scalar space and is consistent with mass conservation. For large values of the scalar forcing rate, the method produces statistically stationary quasi-double-$\delta$ scalar PDFs. Quasiuniform, Gaussian, and stretched exponential scalar statistics are recovered for smaller values of the scalar forcing rate. The shape of the scalar PDF can be further controlled by changing the stoichiometric coefficients of the reaction. The ability of the new method to produce fully developed passive scalar fields with quasi-Gaussian PDFs is also investigated, by exploring the convergence of the scalar variance spectrum to the Obukhov-Corrsin scaling and of the third-order mixed structure function to the “four-thirds” Yaglom's law.

Dielectric heating occurs in situations where an alternating electric field is applied on an insulating dielectric material. This effect can produce thermal convection in dielectric fluid through the thermoelectric coupling by the dielectrophoretic (DEP) force. The onset and the flow properties of the convection are investigated in a spherical gap geometry. The thermoelectrohydrodynamical equations often adopted in the modeling of the DEP-force-driven thermal convection are extended by an additional source term arising from the dielectric heating in the energy equation. Three-dimensional direct numerical simulations are performed, under microgravity conditions and without any imposed temperature gradient to highlight the effects of dielectric heating. In the conduction state, dielectric heating creates a parabolic temperature profile with a maximum in the interior of the spherical gap. In the convection state, the temperature distribution is more homogeneous with a lower maximum temperature. Numerical results are compared with interferograms from the GeoFlow II experiment performed on the International Space Station to validate the model. For the comparison, a numerical interferogram is applied to temperature fields obtained in the simulation. The onset of convection and basic spatial properties of the resulting internally heated convective zone are in good agreement with the experiment. The computed velocity fields reveal strong downdrafts which lead to recognizable fringe patterns in the interferograms.

In microfluidic devices, inertia drives particles to focus on a finite number of inertial focusing streamlines. Particles on the same streamline interact to form one-dimensional microfluidic crystals (or “particle trains”). Here we develop an asymptotic theory to describe the pairwise interactions underlying the formation of a one-dimensional crystal. Surprisingly, we show that particles assemble into stable equilibria, analogous to the motion of a damped spring. The damping of the spring is due to inertial focusing forces, and the spring force arises from the interplay of viscous particle-particle and particle-wall interactions. The equilibrium spacing can be represented by a quadratic function in the particle size and therefore can be controlled by tuning the particle radius.

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.

The flow of wormlike micellar solutions around a 90° sharp microfluidic bend was studied using rheometry, flow visualization, and velocimetry. By carefully choosing the composition of the test solutions, all four combinations of linear or branched micelles and shear-banding or non-shear-banding solutions were accessed using four wormlike micellar solutions. The flow behavior of the solutions was examined in similar conditions of about 1 < Wi < 300 and ${10}^{-6}<Re<{10}^{-2}$. When comparing the flow around the microbend of the two shear-banding solutions with the two non-shear-banding ones, the secondary flows showed distinct differences at about 10< Wi <100. Flow visualization showed that a steady lip vortex formed at the inner upstream corner of the microbend in the non-shear-banding solutions, while a lip (inner upstream corner) vortex and an outer corner vortex formed in the shear-banding solutions. On the other hand, when comparing the solutions with similar rheological characteristics but different micelle morphology (linear versus branched), no significant differences in the flow behavior were observed. These results suggest that shear-banding plays a central role in determining the secondary flow behavior around the microbend, while the effect of micelle morphology is minimal for wormlike micelle solutions. Additional particle tracking velocimetry measurements were carried out both upstream of and around the microbend. The resulting velocity profiles in the shear-banding solutions show marked disagreement with calculations based on the shear-rate-dependent apparent viscosity using the Carreau model. These results suggest that the shear-banding effect on the flow around the microbend could be correlated to the development of a “jetting” flow regime upstream of the bend, which could be a result of the nonmonotonic stress – shear rate relationship in shear-banding wormlike micellar solutions.

