The hydrodynamics of liquid flowing past gas sectors of unidirectional superhydrophobic surfaces is revisited. Attention is focused on the local slip boundary condition at the liquid-gas interface, which is equivalent to the effect of a gas cavity on liquid flow. The system is characterized by a large viscosity contrast between liquid and gas $\mu /{\mu }_g\gg 1$. We interpret earlier results, namely, the dependence of the local slip length on the flow direction, in terms of a tensorial local slip boundary condition and relate the eigenvalues of the local local slip tensor to the texture parameters, such as the width of the groove $\delta$ and the local depth of the groove $e(y,\alpha )$. The latter varies in the direction $y$, orthogonal to the orientation of stripes, and depends on the bevel angle of the groove's edges, $\pi /2-\alpha$, at the point where three phases meet. Our theory demonstrates that when grooves are sufficiently deep their eigenvalues of the local slip length tensor depend only on $\mu /{\mu }_g,\delta$, and $\alpha$, but not on the depth. The eigenvalues of the local slip length of shallow grooves depend on $\mu /{\mu }_g$ and $e(y,\alpha )$, although the contribution of the bevel angle is moderate. In order to assess the validity of our theory we propose an approach to solve the two-phase hydrodynamic problem, which significantly facilitates and accelerates calculations compared to conventional numerical schemes. The numerical results show that our simple analytical description obtained for limiting cases of deep and shallow grooves remains valid for various unidirectional textures.

Single-point hot-wire measurements are made downstream of a series of spanwise repeating obstacles that are used to generate an artificially thick turbulent boundary layer. The measurements are made in the near field, in which the turbulent boundary layer is beginning to develop from the wall-bounded wakes of the obstacles. The recent paper of Rodríguez-López et al. [E. Rodríguez-López et al., Phys. Rev. Fluids 1, 074401 (2016)] broadly categorized the mechanisms by which canonical turbulent boundary layers eventually develop from wall-bounded wakes into two distinct mechanisms, the wall-driven and wake-driven mechanisms. In the present work we attempt to identify the geometric parameters of tripping arrays that trigger these two mechanisms by examining the spectra of the streamwise velocity fluctuations and the intermittent outer region of the flow. Using a definition reliant upon the magnitude of the velocity fluctuations, an intermittency function is devised that can discriminate between turbulent and nonturbulent flow. These results are presented along with the spectra in order to try to ascertain which aspects of a trip's geometry are more likely to favor the wall-driven or wake-driven mechanism. The geometrical aspects of the trips tested are the aspect ratio, the total blockage, and the blockage at the wall. The results indicate that the presence, or not, of perforations is the most significant factor in affecting the flow downstream. The bleed of fluid through the perforations reenergizes the mean recirculation and leads to a narrower intermittent region with a more regular turbulent-nonturbulent interface. The near-wall turbulent motions are found to recover quickly downstream of all of the trips with a wall blockage of 50%, but a clear influence of the outer fluctuations, generated by the tip vortices of the trips, is observed in the near-wall region for the high total blockage trips. The trip with 100% wall blockage is found to modify the nature of the inner-wall peak of turbulent kinetic energy.

