We conduct experiments to investigate the rotations of freely moving particles in a homogeneous isotropic turbulent flow. The particles are nearly neutrally buoyant and the particle size exceeds the Kolmogorov scale so that they are too large to be considered passive tracers. Particles of several different shapes are considered including those that break axisymmetry and fore-aft symmetry. We find that regardless of shape the mean-square particle angular velocity scales as ${d_{eq}}^{-4/3}$, where $d_{eq}$ is the equivalent diameter of a volume-matched sphere. This scaling behavior is consistent with the notion that velocity differences across a length $d_{eq}$ in the flow are responsible for particle rotation. We also find that the probability density functions (PDFs) of particle angular velocity collapse for particles of different shapes and similar $d_{eq}$. The significance of these results is that the rotations of an inertial, nonspherical particle are only functions of its volume and not its shape. The magnitude of particle angular velocity appears log-normally distributed and individual Cartesian components show long tails. With increasing $d_{eq}$, the tails of the PDF become less pronounced, meaning that extreme events of angular velocity become less common for larger particles.

Impacting liquids can be reflected by moving solid plates, provided the surface is fast enough. We describe and model here the threshold speed of bouncing, in particular as a function of the impact velocity of the incoming liquid. We also demonstrate that the aerodynamic force responsible for the nonwetting behavior induces an oblique rebound, which contributes to the liquid removal. In summary, this situation repels viscous, low surface tension drops of any size, all kinds of cases where repellency is impossible to achieve by other means.

We experimentally study the properties of nonlinear surface gravity waves in a large-scale basin. We consider two different configurations: a one-dimensional (1D) monochromatic wave forcing, and a two-dimensional (2D) forcing with bichromatic waves satisfying resonant-wave interaction conditions. For the 1D forcing, we find a discrete wave-energy spectrum dominated at high frequencies by bound waves whose amplitudes decrease as a power law of the frequency. Bound waves (e.g., to the carrier) are harmonics superimposed on the carrier wave propagating with the same phase velocity as the one of the carrier. When a narrow frequency random modulation is applied to this carrier, the high-frequency part of the wave-energy spectrum becomes continuous with the same frequency-power law. Similar results are found for the 2D forcing when a random modulation is also applied to both carrier waves. Our results thus show that all these nonlinear gravity wave spectra are dominated at high frequencies by the presence of bound waves, even in the configuration where resonant interactions occur. Moreover, in all these configurations, the power-law exponent of the spectrum is found to depend on the forcing amplitude with the same trend as the one found in previous gravity wave turbulence experiments. Such a set of bound waves may thus explain this dependence that was previously poorly understood.

Non-Gaussian fluctuations with an exponential tail in their probability density function (PDF) are often observed in nonequilibrium steady states (NESSs) and one does not understand why they appear so often. Turbulent Rayleigh-Bénard convection (RBC) is an example of such a NESS, in which the measured PDF $P\left(\delta T\right)$ of temperature fluctuations $\delta T$ in the central region of the flow has a long exponential tail. Here we show that because of the dynamic heterogeneity in RBC, the exponential PDF is generated by a convolution of a set of dynamics modes conditioned on a constant local thermal dissipation rate $\epsilon$. The conditional PDF $G\left(\delta T\right|\epsilon )$ of $\delta T$ under a constant $\epsilon$ is found to be of Gaussian form and its variance ${\sigma }_T^2$ for different values of $\epsilon$ follows an exponential distribution. The convolution of the two distribution functions gives rise to the exponential PDF $P\left(\delta T\right)$. This work thus provides a physical mechanism of the observed exponential distribution of $\delta T$ in RBC and also sheds light on the origin of non-Gaussian fluctuations in other NESSs.

The cavity and central jet generated by the impact of a single water drop on a deep-water surface in a wind field are experimentally studied. Different experiments are performed by varying the impacting drop diameter and wind speed. The contour profile histories of the cavity (also called crater) and central jet (also called stalk) are measured in detail with a backlit cinematic shadowgraph technique. The results show that shortly after the drop hits the water surface an asymmetrical cavity appears along the wind direction, with a train of capillary waves on the cavity wall. This is followed by the formation of an inclined central jet at the location of the drop impact. It is found that the wind has little effect on the penetration depth of the cavity at the early stage of the cavity expansion, but markedly changes the capillary waves during the retraction of the cavity. The capillary waves in turn shift the position of the central jet formation leeward. The dynamics of the central jet are dominated by two mechanisms: (i) the oblique drop impact produced by the wind and (ii) the wind drag force directly acting on the jet. The maximum height of the central jet, called the stalk height, is drastically affected by the wind, and the nondimensional stalk height $H/D$ decreases with increasing $\theta {\text{Re}}^{-1}$, where $D$ is the drop diameter, $\theta$ is the impingement angle of drop impact, and $\text{Re}={\rho }_a{U}_{w}D/{\mu }_a$ is the Reynolds number with air density ${\rho }_a$, wind speed $U_w$, and air viscosity ${\mu }_a$.

