We study the logarithmic behavior of the pressure variance $\langle p^{{+}^2}\rangle$ from the datasets obtained from direct numerical simulations of turbulent channel flow for friction Reynolds number $\mathrm{R}{\mathrm{e}}_{\tau }$ up to $4000$. The higher-order moments of $p$ were found to follow logarithmic behaviors at the same distances from the wall where $\langle p^{{+}^2}\rangle$ shows its log profile. The same results have been confirmed for the spanwise velocity fluctuations $w$ at the same Reynolds numbers, with both $p$ and $w$ following a super-Gaussian behavior. The minimum Reynolds number for $\langle p^{{+}^2}\rangle$ and $\langle w^{{+}^2}\rangle$ log profiles to appear is $\mathrm{R}{\mathrm{e}}_{\tau }\approx 500$, where flow structures $\mathcal{O}\left(h\right)$ or less were found to significantly contribute to these profiles. The configuration of the hairpin eddy structures obtained from the conditional sampling at different wall-normal locations showed a strong link between $p$ and $w$ fluctuations. Positive pressure fluctuations are located between the legs of the hairpin eddy, while the negative pressure fluctuations are consistent with the head part of the hairpin eddy. Positive and negative spanwise velocity fluctuations are strongly positioned with the legs of the hairpin eddy, consistent with the counter-rotating motion resulting from the eddy legs. The structures were also found to be geometrically self-similar such that their length and their width increase linearly with the distance from the wall.

The transport of self-propelled particles such as bacteria and phoretic swimmers through crowded heterogeneous environments is relevant to many natural and engineering processes, from biofilm formation and contamination processes to transport in soils and biomedical devices. While there has been experimental progress, a theoretical understanding of mean transport properties in these systems has been lacking. In this work, we apply generalized Taylor dispersion theory to analyze the long-time statistics of an active self-propelled Brownian particle transported under an applied flow through the interstices of a periodic lattice that serves as an idealization of a porous medium. Our theoretical model, which we validate against Brownian dynamics simulations, is applied to unravel the roles of motility, fluid flow, and lattice geometry on asymptotic mean velocity and dispersivity. In weak flows, transport is dominated by active dispersion, which results from self-propulsion in the presence of noise and is hindered by the obstacles that act as entropic barriers. In strong flows, shear-induced Taylor dispersion becomes the dominant mechanism for spreading, with pillars now acting as regions of shear production that enhance dispersion. The interplay of these two effects leads to complex and unexpected trends, such as a nonmonotonic dependence of axial dispersivity on flow strength and a reduction in dispersion due to swimming activity in strong flows. Brownian dynamics are used to cast light on the preasymptotic regime, where tailed distributions are observed in agreement with recent experiments on motile microorganisms. Our results also highlight the subtle effects of pillar shape, which can be used to control the magnitude of dispersion and to drive a net particle migration in quiescent systems.

This work presents two-dimensional (2D) simulations on a cylindrical Richtmyer-Meshkov instability (RMI) in magnetohydrodynamics (MHD). Three studies are presented in an effort to quantify and qualify the evolution of the MHD RMI by varying the magnetic field orientation, strength of the magnetic field, and strength of the shock wave driving the instability. The orientations considered herein are either parallel or perpendicular to the shock wave motion. The second study varies the magnetic fields between 100, 250, and 500 gauss (G), while the third study considers incident shock wave Mach numbers $M=1.2,M=1.66$, and $M=2.2$. These parameter ranges were selected to be easily achievable in experiments while the interface perturbation was selected such that its evolution is independent of either the shock wave or magnetic field orientations independently. It was found that the MHD RMI evolution is dependent upon the magnetic field orientation relative to the shock transit direction as well as their individual magnitudes. This is because the mechanism of suppression, attributed to Alfven waves, is a function of the magnetic field strength and the orientation of the magnetic field, while the mechanism of RMI evolution, baroclinic vorticity deposition, is a function of the Mach number. Stronger magnetic fields were found to provide greater mixing suppression and have significant effects on RMI-like interface morphology. Finally, increasing the shock wave strength generated competing effects between higher RMI vorticity deposition and greater vorticity removal from the interface by faster Alfven waves.