We present numerical simulations of steady, laminar, axisymmetric convection of a Boussinesq fluid in a shallow, rotating, cylindrical domain. The flow is driven by an imposed vertical heat flux and shaped by the background rotation of the domain. The geometry is inspired by that of tropical cyclones and the global flow pattern consists of a shallow swirling vortex combined with a poloidal flow in the $r\text{−}z$ plane which is predominantly inward near the bottom boundary and outward along the upper surface. Our numerical experiments confirm that, as suggested in our recent work [L. Oruba et al., J. Fluid Mech. 812, 890 (2017)], an eye forms at the center of the vortex which is reminiscent of that seen in a tropical cyclone and is characterized by a local reversal in the direction of the poloidal flow. We establish scaling laws for the flow and map out the conditions under which an eye will, or will not, form. We show that, to leading order, the velocity scales with $V={\left(\alpha g\beta \right)}^{1/2}H$, where $g$ is gravity, $\alpha$ is the expansion coefficient, $\beta$ is the background temperature gradient, and $H$ is the depth of the domain. We also show that the two most important parameters controlling the flow are $\mathrm{Re}=VH/\nu$ and $\mathrm{Ro}=V/\left(\mathrm{\Omega }H\right)$, where $\mathrm{\Omega }$ is the background rotation rate and $\nu$ the viscosity. The Prandtl number and aspect ratio also play an important, if secondary, role. Finally, and most importantly, we establish the criteria required for eye formation. These consist of a lower bound on $\mathrm{Re}$, upper and lower bounds on $\mathrm{Ro}$, and an upper bound on the Ekman number.

The temporal modal and nonmodal growth of three-dimensional perturbations in the boundary layer flow over an infinite compliant flat wall is considered. Using a wall-normal velocity and wall-normal vorticity formalism, the dynamic boundary condition at the compliant wall admits a linear dependence on the eigenvalue parameter, as compared to a quadratic one in the canonical formulation of the problem. As a consequence, the continuous spectrum is accurately obtained. This enables us to effectively filter the pseudospectra, which is a prerequisite to the transient growth analysis. An energy-budget analysis for the least-decaying hydroelastic (static divergence, traveling wave flutter, and near-stationary transitional) and Tollmien-Schlichting modes in the parameter space reveals the primary routes of energy flow. Moreover, the maximum transient growth rate increases more slowly with the Reynolds number than for the solid wall case. The slowdown is due to a complex dependence of the wall-boundary condition with the Reynolds number, which translates into a transition of the fluid-solid interaction from a two-way to a one-way coupling. Unlike the solid-wall case, viscosity plays a pivotal role in the transient growth. The initial and optimal perturbations are compared with the boundary layer flow over a solid wall; differences and similarities are discussed.

In convergent geometry, the Bell-Plesset (BP) effects modify the growth of hydrodynamic instability in comparison with the planar geometry. They account for acceleration, convergence of the flow, and compressibility of the fluids. To study these effects, the Richtmyer-Meshkov (RM) instability is examined in cylindrical geometry through shock tube experiments. To ease comparisons with models, the canonical single-mode sinusoidal perturbation at the gas interface is considered. The experimental results display a linear time-dependent growth of the amplitude of the instability. First, by cross-checking experiments and numerical simulations with the Hesione code, this peculiar growth for convergent geometry is confirmed. Second, we theoretically explain these results. We derive a new model for the growth of the perturbation in the linear regime of the instability for compressible fluids. Then, it is used to initiate a weakly nonlinear model. This model demonstrates that the linear time-dependent growth of the studied RM instability is due to the nonlinear saturation of the destabilizing BP effects at the interface. This study indicates the importance of taking into account even a slight deceleration of the interface and the compressibility of fluids by correctly describing the background velocity field, which is generated by converging shock waves.

In molecular dynamics simulations, nanochannel flows are usually driven by a constant force, that aims to represent a pressure difference between inlet and outlet, and periodic boundary conditions are applied in the streamwise direction resulting in an homogeneous flow. The homogeneity hypothesis can be eliminated adding reservoirs at the inlet and outlet of the channel which permits us to predict streamwise variation of flow properties. It also opens the door to drive the flow by applying a pressure gradient instead of a constant force. We analyze the impact of these modeling modifications in the prediction of the flow properties, and we show when they make a difference with respect to the standard approach. It turns out that both assumptions are irrelevant when low pressure differences are considered, but important differences are observed at high pressure differences. They include the density and velocity variation along the channel (the mass flow rate is constant) but, more importantly, the temperature increase and slip length decrease. Because viscous heating is important at high shear rates, these modeling issues are also linked to the use of thermostating procedures. Specifically, selecting the region where the thermostat is applied has a critical influence on the results. Whereas in the traditional homogeneous model the choices are limited to the fluid and/or the wall, in the inhomogeneous cases the reservoirs are also available, which permits us to leave the region of interest, the channel, unperturbed.

