This paper is associated with a video winner of a 2019 American Physical Society's Division of Fluid Dynamics (DFD) Gallery of Fluid Motion Award for work presented at the DFD Gallery of Fluid Motion. The original video is available online at the Gallery of Fluid Motion, https://doi.org/10.1103/APS.DFD.2019.GFM.V0067.

This paper is associated with a poster winner of a 2019 American Physical Society's Division of Fluid Dynamics (DFD) Milton van Dyke Award for work presented at the DFD Gallery of Fluid Motion. The original poster is available online at the Gallery of Fluid Motion, https://doi.org/10.1103/APS.DFD.2019.GFM.P0034.

This paper is associated with a video winner of a 2019 American Physical Society's Division of Fluid Dynamics (DFD) Milton van Dyke Award for work presented at the DFD Gallery of Fluid Motion. The original video is available online at the Gallery of Fluid Motion, https://doi.org/10.1103/APS.DFD.2019.GFM.V0082.

This paper is associated with a poster winner of a 2019 American Physical Society's Division of Fluid Dynamics (DFD) Gallery of Fluid Motion Award for work presented at the DFD Gallery of Fluid Motion. The original poster is available online at the Gallery of Fluid Motion, https://doi.org/10.1103/APS.DFD.2019.GFM.P0031.

Due to the net interfacial consumption of solute, the two-dimensional problem of phoretic swimming is ill posed in the standard description of diffusive transport, where the solute concentration satisfies Laplace's equation. It becomes well posed when solute advection is accounted for. We consider here the case of weak advection, where solute transport is analyzed using matched asymptotic expansions in two separate asymptotic regions, a near-field region in the vicinity of the swimmer and a far-field region where solute advection enters the dominant balance. We carry out the analysis for a standard Janus configuration, where half of the particle boundary is active and the other half is inert. Our main focus lies in the limit of fast reaction, which leads to a mixed boundary-value problem in the near field. That problem is solved using conformal mapping techniques. Our asymptotic scheme furnishes an implicit equation for the particle velocity $s$ in the direction of the active portion of its boundary, $2s\left(8ln\frac{8D}{\left|s\right|a}-\gamma \right)=b{c}_{\infty }/a$, wherein $a$ is the particle radius, $D$ the solute diffusivity, $c_{\infty }$ its far-field concentration, $b$ the diffusio-osmotic slip coefficient, and $\gamma$ the Euler-Mascheroni constant. The nonlinear dependence of $s$ upon $b{c}_{\infty }$ is a signature of the nonvanishing effect of solute advection.

Helical propulsion is ubiquitously adopted by swimming bacteria and artificial microswimmers to move in biological fluids, which are typically viscoelastic and shear thinning. Here we present a set of theoretical and computational analyses to show that shear-thinning viscosity alone can cause the substantial enhancement reported for helical propulsion in recent experiments. Our analyses provide direct evidence to elucidate the nonlocal nature of the enhancement mechanism. Since the enhancement predicted here can be more substantial than that due to viscoelasticity, our results also suggest that shear-thinning rheology may play a more dominant role in the observed enhancement of bacterial motility in polymeric fluids.

There has been a growing interest in implementing state-resolved models for flowfield calculations of high-speed reentry applications that are characterized by regions of strong nonequilibrium. To this end, the present work provides a technique to rigorously compute transport collision integrals for vibrationally excited molecules. Collision dynamics calculations are extended to include state-to-state (StS) effects, and vibrationally resolved transport collisional quantities including scattering angles, cross sections, and collision integrals are computed for the $\mathrm{O}+{\mathrm{O}}_2$ system using potential energy surfaces (PESs) by Varga et al. [J. Chem. Phys. 147, 154312 (2017)]. From the nine surfaces provided by Varga et al., the “surface-averaged” collision integrals are computed for the oxygen system, and Gupta-Yos-style fits to the data are provided. It is found that the StS collision integrals depend not only on the vibrational state of the molecule, but also on the spin and spatial degeneracy associated with the PES that governs the interaction. Comparison of the collision integrals from the Varga et al. surfaces with those generated from the Varandas and Pais PES [Mol. Phys. 65, 843 (1988)] shows significant differences at highly excited vibrational states. The highly attractive nature of the Varandas and Pais surface leads to a monotonic increase in the collision integral values with vibrational excitation of ${\mathrm{O}}_2$, while the surface-averaged state-based collision integral values computed from the comparatively repulsive Varga et al. set of surfaces generally increase with vibrational excitation for temperatures up to 6000 K, and decrease with vibrational excitation at higher temperatures. Additionally, due to this nontrivial dependence of the collision integrals on the vibrational state of ${\mathrm{O}}_2$, simple empirical models are found to be unable to correctly estimate vibrational state-based collision integrals. Differences as high as 80% are obtained between the model predictions and values computed directly from the underlying PES. Evaluation of vibrationally resolved viscosity and translational thermal conductivity for the $\mathrm{O}+{\mathrm{O}}_2$ system under equilibrium conditions indicate that both these transport coefficients depend on the vibrational excitation of ${\mathrm{O}}_2$, with the contribution of the excited vibrational states increasing with rising temperature.

