The rapid accumulation of small, finite-size rigid particles along closed rotating threads in high-Prandtl-number thermocapillary liquid bridges is investigated numerically when the flow arises as a traveling hydrothermal wave. For a dilute suspension, different motion models are investigated which could provide the dissipation mechanisms leading to the experimentally observed particle-motion attractors. Making use of a phenomenological particle-boundary interaction model, it is shown that the particle size effect, which becomes important when the particle moves near the thermocapillary free surface, provides the relevant source of dissipation for the remarkably fast particle accumulation. Furthermore, the accumulation phenomenon is tightly correlated with the Kolmogorov-Arnold-Moser (KAM) tori of the flow in the absence of particles. Therefore, KAM tori in the rotating frame of reference, in which the flow field is steady, can be considered templates for the accumulation structures. The numerical results obtained are compared with experimental data for the so-called spiral loop 1 and spiral loop 2 particle accumulation structures. In addition, other accumulation structures are numerically predicted which yet await experimental confirmation.

Intermittency is a hallmark of turbulence, which exists not only in turbulent flows of classical viscous fluids but also in flows of quantum fluids such as superfluid ${}^4\mathrm{He}$. Despite the established similarity between turbulence in classical fluids and quasiclassical turbulence in superfluid ${}^4\mathrm{He}$, it has been predicted that intermittency in superfluid ${}^4\mathrm{He}$ is temperature dependent and enhanced for certain temperatures, which is in striking contrasts to the nearly flow-independent intermittency in classical turbulence. Experimental verification of this theoretical prediction is challenging since it requires well-controlled generation of quantum turbulence in ${}^4\mathrm{He}$ and flow measurement tools with high spatial and temporal resolution. Here we report an experimental study of quantum turbulence generated by towing a grid through a stationary sample of superfluid ${}^4\mathrm{He}$. The decaying turbulent quantum flow is probed by combining a recently developed ${{\text{He}}_2}^{*}$ molecular tracer-line tagging velocimetry technique and a traditional second-sound attenuation method. We observe quasiclassical decays of turbulent kinetic energy in the normal fluid and of vortex line density in the superfluid component. For several time instants during the decay, we calculate the transverse velocity structure functions. Their scaling exponents, deduced using the extended self-similarity hypothesis, display nonmonotonic temperature-dependent intermittency enhancement, in excellent agreement with a recent theoretical and numerical study [L. Biferale et al., Phys. Rev. Fluids 3, 024605 (2018)].

Gravity force, surface tension, oscillating boundary layers, viscous dissipation, static meniscus, contact angle hysteresis, and moving contact lines are typical features of sloshing dynamics. All these ingredients influence capillary-gravity waves in a container and have been investigated theoretically, usually building on the standard potential flow solution [Lamb, Hydrodynamics (Cambridge University Press, Cambridge, 1932)], without dealing with their combined effects. We propose here a theoretical framework to study viscous sloshing waves in a circular cylinder incorporating a realistic contact angle model observed experimentally [Dussan, Annu. Rev. Fluid Mech. 11, 371 (1979)] as a boundary condition at the contact line. The resulting nonlinear system of equations, which accounts for contact angle hysteresis, is then solved asymptotically in order to determine the effect of the nonlinear relation between the contact line velocity and the dynamic contact angle on the viscous dissipation and, as a consequence, on the wave-damping rate and frequency.

We apply Lighthill's theory of aeroacoustic sound generation to shallow water gravity waves generated by spatially confined two-dimensional turbulence. We show that the frequency spectrum of surface waves at large distances from the source of turbulence is, under suitable conditions, proportional to the spatiotemporal spectrum of the energy momentum tensor associated with the turbulent fields acting as the wave source and hence that it follows a power-law behavior. We compute the exponent for shallow water waves generated by isotropic two-dimensional turbulence and show that the integrated power radiated scales as ${\omega }^{-3}$ when the turbulent fluctuations arise from an inverse energy cascade and as ${\omega }^{-7}$ when they arise from the enstrophy cascade.