In the development of drug delivery technologies for treating complex diseases, encapsulating multiple compounds and manipulating their sustained-release kinetics independently (for optimal therapeutic effect) can be challenging. Toward this goal, we previously developed a fluid-dynamic technology based on multidrop interactions to produce solid toroidal-spiral (TS) particles. During sedimentation in a miscible, viscous liquid, polymeric drops self-assemble into a reproducible and controllable TS structure, which can be solidified into particles by photoinitiated cross-linking of the polymer. The goal of encapsulating multiple drops of different physical properties (such as size and density) generally requires complicated and time-consuming laboratory iteration on the starting conditions, because all satellite drops (containing drugs) must catch up and coalesce simultaneously with the main drop that forms the surrounding matrix upon solidification. In this paper we consider a model system for multidrop entrainment that features a main drop followed by three smaller satellite drops arranged in a horizontal, triangular array. Experiments visualized with a high-speed camera are used to validate computer simulations based upon a swarm-of-Stokeslets method. The simulations accurately track complex drop configurations involving intertwined interfaces. Replacing the actual starting drop shapes with suitably positioned, volume-equivalent spheres yields very similar configurations: the crucial deformations and interactions occur during sedimentation, as opposed to during the initial injection of the drops. The simulations are then used to formulate two robust “rules of thumb” by which further trial-and-error (whether in the laboratory or by computation) can be avoided toward encapsulating multiple satellite drops with different properties. The first rule applies to satellite drops of different properties but symmetric starting positions, and establishes the single-drop Hadamard-Rybczynski (HR) sedimentation velocity as the crucial parameter. The second rule makes use of a universal “entrainment map” by which three satellite drops of the same radius but different densities and asymmetric starting positions can all be encapsulated at an arbitrarily prescribed distance of sedimentation. Two final simulations demonstrate how both rules can be combined to successfully design an (asymmetric) injection geometry to encapsulate three satellite drops of different radii and densities, at an arbitrarily prescribed distance of sedimentation. Understanding fundamental hydrodynamics of interaction between multiple drops could lead to potential scale-up of production of TS particles and also impact applications of mixing and printing in general.

The dominant polarity of the magnetic field in rapidly rotating spherical dynamos is the axial dipole. Studies of the onset of magnetoconvection in the limit of vanishing Ekman number have proposed that the dipole is favored over other polarities because its equatorial symmetry generates kinetic helicity that would be otherwise absent in nonmagnetic convection. This study explores the effect of the magnetic field in the selection of the axial dipole in rapidly rotating, supercritical dynamos. The strength of convection is such that the axial dipole grows from a starting seed field in the nonlinear dynamo but fails to grow in the kinematic dynamo at the same parameters. The magnetic field is shown to excite convection over a range of length scales larger than the energy injection scale and at the same time extract energy from smaller scales through the Lorentz force in order to feed itself. This leads to substantial helicity generation in a range of length scales and helicity loss in smaller scales, both relative to nonmagnetic convection. The crossover point between the helicity surplus and deficit regions is displaced to smaller length scales as the rotation rate is increased (by decreasing the Ekman number). The helicity deficit occurs in the region of the spectrum where the Lorentz force approximately balances the Coriolis force in the vorticity equation, so that energy may be drawn from these scales via vortex stretching. The timescale for the increase in convection intensity relative to the nonmagnetic state approximately coincides with the timescale for the formation of the axial dipole, which indicates that the Lorentz force has an important role in polarity selection. Crucially, the dipole forms from a chaotic state well before the saturation of the dynamo, implying that planetary dynamos choose their polarity during their nonlinear growth phase. The generation of the toroidal part of the dipole field is primarily through the classical $\mathrm{\Omega }$ effect, although the pattern of the zonal flow switches from spherical harmonic degree $l=1$ to $l=3$ in the presence of the magnetic backreaction.

An external force is required to maintain the relative movement of horizontal plates. It is shown that this force is reduced when the plates are subject to a spatially distributed heating. The largest reduction occurs for heating wavelengths of the order of distance between the plates with its magnitude increasing proportionally to the second power of the relevant Rayleigh number. It is shown that a sufficiently strong heating eliminates the need for the driving force altogether. The drag-reducing effect is active only in small Reynolds number flows and is stronger in fluids with smaller Prandtl numbers.

Expansion waves propagating into particle beds are found in many manmade and natural applications. Rapid decompression of a highly pressurized powder bed or a volcanic eruption are two such examples. In this investigation, we perform fully resolved simulations of expansion waves propagating into particle beds of three different volume fractions using the discontinuous Galerkin spectral element method code, cmt-nek. We validate state-of-the-art drag models for a particle in an unsteady compressible flow and show good agreement, particularly at lower volume fractions. We model the particle bed as a nozzle or area reduction and, using isentropic flow relations, predict the final pressure, temperature, and Mach number extremely well in each case.