The modal and nonmodal linear stability of a stably stratified Blasius boundary layer flow, composed of a velocity and a thermal boundary layer, is investigated. The temporal and spatial linear stability of such flow is investigated for several Richardson, Reynolds, and Prandtl numbers. While increasing the Richardson number stabilizes the flow, a more complex behavior is found when changing the Prandtl number, leading to a stabilization of the flow up to $\text{Pr}=7$, followed by a destabilization. The nonmodal linear stability of the same flow is then investigated using a direct-adjoint procedure optimizing four different approximations of the energy norm based on a weighted sum of the kinetic and the potential energies. No matter the norm approximation, for short target times an increase of the Richardson number induces a decrease of the optimal energy gain and time at which it is obtained and an increase of the optimal streamwise wave number, which considerably departs from zero. Moreover, the dependence of the energy growth on the Reynolds number transitions from quadratic to linear, whereas the optimal time, which varies linearly with Re in the nonstratified case, remains constant. This suggests that the optimal energy growth mechanism arises from the joint effect of the lift-up and the Orr mechanism, that simultaneously act to increase the shear production term on a rather short timescale, counterbalancing the stabilizing effect of the buoyancy production term. Although these short-time mechanisms are found to be robust with respect to the chosen norm, a different amplification mechanism is observed for long target times for three of the proposed norms. This strong energy growth, due to the coupling between velocity and temperature perturbations in the free stream, disappears when the variation of the stratification strength with height is accurately taken into account in the definition of the norm.

Stabilizing and destabilizing films of liquid by design is not a simple challenge to overcome. Megahertz-frequency surface acoustic waves (SAWs), which propagate in a solid substrate, may stabilize liquid films against capillary forces, which otherwise promote the film breakup and the dewetting of the substrate. Here we explore the contribution of SAWs to the dynamics of micron- and submicron-thick films of water, which intervene between a bubble and a solid substrate. The investigation in this paper was inspired by a previous theoretical work on the acoustic Landau-Levich coating problem, which predicts the onset of stable and unstable coating films under the excitation of SAWs. We observe that the parametric regime of the stable Landau-Levich coating film translates to stable water films in our experiments. Moreover, we observe that unlike previous experiments with silicon oil, water films do not collapse under the parametric regime of the unstable Landau-Levich coating film, but appear to remain stable. A key to this controversy appears to be the presence of the stabilizing, long range, electrical double layer force in water, which is anticipated to alter the film response to the SAW.

The influence of inertial migration of neutrally buoyant particles on inertial flow transitions in Taylor-Couette (TC) flow of a suspensions is studied; this work considers primarily transitions associated with the circular Couette flow (CCF) and Taylor vortex flow (TVF) regimes. A concentric cylinder Taylor-Couette device with a stationary outer cylinder and rotating inner cylinder is considered. The device has an inner to outer radius ratio of $\eta =d_i/d_o=0.877$, where $d_i$ and $d_o$ are the inner and outer diameters of the flow annulus. The ratio of the axial length to the radial gap of the annulus $\mathrm{\Gamma }=L/\delta =20.5$, where $\delta =(d_o-d_i)/2$. The ratio of radial gap $\delta$ and the particle diameter $d_p$ is $\alpha =\delta /d_p=30.4$ and the particle volume fraction considered in this work is $\varphi =0.10$. A flow structure (CCF or TVF) near the transition boundary with either uniform distribution across the annular region or fully migrated concentration profile is established. The Reynolds number (Re) is subjected to a rapid step change to study the effect of the concentration profile on the flow transition Re and resulting flow structure evolution; here the Reynolds number is $\text{Re}=\delta d_i{\omega }_i\rho /2{\mu }_s$, where ${\omega }_i$ is the rotation rate of the inner cylinder and $\rho$ and ${\mu }_s$ are the density and effective viscosity of the suspension. Our results show that, relative to uniform concentration, the particle distribution following inertial migration destabilizes the CCF state near the CCF-nonaxisymmetric flow transition boundary. In contrast to this destabilizing effect in CCF, migration of particles in the TVF regime has a stabilizing effect on the TVF-wavy Taylor vortex and TVF-nonaxisymmetric flow transition boundaries. The transition away from the TVF exhibits clear hysteresis associated with migration, as once initiated TVF could be sustained below and above the transition boundaries observed for suspension TC flow with uniform concentration.