The low-speed vertical entry of a sphere onto a two-phase fluid consisting of an oil lens floating on a water surface is examined in experiments using spheres with different radii, densities, and materials. Oil coats both the leading edge of the sphere as it penetrates the free surface of the two-phase fluid and the wall of the air-entraining cavity that forms behind the descending sphere. Spheres with lower inertia form smooth cavities whereas spheres with higher inertia develop a three-dimensional crumpled morphology along the cavity wall that we demonstrate is due to a shear-induced instability between the oil layer and surrounding water near the sphere front. Despite these different dynamics, the sphere depth at collapse, either by deep seal or rupture, scales logarithmically with sphere mass for all of the spheres examined. We also observe, for the first time to our knowledge, the following phenomena: As air evacuates the necked region of the cavity, the oil coating the cavity forms an oil filament tethering the two disjoint air cavities together before eventually breaking up into satellite drops. For the experimental conditions in this study, the oil lens at the free surface is critical to forming an air-entraining cavity; with no oil lens, only a small air pocket forms as the water completely wets the spheres either sealing the free surface or forming a quasistatic cavity.

Thermochemical nonequilibrium is one of the most challenging issues when dealing with hypersonic flows experienced by objects (space vehicles, meteoroids, space debris) at atmospheric entry. The case of a hypersonic flow past a sphere is considered as a test model for systems in strong chemical and thermal nonequilibrium conditions, mimicking the extreme environment experienced by objects entering a planetary atmosphere. The problem has been studied using the state-to-state approach, calculating directly the distribution of vibrational levels of ${\mathrm{O}}_2$ and ${\mathrm{N}}_2$, together with the flow field, including also viscous effects. Nonequilibrium distributions are observed and the results have been compared with macroscopic experimental data, showing that the state-to-state model is able to provide better capabilities for predicting experimental results than the traditional multitemperature approach. The use of graphics processing units allowed us to obtain these results in a two-dimensional configuration, opening additional perspectives in the investigation of reacting flows.

A conventional and a high fidelity direct simulation Monte Carlo approach of internal energy transfer and chemical reactions are considered in application to a number of cases where validation data are available. Normal shock wave, hypersonic flow over a wedge, a sphere, and a double cone are considered, and measured and computed flow and surface properties are compared. The primary objective is to examine the impact of the model of each particular physical process which contributes to flow thermal and chemical nonequilibrium. For the considered conditions, with free stream gases of oxygen, nitrogen, and air, flow velocities ranging from 3 to 6 km/s, and Knudsen numbers on the order of 0.001, the change in the internal energy transfer and chemical reaction models was found to have a relatively small effect on the surface properties. The only notable exception is nitrogen gas-phase recombination, which drastically increases the heat flux to the wall.

We investigate the effects of topological disorder and wettability on fluid displacement in porous media. A modified disorder index $I_v$ is proposed to characterize the disorder of porous media. By changing $I_v$, different displacement patterns (stable displacement and fingering) under the same flow condition and fluid property are obtained. We analytically demonstrate how increase in disorder promotes fingering due to uneven distribution of local capillary pressure. It is shown that the displacement efficiency for different wettability conditions and disorder well correlates with the distribution of local capillary pressure. A power-law relation between fluid-fluid interfacial length and saturation of invading fluid is proposed by taking geometry into account, where the parameters in power-law relation can be predicted by the capillary index, $I_c$, unifying the effects of topological disorder and wettability.