The maximum spreading diameter of complex fluid droplets has been extensively studied and explained by numerous physical models. This research focuses therefore on a different aspect, the bulging outer rim observed after evaporation on the final dried pattern of blood droplets. A correlation is found between the inner diameter, the maximum outer diameter, and the impact speed. This shows how the drying mechanism of a blood drip stain is influenced by the impact energy, which induces a larger spreading diameter and thus a different redistribution of red blood cells inside the droplet. An empirical relation is established between the final dried pattern of a passive bloodstain and its impact speed, yielding a possible forensic application. Indeed, being able to relate accurately the energy of the drop with its final pattern would give a clue to investigators, as currently no such simple and accurate tool exists.

Pulsating bubbles have proved to be a versatile tool for trapping and sorting particles. In this article, we investigate the different streaming patterns that can be obtained with a group of bubbles in a confined geometry under ultrasound. In the presence of an external flow strong enough to oppose the streaming velocities but not drag the trapped bubbles, we observe either the appearance of exclusion zones near the bubbles or asymmetric streaming patterns that we interpret as the superposition of a two-dimensional (2D) streaming function and of a potential flow. When studying a lattice of several bubbles, we show that the streaming pattern can be accurately predicted by superimposing the contributions of every pair of bubbles present in the lattice, thus allowing one to predict the sizes and the shapes of exclusion zones created by a group of bubbles under acoustic excitation. We suggest that such systems could be used to enhance mixing at a small scale or to catch and release chemical species initially trapped in vortices created around bubble pairs.

The spectrally truncated, or finite dimensional, versions of several equations of inviscid flows display transient solutions which match their viscous counterparts, but which eventually lead to thermalized states in which energy is in equipartition between all modes. Recent advances in the study of the Burgers equation show that the thermalization process is triggered after the formation of sharp localized structures within the flow called “tygers.” We show that the process of thermalization first takes place in well defined subdomains, before engulfing the whole space. Using spatio-temporal analysis on data from numerical simulations, we study propagation of tygers and find that they move at a well defined mean speed that can be obtained from energy conservation arguments.

Ice crystals are present in a variety of clouds, at sufficiently low temperature. We consider here mixed-phase clouds which, at temperature $\gtrsim -20{}^{\circ }\text{C}$, contain ice crystals, shaped approximately as thin oblate ellipsoids. We investigate the motion of these particles transported by an isotropic turbulent flow and, in particular, the collision between these crystals, a key process in the formation of graupels. Using fully resolved direct numerical simulations, and neglecting the effects of fluid inertia on the particle motion, we determine the influence of the turbulence intensity and of gravitational settling, in a realistic range of parameters. At small turbulent energy dissipation rate, collisions are induced mainly by differential gravitational settling between particles with different orientations. The effect has a clear signature on the relative orientation of colliding ellipsoids. As the turbulent energy dissipation rate increases, however, the influence of the turbulent velocity fluctuations becomes the dominant effect determining the collision rate. Using simple estimates, we propose an elementary understanding of the relative importance of gravitational settling and turbulent fluctuations.