The wall-bounded turbulent flows are populated by coherent motions with different scales. The inner motions (near-wall cycle) have been well recognized in wall turbulence. Since the last decade, it has also been reported that a distinct outer peak will emerge in the premultiplied spectra of streamwise velocity fluctuations in canonical-wall-flow configurations at high Reynolds numbers. It is an important energetic signature of the very-large-scale motions or the outer motions herein. However, at low to moderate Reynolds numbers, both the wall-normal locations and length scales of the inner and outer motions are very close to each other, imposing significant difficulties to separate them. Even more, we still do not know the critical Reynolds number for the emergence of the energetic outer motions. In the present study, we propose an assumption that the inner motions that are free of outer motions and transitional effects should be well scaled by wall units, for which we name “the turbulence with only inner motions” (TIM). By carrying out direct numerical simulation (DNS) at low Reynolds numbers, the critical Reynolds number is determined to be ${\text{Re}}_{\tau }\approx 110$, where ${\text{Re}}_{\tau }$ is the friction Reynolds number. Empirical fitting formulas for the broadband streamwise turbulence intensity and premultiplied spectra of TIM are proposed based on the DNS data. Furthermore, with publicly available DNS database of Reynolds number up to ${\text{Re}}_{\tau }=5200$, the turbulence energy contributions by the outer motions are studied by subtracting that of TIM from the total. The result implies possibly distinct modulation effects on motions with different scales.

We investigate the Rayleigh-Taylor instability of a thin viscous film coating the inside of a spherical substrate. The aim of this work is to find and characterize the instability pattern in this spherical geometry. In contrast to the Rayleigh-Taylor instability under a planar substrate, where the interface is asymptotically unstable with respect to infinitesimal perturbations, the drainage induced by the component of gravity tangent to a curved substrate stabilizes the liquid interface, making the system linearly asymptotically stable. By performing a linear optimal transient growth analysis we show that the double curvature of a spherical substrate yields a critical Bond number, prescribing the ratio between gravitational and capillary forces, before an initial growth of perturbations is possible two-times larger than for a circular cylindrical substrate. This linear transient growth analysis however does not yield any selection principle for an optimal azimuthal wave number and we have to resort to a fully nonlinear analysis. By numerically solving the nonlinear lubrication equation we find that the most amplified azimuthal wave number increases with the Bond number. Nonlinear interactions are responsible for the transfer of energy to higher-order harmonics. The larger the Bond number and the farther away from the apex of the sphere, the richer the wave-number spectrum.

Models that describe two-fluid flow in porous media suffer from a widely recognized problem that the constitutive relationships used to predict capillary pressure as a function of the fluid saturation are nonunique, thus requiring a hysteretic description. As an alternative to the traditional perspective, we consider a geometric description of the capillary pressure, which relates the average mean curvature, the fluid saturation, the interfacial area between fluids, and the Euler characteristic. The state equation is formulated using notions from algebraic topology and cast in terms of measures of the macroscale state. Synchrotron-based x-ray microcomputed tomography and high-resolution pore-scale simulation is applied to examine the uniqueness of the proposed relationship for six different porous media. We show that the geometric state function is able to characterize the microscopic fluid configurations that result from a wide range of simulated flow conditions in an averaged sense. The geometric state function can serve as a closure relationship within macroscale models to effectively remove hysteretic behavior attributed to the arrangement of fluids within a porous medium. This provides a critical missing component needed to enable a new generation of higher fidelity models to describe two-fluid flow in porous media.

Multifluid flows in a vertical channel are examined by direct numerical simulations, for situations where the topology of the interface separating the different fluids changes. Several bubbles are initially placed in a turbulent channel flow at a sufficiently high void fraction so that the bubbles collide and the liquid film between them becomes very thin. This film is ruptured at a predetermined thickness and the bubbles are allowed to coalesce. For the cases with high surface tension the bubbles continue to coalesce, eventually forming one large bubble. At low surface tension, on the other hand, the large bubbles break up again, sometimes undergoing repeated coalescence and breakup. The evolution of various integral quantities, such as the average flow rate, wall shear, and interface area, are monitored and compared for different governing parameters. Averages of the flow field and the phase distribution over planes parallel to the walls are also examined, and the microstructure, at statistically steady state, is examined using low-order probability functions.