The structure of inner-outer interactions in a smooth-wall turbulent boundary layer is investigated using high-frame-rate particle image velocimetry (PIV) with two overlapping fields of view. A refractive-index-matched facility is used to enable the resolution of turbulent structures very close to the wall where these modulation effects are dominant. Amplitude and frequency modulation correlation coefficients were first investigated by computing single-, two-, and multiple-point correlation analyses now routinely reported in the literature. The wall-normal trends in amplitude modulation for the streamwise and wall-normal velocities and in frequency modulation for the streamwise velocity are consistent with those previously reported in the literature, validating the efficacy of the PIV approach used herein. The frequency modulation behavior for wall-normal velocity, however whose behavior in this regard has received little attention in the literature, differs from its amplitude modulation counterpart in the near-wall region. It is not clear whether this difference is physical or a by-product of enhanced sensitivity to measurement noise and/or finite spatial resolution of the measurements. Leveraging the spatial and temporal nature of the PIV data, a conditional average-based method is extended to the PIV data to directly capture the spatiotemporal signature of these interactions. This spatiotemporal picture reveals that the small-scale variance in streamwise and wall-normal velocity fluctuations not only correlates with the slow variations of the large scales in the logarithmic region, but also leads the local large scales (measured using a single hot wire, for example). These observations clearly indicate a structure akin to that proposed by Baars et al. [W. J. Baars et al., Exp. Fluids 56, 188 (2015)], including the relative positions of the modulated and modulating scales. The independence of these observations from filter choice is also shown, with equivalent correlation coefficients developed based on the conditional averaging analysis.

We study the contact line dynamics of a liquid drop on a substrate at temperature $T_s$ colder than the freezing temperature $T_m$. The purpose is to determine experimentally the criterion for a solidification-induced pinning of the liquid at its triple line. The sub- strate is driven at constant velocity, while the upper part of the drop is pinned to the injection pipe. Within a certain range of substrate velocity and temperature difference $T_m-T_s$, the solidification can induce contact-line pinning. This pinning occurs when the velocity of the substrate is slower than a critical value $V_c$ and leads to a discontinuous stick-slip dynamics of the contact line, while at high enough velocity the contact-line motion remains continuous. Stick-slip dynamics appear when the solid front, showing dendritic structure, catches up the advancing contact line. We study the dynamics of the stick-slip regime at different substrate velocities $V_s$, $T_m-T_s$, and injection flow rate $Q$. We relate the dependence of $V_c$ on $T_m-T_s$ to the velocity of the solidification front $V_f$ calculated and measured with an independent experiment. These results are consistent with a mechanism of kinetic undercooling where the front velocity follows a trend reminiscent to that measured and predicted in dendritic solidification front growth.

In this paper, we present a generalized framework of incorporating vortex identifiers into subgrid-scale (SGS) models for large-eddy simulation. This research is inspired by the keystone principle of modern turbulence theory that kinetic energy is cascaded from large to small scales by the vortex stretching mechanism. We propose that regions without local vortex structures do not possess significant subgrid motions due to the lack of energy cascade and therefore do not need significant SGS stresses/dissipation, whereas strong local SGS dissipation should be applied in regions with strong small-scale (close to the cutoff length scale) vortices owing to the subgrid motions enhanced by the vortex stretching mechanism. Following this idea, four new SGS models are constructed based on four different vortex identifiers. The new models possess some important characteristics of the vortex identifiers, including sensitivity to small-scale vortices and Galilean invariance. The correct near-wall cubic asymptotic behavior for the SGS viscosity is also satisfied by the new models. The proposed models are validated using three test cases, including isotropic decaying turbulence, isotropic forced turbulence, and fully developed turbulent channel flow. The proposed models are robust without any local clipping/filtering or averaging along homogeneous direction(s). The results indicate that the proposed models automatically apply stronger SGS dissipation to small-scale motions, and predict satisfactory turbulence statistics with less computational expense compared with the conventional dynamical Smagorinsky model.

In the linear approximation, we study long-wave scattering on an axially symmetric flow in a shallow water basin with a drain in the center. Besides of academic interest, this problem is applicable to the interpretation of recent laboratory experiments with draining bathtub vortices and description of wave scattering in natural basins, and also can be considered as the hydrodynamic analog of scalar wave scattering on a rotating black hole in general relativity. The analytic solutions are derived in the low-frequency limit to describe both pure potential perturbations (surface gravity waves) and perturbations with nonzero potential vorticity. For the moderate frequencies, the solutions are obtained numerically and illustrated graphically. It is shown that there are two processes governing the dynamics of surface perturbations, the scattering of incident gravity water waves by a central vortex, and emission of gravity water waves stimulated by a potential vorticity. Some aspects of their synergetic actions are discussed.