The three-dimensional structure of the flow downstream of a circular cylinder, either fixed or subjected to vortex-induced vibrations, is investigated by means of numerical simulation, at Reynolds number 3900, based on the cylinder diameter and current velocity. The flow exhibits pronounced fluctuations distributed along the span in all studied cases. Qualitatively, it is characterized by spanwise undulations of the shear layers separating from the body and the development of vortices elongated in the plane normal to its axis (planar vortices). A quantitative analysis of crossflow vorticity fluctuations in the spanwise direction reveals a peak of fluctuation amplitude in the near region (i.e., area of formation of the spanwise wake vortices) and opposite trends of the spanwise wavelength in the shear layer and wake regions; the wavelength tends to decrease as a function of the streamwise distance in the shear layers down to a minimum value close to 0.5 body diameters and then slowly increases further in the wake. The spanwise structure of the flow is differently altered in these two regions, once the cylinder vibrates. In the shear layer region, body motion is associated with an enhancement of planar vortex formation. The amplification of vorticity spanwise fluctuations in this region is accompanied by a reduction of the spanwise wavelength; it is found to decrease as a function of the instantaneous Reynolds number based on the instantaneous flow velocity seen by the moving body, following the global trend of the wavelength versus Reynolds number previously reported for fixed cylinders. In the wake region, the flow spanwise structure is essentially unaltered compared to the fixed body case, in spite of the major distortions of the streamwise and crossflow length scales.

The dynamics of an incompressible turbulent air jet from an annular source into otherwise quiescent surroundings are investigated. Focusing on a slender annulus with an open core, the development of the jet is examined using planar and stereoscopic particle image velocimetry (PIV) from the source to 16 (outer) source diameters downstream. Unique to these annular sources, the jet induces a flow through the open core—in other words, the core is “ventilated.” Our measurements indicate that the volume flux drawn through the core exceeds that from the source by approximately 20%. Based on the streamwise development of the jet, we identify four distinct regions: (i) an internal region of induced flow that is bounded by the jet; (ii) a near-field planar-jet-like region; (iii) a transition region; and, ultimately, (iv) a far-field round-jet-like region. We explore the evolution of the jet toward self-similar behavior based on cross-stream profiles of time-averaged velocity and turbulence statistics within these different regions. Four distinct length scales are shown to characterize the streamwise extents and behaviors within the regions identified. Finally, to highlight the role of the open-core (ventilated) annular geometry on jet development, comparisons are made with PIV measurements of turbulent jets issuing from circular sources. These comparisons reveal that the ventilated geometry significantly enhances dilution in the near field.

We study, using direct numerical simulations, the effect of geometrical confinement on heat transport and flow structure in Rayleigh-Bénard convection in fluids with different Prandtl numbers. Our simulations span over two decades of Prandtl number Pr, $0.1\le \mathrm{Pr}\le 40$, with the Rayleigh number Ra fixed at ${10}^8$. The width-to-height aspect ratio $\mathrm{\Gamma }$ spans between 0.025 and 0.25, while the length-to-height aspect ratio is fixed at one. We first find that for $\mathrm{Pr}\ge 0.5$, geometrical confinement can lead to a significant enhancement in heat transport as characterized by the Nusselt number Nu. For those cases, Nu is maximal at a certain $\mathrm{\Gamma }={\mathrm{\Gamma }}_{\mathrm{opt}}$ and the maximal relative enhancement generally increases with Pr over the explored parameter range. As opposed to the situation of $\mathrm{Pr}\ge 0.5$, confinement-induced enhancement in Nu is not realized for smaller values of Pr, such as 0.1 and 0.2. The Pr dependence of the heat transport enhancement can be understood in its relation to the coverage area of the thermal plumes over the thermal boundary layer (BL) where larger coverage is observed for larger Pr due to a smaller thermal diffusivity. We further show that ${\mathrm{\Gamma }}_{\mathrm{opt}}$ is closely related to the crossing of thermal and momentum BLs and find that Nu declines sharply when the thickness ratio of the thermal and momentum BLs exceeds a certain value of about one. In addition, through examining the temporally averaged flow fields and two-dimensional mode decomposition, it is found that for smaller Pr the large-scale circulation is robust against the geometrical confinement of the convection cell. We further found that ${\mathrm{\Gamma }}_{\mathrm{opt}}$ exhibits a power-law relation with Pr as ${\mathrm{\Gamma }}_{\mathrm{opt}}=0.11{\mathrm{Pr}}^{-0.060\pm 0.004}$. Together with the result ${\mathrm{\Gamma }}_{\mathrm{opt}}=29.37{\mathrm{Ra}}^{-0.31}$ found by Chong et al. [Phys. Rev. Lett. 115, 264503 (2015)], our findings provide a more complete picture of the geometrical confinement.