The settling behavior of small inertial particles in turbulent convection is a fundamental problem across several disciplines, from geophysics to metallurgy. In a geophysical context, the settling of dense crystals controls the mode of solidification of magma chambers and planetary scale magma oceans, while rising of light bubbles of volatiles drives volcanic outgassing and the formation of primordial atmospheres. Motivated by these geophysical systems, we perform a systematic numerical study on the settling rate of particles in a rectangular two-dimensional Rayleigh-Bénard system with Rayleigh number up to ${10}^{12}$ and Prandtl number from 10 to 50. Under the idealized condition of spherically shaped particles with small Reynolds number, two limiting behaviors exist for the settling velocity. On the one hand, Stokes law applies to particles with small but finite response time, leading to a constant settling rate. On the other hand, particles with a vanishing response time are expected to settle at an exponential rate. Based on our simulations, we present a physical model that bridges the gap between the above limiting behaviors by describing the sedimentation of inertial particles as a random process with two key components: (i) the transport of particles from vigorously convecting regions into sluggish, low-velocity “piles” that naturally develop at the horizontal boundaries of the system, and (ii) the probability that particles escape such low-velocity regions without settling at their base. In addition, we identify four distinct settling regimes and analyze the horizontal distribution of sedimented particles. For two of these regimes settling is particularly slow and the distribution is strongly nonuniform, with dense particles being deposited preferentially below major clusters of upwellings. Finally, we apply our results to the crystallization of a magma ocean. Our prediction of the characteristic residence times is consistent with fractional crystallization, i.e., with the efficient separation of dense crystals from the residual lighter fluid. In absence of an efficient mechanism to reentrain settled particles, equilibrium crystallization appears possible only for particles with extremely small density contrasts.

As the size of turbulent flow simulations continues to grow, in situ data compression is becoming increasingly important for visualization, analysis, and restart checkpointing. For these applications, single-pass compression techniques with low computational and communication overhead are crucial. In this paper we present a deep-learning approach to in situ compression using an autoencoder architecture that is customized for three-dimensional turbulent flows and is well suited for contemporary heterogeneous computing resources. The autoencoder is compared against a recently introduced randomized single-pass singular value decomposition (SVD) for three different canonical turbulent flows: decaying homogeneous isotropic turbulence, a Taylor-Green vortex, and turbulent channel flow. Our proposed fully convolutional autoencoder architecture compresses turbulent flow snapshots by a factor of 64 with a single pass, allows for arbitrarily sized input fields, is cheaper to compute than the randomized single-pass SVD for typical simulation sizes, performs well on unseen flow configurations, and has been made publicly available. The results reported here show that the autoencoder dramatically outperforms a randomized single-pass SVD with similar compression ratio and yields comparable performance to a higher-rank decomposition with an order of magnitude less compression in regard to preserving a number of important statistical quantities such as turbulent kinetic energy, enstrophy, and Reynolds stresses.

We study the energy convergence of the Karhunen-Loève decomposition of the turbulent velocity field in a high-Reynolds-number pressure-driven boundary layer as a function of the number of modes. An energy-optimal Karhunen-Loève (KL) decomposition is obtained from wall-modeled large-eddy simulations at “infinite” Reynolds number. By explicitly using Fourier modes for the horizontal homogeneous directions, we are able to construct a basis of full rank, and we demonstrate that our results have reached statistical convergence. The KL dimension, corresponding to the number of modes per unit volume required to capture $90\%$ of the total turbulent kinetic energy, is found to be $2.4\times {10}^5\left|\mathrm{\Omega }\right|/H^3$ (with $\left|\mathrm{\Omega }\right|$ the domain volume and $H$ the boundary layer height). This is significantly higher than current estimates, which are mostly based on the method of snapshots. In our analysis, we carefully correct for the effect of subgrid scales on these estimates.