Evaporation of a binary liquid into near-vacuum conditions has been studied using numerical solutions of a system of two coupled Enskog-Vlasov equations. Liquid-vapor coexistence curves have been mapped out for different liquid compositions. The evaporation process has been investigated at a range of liquid temperatures sufficiently lower than the critical one for the vapor not to significantly deviate from the ideal behavior. It is found that the shape of the distribution functions of evaporating atoms is well approximated by an anisotropic Maxwellian distribution with different characteristic temperatures for velocity components normal and parallel to the liquid-vapor interface. The anisotropy reduces as the evaporation temperature decreases. Evaporation coefficients are computed based on the separation temperature and the maximum concentration of the less volatile component close to the liquid-vapor interface. This choice leads to values which are almost constant in the simulation conditions.

The temporal statistics of incompressible fluid velocity and passive scalar fields in developed turbulent conditions is investigated by means of direct numerical simulations along the trajectories of self-propelled pointlike probes drifting in a flow. Such probes are characterized by a propulsion velocity which is fixed in intensity and direction; however, like vessels in a flow they are continuously deviated on their intended course as the result of local sweeping of the fluid flow. The recorded time series by these moving probes represent the simplest realization of transect measurements in a fluid flow environment. We investigate the nontrivial combination of Lagrangian and Eulerian statistical properties displayed by the transect time series. We show that, as a result of the homogeneity and isotropy of the flow, the single-point acceleration statistics of the probes follows a predictable trend at varying the propulsion speed, a feature that is also present in the scalar time-derivative fluctuations. Further, by focusing on two-time statistics we characterize how the Lagrangian-to-Eulerian transition occurs at increasing the propulsion velocity. The analysis of intermittency of temporal increments highlights in a striking way the opposite trends displayed by the fluid velocity and passive scalars.

Miscible displacement of fluids in porous media is often characterized by the scaling of the mixing zone length with displacement time. Depending on the viscosity contrast of fluids, the scaling law varies between the square root relationship, a sign for dispersive transport regime during stable displacement, and the linear relationship, which represents the viscous fingering regime during an unstable displacement. The presence of heterogeneities in a porous medium significantly affects the scaling behavior of the mixing length as it interacts with the viscosity contrast to control the mixing of fluids in the pore space. In this study, the dynamics of the flow and transport during both unit and adverse viscosity ratio miscible displacements are investigated in heterogeneous packings of circular grains using pore-scale numerical simulations. The pore-scale heterogeneity level is characterized by the variations of the grain diameter and velocity field. The growth of mixing length is employed to identify the nature of the miscible transport regime at different viscosity ratios and heterogeneity levels. It is shown that as the viscosity ratio increases to higher adverse values, the scaling law of mixing length gradually shifts from dispersive to fingering nature up to a certain viscosity ratio and remains almost the same afterwards. In heterogeneous media, the mixing length scaling law is observed to be generally governed by the variations of the velocity field rather than the grain size. Furthermore, the normalization of mixing length temporal plots with respect to the governing parameters of viscosity ratio, heterogeneity, medium length, and medium aspect ratio is performed. The results indicate that mixing length scales exponentially with log-viscosity ratio and grain size standard deviation while the impact of aspect ratio is insignificant. For stable flows, mixing length scales with the square root of medium length, whereas it changes linearly with length during unstable flows. This scaling procedure allows us to describe the temporal variation of mixing length using a generalized curve for various combinations of the flow conditions and porous medium properties.