When a polymer solution is uniaxially stretched and held fixed at both ends, the solution quickly separates into droplets connected by strings and takes the beads-on-string structure. The string then becomes thinner by capillary forces. Here we develop a theoretical framework on viscoelastic fluids based on the Onsager principle and apply it to the dynamics of viscoelastic filaments. We show that the beads-on-string structure is a thermodynamic quasi-equilibrium state and derive an equation for the coexistence condition in the pseudo-equilibrium state. Using the condition, we solve the evolution equation analytically and show that the string radius and the tensile stress vary exponentially as predicted by the classical theory of Entov and Hinch [J. Non-Newtonian Fluid Mech. 72, 31 (1997)], but the prefactor for the tensile stress is different from their theory and agrees with the numerical solutions of Clasen et al. [J. Fluid Mech. 556, 283 (2006)].

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.

Turbulence forcing techniques are often required in the numerical simulation of statistically stationary turbulent flows. However, the existing forcing techniques are not based on physics, but rather arbitrary numerical methods that sustain the turbulent kinetic energy. In this work, a forcing technique is devised to reproduce the centerline turbulent characteristics of round jets in a triply periodic box. It is derived from the Navier-Stokes equations by applying a Reynolds decomposition with the mean velocity of the axisymmetric jet. The result is an anisotropic linear forcing term, which is intended to be used in a three-dimensional box to create turbulence. Four direct numerical simulations with different ${\text{Re}}_{\lambda }$ have been performed with these forcing terms. The budget of the terms in the kinetic energy equation is very close to the experimental measurement on the centerline. The anisotropy, kinetic energy $k$, and dissipation rate $\varepsilon$ of the simulations are also comparable to experimental values. Finally, the kinetic energy spectrum in the axial direction, $\varphi \left({\kappa }_1\right)$, is presented. With appropriate normalizations, the spectrum agrees well with the round jet spectrum on its centerline.

The interaction of a vortex ring impinging on a rigid wall with a coaxial aperture is examined experimentally with various aperture sizes and vortex ring Reynolds numbers. Flow visualization and particle image velocimetry are utilized to investigate the dynamics of the impact interaction. For large aperture-to–ring radius ratios, the vortex ring passes through the aperture relatively unabated, while for smaller ratios, the incoming ring can be partially or completely blocked. For cases where the vortex ring is slightly smaller than the aperture, the vortex ring passes through, but suffers a significant loss in energy because of the influence of the wall. For apertures smaller than the ring, the vortex ring–wall interaction is similar to the dynamics of a vortex ring impacting a full wall; that is, the vortex ring-induced boundary layer separates and rolls up into a secondary vortex ring. Flow through the aperture, however, causes the formation of a new vortex ring. A semianalytical model is introduced to predict the strength of the newly formed vortex ring for small aperture-to-ring radius cases.

Atomization and spray generation naturally occur around us in a wide variety of situations ranging from drop impacts to bubble bursting. However, controlling this process is key in many applications such as internal combustion engines, gas turbines, and agricultural spraying. Here we show how a drop can be fragmented into thousands of smaller droplets by impacting it onto a mesh. We demonstrate the unexpected possibility to transfer liquid outside the projected impact area of the drop and the existence of a well-defined cone envelope for the resulting spray. Self-similarity of the flow studied at the primary repeating unit—the hole—allows us to predict the global nature of the atomization process: mass transfer and spray geometry. We explain how these elementary units capture the momentum of the flow atop them and how side wall interactions can lead to saturation effects. At the grid level, this translates into surface fraction and hole aspect ratio being governing parameters of the system that can be tuned to control and optimize spray characteristics. As a result of the fragmentation, the momentum exerted on the target is reduced—a major advantage in crop protection and pathogen dispersion prevention under rain. In addition, pesticide drift in agricultural sprays can be controlled by using initially large drops that are subsequently atomized and conically sprayed by a mesh atop the crop. Beyond droplet-substrate interaction, this inexpensive spraying method enhances surface exchange phenomena such as evaporation and has major implications in many applications such as cooling towers or multieffect desalination.