Precise measurements of the torque in a von Kármán swirling flow between a rotating and a stationary smooth disk in three Newtonian fluids with different dynamic viscosities are reported. From these measurements the dependence of the normalized torque, called the friction coefficient, on $\text{Re}$ is found to be of the form $C_f=1.17(\pm 0.03){\text{Re}}^{-0.46\pm 0.003}$ where the scaling exponent and coefficient are close to that predicted theoretically for an infinite, unshrouded, and smooth rotating disk which follows from an exact similarity solution of the Navier-Stokes equations, obtained by von Kármán. An error analysis shows that deviations from the theory can be partially caused by background errors. Measurements of the azimuthal $V_{\theta }$ and axial velocity profiles along radial and axial directions reveal that the flow core rotates at $V_{\theta }/r\mathrm{\Omega }\simeq 0.22$ (up to $z\approx 4$ cm from the rotating disk and up to $r_0/R\simeq 0.25$ in the radial direction) in spite of the small aspect ratio of the vessel. Thus the friction coefficient shows scaling close to that obtained from the von Kármán exact similarity solution, but the observed rotating core provides evidence of the Batchelor-like solution [Q. J. Mech. Appl. Math. 4, 29 (1951)] different from the von Kármán [Z. Angew. Math. Mech. 1, 233 (1921)] or Stewartson [Proc. Camb. Philos. Soc. 49, 333 (1953)] one.

Recent reports of surface forces across nanoconfined ionic liquids have revealed the existence of an anomalously long-ranged interaction apparently of electrostatic origin. Ionic liquids are viscous, and therefore it is important to inspect rigorously whether the observed repulsive forces are indeed equilibrium forces or, rather, arise from the viscous force during drainage of the fluid between two confining surfaces. In this paper we present our direct measurements of surface forces between mica sheets approaching in the ionic liquid $\left[{\mathrm{C}}_2{\mathrm{C}}_1\mathrm{Im}\right]\left[{\mathrm{NTf}}_2\right]$, exploring three orders of magnitude in approach velocity. Trajectories are systematically fitted by solving the equation of motion, allowing us to disentangle the viscous and equilibrium contributions. First, we find that the drainage obeys classical hydrodynamics with a negative slip boundary condition in the range of the structural force, implying that a $\mathrm{nanometer}$-thick portion of the liquid in the vicinity of the solid surface is composed of ordered molecules that do not contribute to the flow. Second, we show that a long-range static force must indeed be invoked, in addition to the viscous force, in order to describe the data quantitatively. This equilibrium interaction decays exponentially and with decay length in agreement with the screening length reported for the same system in previous studies. In those studies the decay was simply checked to be independent of velocity and measured at a low approach rate, rather than explicitly taking account of viscous effects: we explain why this gives indistinguishable outcomes for the screening length by noting that the viscous force is linear to very good approximation over a wide range of distances.

The propulsion of active colloids made from silica microspheres half coated with platinum is experimentally probed in solutions of hydrogen peroxide as a function of solution viscosity. The velocity is shown to decay approximately inversely with viscosity. Further, the type of viscosifier used affects the interaction between fuel molecules and motor, which affects propulsion. The quantification of how a viscosifier alters both viscosity and interactions is interpreted using existing diffusion-reaction models of self-diffusiophoresis.