The understanding of the dynamics of the velocity gradients in turbulent flows is critical to understanding various nonlinear turbulent processes. Several simplified dynamical equations have been proposed earlier that model the Lagrangian velocity gradient evolution equation. A robust model for the velocity gradient evolution equation can ultimately lead to the closure of the system of equations in the Lagrangian probability distribution function method. The pressure Hessian and the viscous Laplacian are the two important processes that govern the Lagrangian evolution of the velocity gradients. These processes are nonlocal in nature and unclosed from a mathematical point of view. The recent fluid deformation closure model (RFDM) has been shown to retrieve excellent statistics of the viscous process. However, the pressure Hessian modeled by the RFDM has various physical limitations. In this work, we first demonstrate such limitations of the RFDM. Subsequently, we employ a tensor basis neural network (TBNN) to model the pressure Hessian using the information about the velocity gradient tensor itself. Our neural network is trained on high-resolution data obtained from direct numerical simulation (DNS) of isotropic turbulence at the Reynolds number of 433. The predictions made by the TBNN are evaluated against several other DNS datasets. Evaluation is made in terms of the alignment statistics of the pressure-Hessian eigenvectors with the strain-rate eigenvectors. Our analysis of the predicted solution leads to the finding of ten unique coefficients of the tensor basis of the strain-rate and the rotation-rate tensors, the linear combination of which is used to accurately capture key alignment statistics of the pressure-Hessian tensor.

Internal gravity waves propagating within homogeneous stratified turbulence are the subject of the present study. A spatiotemporal analysis is carried out on the results of direct numerical simulations including a forcing term, with the aim of showing the energy content of the simulations as a function of frequency, $\omega$, and wave-vector inclination to the horizontal, $\theta$. Clear signatures of the dispersion relation of internal gravity waves, $\omega =\pm Ncos\theta$, where $N$ is the Brunt-Väisälä frequency, are observed in all our simulations, which have low Froude number, ${\text{Fr}}_h\ll 1$, and increasing buoyancy Reynolds number up to ${\text{Re}}_b\approx 10$. Interestingly, we observe the presence of high-frequency waves with $\omega \sim N$ and a corresponding low-frequency vortex mode, both containing a non-negligible amount of energy. These waves are large-scale waves, their energy signature being found at scales larger than the forcing scales. We also observe the growth of energy in the shear modes, constituting a horizontal mean flow, and we show that their continuous growth is due to an upscale energy transfer, from the forcing scales to larger horizontal as well as vertical scales. These shear modes are found to be responsible for Doppler shifting the frequency of the large-scale waves. When considering the wave energy across the simulations at varying ${\text{Re}}_b$, such energy is seen to reduce as ${\text{Re}}_b$ is increased and the flow enters the strongly stratified turbulence regime. The classical wave-vortex decomposition, based on a purely spatial decomposition of instantaneous snapshots of the flow, is analyzed within the current framework and is seen to correspond relatively well to the “true” wave signal identified by the spatiotemporal analysis, at least for the large-scale waves with $\omega \sim N$. Distinct energy peaks in $\theta \text{−}\omega$ space highlight that the waves have preferential directions of propagation, specifically $\theta ={45}^{\circ }$ and $\theta \approx {55}^{\circ }$, similar to observations in studies of wave radiation from localized regions of turbulence. This suggests that the same wave-generation mechanisms may be relevant for homogeneous and inhomogeneous stratified turbulent flows.