Wetting of a liquid over another, pre-existing liquid film governs several natural phenomena and technical applications, such as coating and oil recovery. The dynamics of this everyday process are poorly understood due to the lack of space and time-resolved techniques, which can discriminate between the two liquids. Here we image a water front moving on a micrometer-thick film of a solid supported silicone oil using laser scanning confocal microscopy. The silicone oil forms a meniscus around the water front. We resolve the spreading dynamics within the meniscus in 3D using tracer microparticles. Capillary suction induces local thinning of the oil film adjacent to the meniscus. When moving the water front forward, viscous forces deform the oil meniscus, giving rise to a wavelike film profile with local backflows. For high velocities, the film profile can be modeled within the Landau-Levich-Bretherton framework. The theory fails to predict the film profile at low velocities where strong capillary-suction-induced backflows occur.

Particle aggregates are frequently encountered in many natural and industrial environments. We describe here the stationary state of the fragmentation process of inertial scale particle aggregates in turbulence, i.e., when the particles and the aggregates are larger than the Kolmogorov dissipative scale $\eta$. For this purpose, we place at the initial time a large aggregate of millimetric, nearly neutrally buoyant magnetic particles in a high-Reynolds-number turbulent von Kármán flow. Turbulent fluctuations impose external stresses that tend to fragment the initial and the subsequent aggregates, contrary to the magnetic dipoles that impose torques and forces on the magnets responsible for cohesion. Using video image analyses, we perform the three-dimensional reconstruction of the aggregates and measure their characteristic sizes. The average number of particles inside each aggregate can then be deduced as a function of the intensity of turbulence. Assuming a Kolmogorov inertial scaling law for the turbulent velocity increments, we predict theoretically an aggregate mean size which is in agreement with our experimental results.

The hydrodynamic dispersion of a neutral solute released into a pulsatile electro-osmotic flow in a microcapillary that is affected by slippage at the wall (modeled by the Navier slip condition) is studied theoretically. The long-time Taylor dispersion is analytically derived using the homogenization method with multiple scales. The results indicate that the effective dispersion coefficient depends on a dimensionless slip length, an angular Reynolds number, the amplitude of the oscillatory component of the external electric field, and an electrokinetic parameter that relates the radius of the microcapillary with the Debye length. Our results suggest that in the presence of the Navier slip condition, the dispersivity is maximized by up to two orders of magnitude compared with that obtained through the classical no-slip condition.

Direct numerical simulations are employed to investigate a shock wave impinging on a turbulent boundary layer at free-stream Mach number $M_{\infty }=2.28$ with different wall thermal conditions, including adiabatic, cooled, and heated, for a wide range of deflection angles. It is found that the thermal boundary condition at the wall has a large effect on the size of the interaction region and on the level of pressure fluctuations. The distribution of the Stanton number shows a good agreement with prior experimental studies and confirms the strong heat transfer and complex pattern within the interaction region. An effort was also made to describe the unsteady features of the flow by means of wall pressure and heat flux spectra. Numerical results indicate that the changes in the interaction length due to the wall thermal condition are mainly linked to the incoming boundary layer, which is in agreement with previous experimental studies.

High-Peclet-number, turbulent convection is a classic system with a large timescale separation between flow speeds and the thermal relaxation time. In this paper, we present a method of fast-forwarding through the long thermal relaxation of convective simulations, and we test the validity of this method. This accelerated evolution (AE) method involves measuring the dynamics of convection early in a simulation and using its characteristics to adjust the mean thermodynamic profile within the domain toward its evolved state. We study Rayleigh-Bénard convection as a test case for AE. Evolved flow properties of AE solutions are measured to be within a few percent of solutions which are reached through standard evolution (SE) over a full thermal diffusion timescale. At the highest values of the Rayleigh number at which we compare SE and AE, we find that AE solutions require roughly an order of magnitude fewer computing hours to evolve than SE solutions.