The present study analyzes differential diffusion and the mechanisms responsible for it with regard to the turbulent/nonturbulent interface (TNTI) with special focus on model development for scale-resolving simulations. In order to analyze differences between resolved and subfilter phenomena, direct numerical simulation (DNS) data are compared with explicitly filtered data. The DNS database stems from a temporally evolving turbulent plane jet transporting two passive scalars with Schmidt numbers of unity and 0.25 presented by Hunger et al. [F. Hunger et al., J. Fluid Mech. 802, R5 (2016)]. The objective of this research is twofold: (i) to compare the position of the turbulent-nonturbulent interface between the original DNS data and the filtered data and (ii) to analyze differential diffusion and the impact of the TNTI with regard to scale resolution in the filtered DNS data. For the latter, differential diffusion quantities are studied, clearly showing the decrease of differential diffusion at the resolved scales with increasing filter width. A transport equation for the scalar differences is evaluated. Finally, the existence of large scalar gradients, gradient alignment, and the diffusive fluxes being the physical mechanisms responsible for the separation of the two scalars are compared between the resolved and subfilter scales.

Turbulent spots surrounded by laminar flow are a landmark of transitional shear flows, but the dependence of their kinematic properties on spatial structure is poorly understood. We here investigate this dependence in pipe flow for Reynolds numbers between 1500 and 5000. We compute spatially localized relative periodic orbits in long pipes and show that their upstream and downstream fronts decay exponentially towards the laminar profile. This allows us to model the fronts by employing the linearized Navier-Stokes equations, and the resulting model yields the spatial decay rate and the front velocity profiles of the periodic orbits as a function of Reynolds number, azimuthal wave number, and propagation speed. In addition, when applied to a localized turbulent puff, the model is shown to accurately approximate the spatial decay rate of its upstream and downstream tails. Our study provides insight into the relationship between the kinematics and spatial structure of localized turbulence and more generally into the physics of localization.

We assess the ability of a self-propelled swimmer to displace a volume of fluid that is large compared to its own volume via the mechanism of partial drift. The swimmer performs rectilinear locomotion in an incompressible, unbounded Newtonian fluid. The partial drift volume $D$ is the volume of fluid enclosed between the initial and final profiles of an initially flat circular disk of marked fluid elements; the disk is initially aligned perpendicular to the direction of locomotion and subsequently distorted due to the passage of the swimmer, which travels a finite distance. To focus on the possibility of large-scale drift, we model the swimmer simply as a force dipole aligned with the swimming direction. At zero Reynolds number ($\mathrm{Re}=0$), we demonstrate that $D$ grows without limit as the radius of the marked fluid disk $h$ is made large, indicating that a swimmer at $\mathrm{Re}=0$ can generate a partial drift volume much larger than its own volume. Next, we consider a steady swimmer at small $\mathrm{Re}$, which is modeled as the force-dipole solution to Oseen's equation. Here, we find that $D$ no longer diverges with $h$, which is due to inertial screening of viscous forces, and is effectively proportional to the magnitude of the force dipole exerted by the swimmer. The validity of this result is extended to $\mathrm{Re}\ge O\left(1\right)$—the realm of intermediate-$\mathrm{Re}$ swimmers such as copepods—by taking advantage of the fact that, in this case, the flow is also described by Oseen's equations at distances much larger than the characteristic linear dimension of the swimmer. Next, we utilize an integral momentum balance to demonstrate that our analysis for a steady inertial swimmer also holds, in a time-averaged sense, for an unsteady swimmer that does not experience a net acceleration over a stroke cycle. Finally, we use experimental data to estimate $D$ for a few real swimmers. Interestingly, we find that $D$ depends heavily on the kinematics of swimming, and, in certain cases, $D$ can be significantly greater than the volume of the swimmer at $\mathrm{Re}\ge O\left(1\right)$. Our work also highlights that $D$ due to a self-propelled body is fundamentally different than that due to a body towed by an external force. In particular, predictions of $D$ in the latter case cannot be utilized to estimate $D$ for a self-propelled swimmer.