Motivated by bacterial transport through porous media, here we study the swimming of an actuated, flexible helical filament in both three-dimensional free space and within a cylindrical tube whose diameter is much smaller than the length of the helix. The filament, at rest, has a native helical shape modeled after the geometry of a typical bacterial flagellar bundle. The finite length filament is a free swimmer and is driven by an applied torque as well as a countertorque (of equal strength and opposite direction) that represents a virtual cell body. We use a regularized Stokeslet framework to examine the shape changes of the flexible filament in response to the actuation as well as the swimming performance as a function of the nondimensional Sperm number that characterizes the elastohydrodynamic system. We also show that a modified Sperm number may be defined to characterize the swimming progression within a tube. Finally, we demonstrate that a helical filament whose axis is not aligned with the tube axis can exhibit centering behavior in the narrowest tubes.

An experiment of thermal convection with significant compressible effects is presented. The high-gravity environment of a centrifuge and the choice of xenon gas enable us to observe an average adiabatic temperature gradient up to $3.5\mathrm{K}{\mathrm{cm}}^{-1}$ over a 4 cm high cavity. At the highest rotation rate investigated, 9990 rpm, the superadiabatic temperature difference applied to the gas layer is less than the adiabatic temperature difference. The convective regime is characterized by a large Rayleigh number, about ${10}^{12}$, and dominant Coriolis forces (Ekman number of order ${10}^{-6}$). The analysis of temperature and pressure fluctuations in our experiments shows that the dynamics of the flow is in a quasigeostrophic regime. Still, a classical power law (exponent $0.3\pm 0.04$) is observed between the Nusselt number (dimensionless heat flux) and the superadiabatic Rayleigh number (dimensionless superadiabatic temperature difference). However, a potential hysteresis is seen between this classical high flux regime and a lower heat flux regime. It is unclear whether this is due to compressible or Coriolis effects. In the transient regime of convection from an isothermal state, we observe a local decrease of temperature which can only be explained by adiabatic decompression.

Viscous fingering patterns can form at the interface between two immiscible fluids confined in the gap between a pair of flat plates; whenever the fluid with lower viscosity displaces the one of higher viscosity the interface is unstable. For miscible fluids the situation is more complicated due to the formation of interfacial structure in the thin dimension spanning the gap. Here we study the effect of the inherent diffusion between the two miscible fluids on this structure and on the viscous fingering patterns that emerge. We discover an unexpected transition separating two distinct regimes where the pattern morphologies and mode of onset are different. This transition is marked by a regime of transient stability as the structure of the fingers evolves from having three-dimensional structure to being quasi-two-dimensional. The presence of diffusion allows an instability to form where it was otherwise forbidden.

The question of the place where a fluid flow separates on a curved obstacle is among the most difficult in fluid mechanics. A criterion based on the cancellation, at that place, of the inviscid flow singularity was proposed by Brillouin [Annal. Chimie Phys. 23, 145 (1911)] and Villat [J. Math. Pures Appl. 10, 231 (1914)], which is at the starting point of the triple-deck theory. A similar question arises for the flow over an erodible sand dune with sharp crest, where the a priori unknown dune profile and location of the crest result from the coupling of the fluid flow with the sand motion at the dune surface. We show, by computing the potential flow with Levi-Civita's conformal transformation and using a standard closure law for the shear stress driving the sand flux, that the Brillouin-Villat condition here provides the appropriate criterion. We emphasize that within the present model where the bed shear stress is in phase with the flow velocity, so that the flat bed is linearly stable, it is the separation which allows the existence of a self-preserving dune shape. For a dune traveling without deformation on a nonerodible ground, the Brillouin-Villat condition eventually selects its velocity. A parallel is drawn with the Kutta-Joukovski condition for the flow around an airfoil.

The streamline segmentation method proposed by Wang is applied to a turbulent wavy channel flow to investigate the impact of pressure-driven strain on the streamline segment probability distribution. While the asymmetrical shape of the probability distribution is known to react to streamwise strains, in regions of detached flow this impact is severely less pronounced. Using tomographic particle-image velocimetry measurements and numerical data in attached and detached flow, the origin for this observation is found in the strong compressive strain during attached flow. The responsible mechanism is determined by introducing a concept of streamline segment locality, adapting the propagation equation for streamline segment statistics to inhomogeneous flow and applying it to the numerical data. A locally increased segment cutting rate is identified to cause the reduced sensitivity of the segment probability distribution to the local strain.