We study the linear spatiotemporal stability of an infinite row of equal point vortices under symmetric confinement between parallel walls. These rows of vortices serve to model the secondary instability leading to the merging of consecutive (Kelvin-Helmholtz) vortices in free shear layers, allowing us to study how confinement limits the growth of shear layers through vortex pairings. Using a geometric construction akin to a Legendre transform on the dispersion relation, we compute the growth rate of the instability in different reference frames as a function of the frame velocity with respect to the vortices. This approach is verified and complemented with numerical computations of the linear impulse response, fully characterizing the absolute/convective nature of the instability. Similar to results by Healey on the primary instability of parallel tanh profiles [J. Fluid Mech. 623, 241 (2009)], we observe a range of confinement in which absolute instability is promoted. For a parallel shear layer with prescribed confinement and mixing length, the threshold for absolute/convective instability of the secondary pairing instability depends on the separation distance between consecutive vortices, which is physically determined by the wavelength selected by the previous (primary or pairing) instability. In the presence of counterflow and moderate to weak confinement, small (large) wavelength of the vortex row leads to absolute (convective) instability. While absolute secondary instabilities in spatially developing flows have been previously related to an abrupt transition to a complex behavior, this secondary pairing instability regenerates the flow with an increased wavelength, eventually leading to a convectively unstable row of vortices. We argue that since the primary instability remains active for large wavelengths, a spatially developing shear layer can directly saturate on the wavelength of such a convectively unstable row, by-passing the smaller wavelengths of absolute secondary instability. This provides a wavelength selection mechanism, according to which the distance between consecutive vortices should be sufficiently large in comparison with the channel width in order for the row of vortices to persist. We argue that the proposed wavelength selection criteria can serve as a guideline for experimentally obtaining plane shear layers with counterflow, which has remained an experimental challenge.

A study is conducted to identify advantages and limitations of existing large-eddy simulation (LES) closures for the subgrid-scale (SGS) kinetic energy using a database of direct numerical simulations (DNS). The analysis is conducted for both reacting and nonreacting flows, different turbulence conditions, and various filter sizes. A model, based on dissipation and diffusion of momentum (LD-D model), is proposed in this paper based on the observed behavior of four existing models. Our model shows the best overall agreements with DNS statistics. Two main investigations are conducted for both reacting and nonreacting flows: (i) an investigation on the robustness of the model constants, showing that commonly used constants lead to a severe underestimation of the SGS kinetic energy and enlightening their dependence on Reynolds number and filter size; and (ii) an investigation on the statistical behavior of the SGS closures, which suggests that the dissipation of momentum is the key parameter to be considered in such closures and that dilatation effect is important and must be captured correctly in reacting flows. Additional properties of SGS kinetic energy modeling are identified and discussed.

The proper scale decomposition in flows with significant density variations is not as straightforward as in incompressible flows, with many possible ways to define a “length scale.” A choice can be made according to the so-called inviscid criterion [Aluie, Physica D 24, 54 (2013)]. It is a kinematic requirement that a scale decomposition yield negligible viscous effects at large enough length scales. It has been proved [Aluie, Physica D 24, 54 (2013)] recently that a Favre decomposition satisfies the inviscid criterion, which is necessary to unravel inertial-range dynamics and the cascade. Here we present numerical demonstrations of those results. We also show that two other commonly used decompositions can violate the inviscid criterion and, therefore, are not suitable to study inertial-range dynamics in variable-density and compressible turbulence. Our results have practical modeling implication in showing that viscous terms in Large Eddy Simulations do not need to be modeled and can be neglected.

In turbulent boundary layers, the wall-normal gradient of the Reynolds shear stress identifies momentum sources and sinks ($T=\partial [-uv]/\partial y$). These motions can be physically interpreted in two ways: (1) as contributors to the turbulence term balancing the mean momentum equation, and (2) as regions of strong local interaction between velocity and vorticity fluctuations. In this paper, the space-time evolution of momentum sources and sinks is investigated in a turbulent boundary layer at the Reynolds number (${\text{Re}}_{\tau }$) = 2700, with time-resolved planar particle image velocimetry in a plane along the streamwise and wall-normal directions. Wave number-frequency power spectra of $T$ fluctuations reveal that the wave velocities of momentum sources and sinks tend to match the local streamwise velocity in proximity to the wall. However, as the distance from the wall increases, the wave velocities of the $T$ events are slightly lower than the local streamwise velocities of the flow, which is also confirmed from the tracking in time of the intense momentum sources and sinks. This evidences that momentum sources and sinks are preferentially located in low-momentum regions of the flow. The spectral content of the $T$ fluctuations is maximum at the wall, but it decreases monotonically as the distance from the wall grows. The relative spectral contributions of the different wavelengths remains unaltered at varying wall-normal locations. From autocorrelation coefficient maps, the characteristic streamwise and wall-normal extents of the $T$ motions are respectively 60 and 40 wall units, independent of the wall distance. Both statistics and instantaneous visualizations show that momentum sources and sinks have a preferential tendency to be organized in positive-negative pairs in the wall-normal direction.