Motivated by numerous geophysical applications, we have carried out laboratory experiments of a reactive (i.e., melting) solid sphere freely falling by gravity in a stratified environment, in the regime of large Reynolds (Re) and Froude numbers. We compare our results to nonreactive spheres in the same regime. First, we confirm, for larger values of Re, the stratification drag enhancement previously observed for low and moderate Re. We also show an even more significant drag enhancement due to melting, much larger than the stratification-induced one. We argue that the mechanism for both enhancements is similar, due to the specific structure of the vorticity field sets by buoyancy effects and associated baroclinic torques, as deciphered for stratification by Zhang et al. [J. Fluid Mech. 875, 622 (2019)]. Using particle image velocimetry, we then characterize the long-term evolution (at time $t\gg 1/N$, with $N$ the Brünt-Väisälä frequency) of the internal wave field generated by the wake of the spheres. The measured wave field is similar for both the reactive and inert spheres: indeed, each sphere fall might be considered as a quasi-impulsive source of energy in time and the horizontal direction, as the falling time (the sphere radius) is much smaller than $N$ (than the tank width). Internal gravity waves are generated by wake turbulence over a broad spectrum, with the least damped component being at the Brünt-Väisälä frequency and the largest admissible horizontal wavelength. About 1% of the initial potential energy of each sphere is converted into kinetic energy in the internal waves, with no significant dependence on the Froude number over the explored range.

This Rapid Communication presents the self-propelled and controllable motion of liquid metal droplets, which is driven by surface tension and does not depend on any external force field. Its motion speed and direction can be controlled just as a projectile fired by a slingshot: The liquid metal droplet is the projectile, and a substrate surface serves as the bowstring. This motion provides a potential mechanism for the application of liquid metals in soft robotics, drug delivery, chip cooling, and other fields.

Two-phase liquid-liquid systems are prevalent in a range of commercial and environmental applications. Understanding the behavior of liquid-liquid systems under various processing conditions requires the study of droplet dynamics under precisely controlled flow fields. Here we trap and control the position of droplets in a microfluidic trap to study their dynamics using hydrodynamic forces alone without an external field. The hydrodynamic trap is adapted from a previously implemented “Stokes trap” by incorporating a drop-on-demand system to generate droplets at a T-junction geometry on the same microfluidic chip. Using the hydrodynamic trap, confined droplet dynamics in response to perturbation are studied by applying a millisecond-pressure pulse to deform trapped droplets. Droplet shape relaxation after cessation of the pressure pulse follows an exponential decay. The characteristic droplet shape relaxation time is obtained from the shape decay curves, for aqueous glycerol droplets of varying viscosities in the dispersed phase with light and heavy mineral oils in the continuous phase. Systems were chosen to provide similar equilibrium interfacial tensions (5–10 mN/m) with wide variations of viscosity ratios. It is found that the droplet shape relaxation in the moderately confined regime shows a strong dependence on droplet radius, and a weaker dependence on the ratio of dispersed to continuous phase viscosity. An empirical scaling relationship is developed, and relaxation times from the experiments are compared to theoretical relaxation times for the limiting regime of unconfined droplets. The droplet response in the moderately confined regime differs from both limiting regimes of unconfined and highly confined droplets with regards to the radius scaling. Droplet shape relaxation time can be used inform the response of droplets in an emulsion when subjected to transient flows in various processing conditions. Finally, an application of this platform for directly visualizing droplet coalescence in planar extensional flow is presented. The microfluidic four-channel hydrodynamic trap can thus be applied for studying the fundamental physics of droplet deformation and droplet-droplet interactions on the microscale.

When a solid plate is withdrawn from a partially wetting liquid, a liquid layer dewets the moving substrate. High-speed imaging reveals alternating thin and thick regions in the entrained layer in the transverse direction at steady state. This paper systematically compares this situation to the reversed process, forced wetting, where a solid entrains an air layer along its surface as it is pushed into a liquid. To quantify the absolute thickness of these steady-state structures precisely, I have developed an optical technique, taking advantage of the angle dependence of interference, combined with a method based on a maximum-likelihood estimation. The data show that the thicknesses of both regions of the film scale with the capillary number, $\mathrm{Ca}$. Further, an additional region is observed during onset, the quantitative explanation of which requires future investigation.

We report that the splash created by a solid impactor moving into a bed of granular media depends sensitively on the temperature of the granular bed. Granules were poured loosely into an open-top container and then heated from below, and a metal ball was then dropped into the hot granular bed. High-speed video experiments reveal that the size and average velocity of the resulting granular splash both decrease significantly as the temperature increases. Complementary experiments show that the composition of the surrounding gas also strongly affects the splash dynamics but that the gas pressure and corresponding density have no significant effect. We interpret these observations in terms of two physical effects: the influence of the temperature- and composition-dependent gas viscosity on the ejecta drag force, and an enhanced static strength within the bed caused by thermal expansion of the granules. Taken together, the results indicate that temperature plays a greater role in granular splashing than previously suspected.