The role of the spatial structure of a turbulent flow in enhancing particle collision rates in suspensions is an open question. We show and quantify, as a function of particle inertia, the correlation between the multiscale structures of turbulence and particle collisions: Straining zones contribute predominantly to rapid head-on collisions compared to vortical regions. We also discover the importance of vortex-strain worm-rolls, which goes beyond ideas of preferential concentration and may explain the rapid growth of aggregates in natural processes, such as the initiation of rain in warm clouds.

Droplets that glide along a bath of the same fluid are seen to scatter from a cylindrical meniscus analogous to Rutherford scattering of like-charged atomic particles. We define the impact parameter, $b$, as the distance between the tangent line to the initial trajectory of the droplet and the parallel radial line from the center of the target. The scattering angle, ${\theta }_S$, and the distance of closest approach, $r_{\mathrm{C}}$, are measured as functions of $b$. Using numerical methods to model the experimental results, we confirm previous theoretical results that the approximate profile of the meniscus is given by a Bessel function for regions distant from the contact line of the meniscus.

The unsteady behavior of an Edney type-IV shock-dominated hypersonic separated flows over a double-wedge geometry for different gas compositions are studied using the time-accurate direct-simulation Monte Carlo (DSMC) and window proper orthogonal decomposition (WPOD) methods. Near steady state, we find that the POD modes can be correlated with the global modes predicted by linear stability theory. The WPOD analyses show that the first mode for each flow quantity outlines the corresponding steady-state solution and that higher spatial POD modes are pronounced in the bow shock, separation, and transmitted shocks and shear layers, thereby coupling these regions. The temporal modes corresponding to each macroscopic flow quantities are observed to have the same decay rates. The effects of three types of gas compositions—molecular nitrogen, nonreacting air consisting of molecular nitrogen and oxygen, and reacting air with oxygen dissociation and the ${\mathrm{N}}_2$ + O exchange reactions—on flow stability are considered. Nonequilibrium thermochemical effects are found to change the shock structures, the size of the separation region, and the time required to reach steady state. The decay rate of the least damped eigenmode for the chemically reacting air case is found to be smaller in comparison to the nonreacting air case since the translational temperatures downstream of the bow shock are lower due to endothermic chemical reactions. The simulated heat fluxes and shock standoff distance are found to be in qualitative agreement with recent experiments where the freestream density is eight times higher than the current DSMC computations.

When evaporated on a substrate, a droplet containing solutes usually deposits the solutes onto the substrate in a coffee-ring pattern. Recent experiments have shown that substrate permeability can suppress the coffee-ring pattern and promote more uniform solute deposition. Motivated by these observations, we have developed a lubrication-theory-based model to describe imbibition and evaporation of droplets of colloidal suspensions on permeable substrates. The model consists of a system of one-dimensional partial differential equations accounting for the changing droplet shape and depth-averaged concentration of colloidal particles. We also incorporate a precursor film, disjoining pressure, and substrate topography to control contact-line motion of the droplet. Solvent evaporation is described using the well-known one-sided model, and imbibition of solvent by the substrate is assumed to only depend on the excess pressure on the liquid side. The governing equations are solved with finite-difference methods. Our results reveal that solvent evaporation and solvent imbibition have the same qualitative effect on the final particle deposition pattern. For the case where the substrate is smooth, we find that increasing imbibition or evaporation leads to a transition from a cone-shaped deposition pattern to a ring-shaped deposition pattern. For the case where the substrate is rough, the droplet contact line is pinned at a defect on the substrate, and the pinning-depinning transition leads to the bull's-eye deposition pattern often observed in experiments. Finally, we also find that particle adsorption onto the substrate can promote more uniform particle deposition patterns for both smooth and rough substrates, and solvent imbibition can indirectly suppress the coffee-ring pattern by inducing more particle adsorption.