We experimentally investigate the boiling behavior of impacting ethanol drops on a heated smooth sapphire substrate at pressures ranging from $P=0.13$ bar to atmospheric pressure. We employ frustrated total internal reflection imaging to study the wetting dynamics of the contact between the drop and the substrate. The spreading drop can be in full contact (contact boiling), it can partially touch (transition boiling), or the drop can be fully levitated (Leidenfrost boiling). We show that the temperature of the boundary between contact and transition boiling shows at most a weak dependence on the impact velocity, but a significant decrease with decreasing ambient gas pressure. A striking correspondence is found between the temperature of this boundary and the static Leidenfrost temperature for all pressures. We therefore conclude that both phenomena share the same mechanism and are dominated by the dynamics taking place at the contact line. On the other hand, the boundary between transition boiling and Leidenfrost boiling, i.e., the dynamic Leidenfrost temperature, increases for increasing impact velocity for all ambient gas pressures. Moreover, the dynamic Leidenfrost temperature coincides for pressures between $P=0.13$ and $0.54$ bar, whereas for atmospheric pressure the dynamic Leidenfrost temperature is slightly elevated. This indicates that the dynamic Leidenfrost temperature is at most weakly dependent on the enhanced evaporation by the lower saturation temperature of the liquid.

The flow generated by a free-moving magnet floating in a thin electrolyte layer is studied experimentally and numerically. The magnet is dragged by a traveling vortex dipole produced by a Lorentz force created when a uniform dc current injected in the electrolyte interacts with the magnetic field of the same magnet. The problem represents a typical case of fluid-solid interaction but with a localized electromagnetic force promoting the motion. Classical wake flow structures are observed when the applied current varies in the range of 0.2 to 10 A. Velocity fields at the surface of the electrolyte are obtained for different flow conditions through particle image velocimetry. Quasi-two-dimensional numerical simulations, based on the immersed boundary technique that incorporates the fluid-solid interaction, reproduce satisfactorily the dynamics observed in the experiments.

Magnetic resonance imaging (MRI) velocimetry methods are used to study fully developed axially symmetric fluid flow in a model porous medium of cylindrical symmetry with a transverse permeability discontinuity. Spatial mapping of fluid flow results in radial velocity profiles. High spatial resolution of these profiles allows estimating the slip in velocities at the boundary with a permeability discontinuity zone in a sample. The profiles are compared to theoretical velocity fields for a fully developed axially symmetric flow in a cylinder derived from the Beavers-Joseph [G. S. Beavers and D. D. Joseph, J. Fluid Mech. 30, 197 (1967)] and Brinkman [H. C. Brinkman, Appl. Sci. Res. A 1, 27 (1947)] models. Velocity fields are also computed using pore-scale lattice Boltzmann modeling (LBM) where the assumption about the boundary could be omitted. Both approaches give good agreement between theory and experiment, though LBM velocity fields follow the experiment more closely. This work shows great promise for MRI velocimetry methods in addressing the boundary behavior of fluids in opaque heterogeneous porous media.

A two-dimensional hybrid numerical method that allows full coupling of the elastic motion in a piezoelectric solid (modeled using a finite-difference time-domain technique) with the resultant compressional flow in a fluid (simulated using a lattice Boltzmann scheme) is developed to study the acoustic streaming that arises in both microchannels and nanochannels under surface acoustic wave (SAW) excitation. In addition to verifying the model through a comparison of the simulations with results from experimental and numerical studies of microchannel and nanochannel flows driven by both standing and traveling SAWs in the literature, we highlight salient features of the flow field that arise and discuss the underlying mechanisms responsible for the flow. In microchannels, boundary layer streaming is the dominant mechanism when the channel height is below the sound wavelength in the liquid, whereas Eckart streaming—arising as a consequence of the attenuation of the sound wave in the liquid—dominates in the form of periodic vortices for larger channel heights. The absence of Eckart streaming and the overlapping of boundary layers in nanochannels with heights below the boundary layer thickness, on the other hand, give rise to a time-averaged dynamic acoustic pressure that results in an inertial-dominant flow, which paradoxically possesses a parabolic-like velocity profile resembling pressure-driven laminar flow. In contrast, if the nanochannel were to be filled instead with air, the significantly lower fluid density leads to a considerable reduction in the dynamic acoustic pressure and hence inertial forcing such that boundary layer streaming once again dominates, asymptotically imposing a slip condition along the channel surface that results in a negative pluglike velocity profile.

This work examines the effect of hydrodynamic interaction between two closely spaced waving elastic filaments on the propulsion and maneuvering of an artificial microswimmer. The filaments are actuated by a forced oscillation of the slope at their clamped end and are free at the opposite end. We obtain an expression for the interaction force and apply an asymptotic expansion based on a small parameter representing the ratio between the elastic deflections and the distance between the filaments. The leading-order interaction forces yield asymmetric oscillation patterns at the two frequencies $\left({\omega }_1,{\omega }_2\right)$ in which the filaments are actuated. Higher orders oscillate at frequencies which are combinations of the actuation frequencies, where the first order includes the $2{\omega }_1,2{\omega }_2,{\omega }_1+{\omega }_2$, and ${\omega }_1-{\omega }_2$ harmonics. For configurations with ${\omega }_1\approx {\omega }_2$, the ${\omega }_1-{\omega }_2$ mode represents the dominant first-order interaction effect due to significantly smaller effective Sperm number. For in-phase actuation with ${\omega }_1={\omega }_2$, the deflection dynamics are identical to an isolated filament with a modified Sperm number. Phase difference between the filaments is shown to have significant effect on the time-averaged forces. Optimal Sperm numbers for in-phase and antiphase actuation are calculated. Turning moments due to phase difference between the filaments are presented, yielding optimal maneuvering for phase of ${90}^{\circ }$. Calculation of the effect of hydrodynamic interaction on the propulsive forces yielded that antiphase beating is more efficient than the in-phase scenario, in contrast with the commonly used assumption of maximal efficiency of the synchronized state. Experiments are conducted to verify and illustrate some of the theoretical predictions.

The problem of two-phase flow in straight capillaries of polygonal cross section displays many of the dynamic characteristics of rapid interfacial motions associated with pore-scale displacements in porous media. Fluid inertia is known to be important in these displacements but is usually ignored in network models commonly used to predict macroscopic flow properties. This study presents a numerical model for two-phase flow which describes the spatial and temporal evolution of the interface between the fluids. The model is based on an averaged Navier-Stokes equation and is shown to be successful in predicting the complex dynamics of both capillary rise in round capillaries and imbibition along the corners of polygonal capillaries. The model can form the basis for more realistic network models which capture the effect of capillary, viscous, and inertial forces on pore-scale interfacial dynamics and consequent macroscopic flow properties.

Natural sculpting processes such as erosion or dissolution often yield universal shapes that bear no imprint or memory of the initial conditions. Here we conduct laboratory experiments aimed at assessing the shape dynamics and role of memory for the simple case of a dissolvable boundary immersed in a fluid. Though no external flow is imposed, dissolution and consequent density differences lead to gravitational convective flows that in turn strongly affect local dissolving rates and shape changes, and we identify two distinct behaviors. A flat boundary dissolving from its lower surface tends to retain its overall shape (an example of near perfect memory) while bearing small-scale pits that reflect complex near-body flows. A boundary dissolving from its upper surface tends to erase its initial shape and form an upward spike structure that sharpens indefinitely. We propose an explanation for these different outcomes based on observations of the coupled shape dynamics, concentration fields, and flows.

Active particles moving through fluids generate disturbance flows due to their activity. For simplicity, the induced flow field is often modeled by the leading terms in a far-field approximation of the Stokes equations, whose coefficients are the force, torque, and stresslet (zeroth- and first-order force moments) of the active particle. This level of approximation is quite useful, but may also fail to predict more complex behaviors that are observed experimentally. In this study, to provide a better approximation, we evaluate the contribution of the second-order force moments to the flow field and, by reciprocal theorem, present explicit formulas for the stresslet dipole, rotlet dipole, and potential dipole for an arbitrarily shaped active particle. As examples of this method, we derive modified Faxén laws for active spherical particles and resolve higher-order moments for active rod-like particles.