An experiment has been performed in order to provide support for wave-packet jet-noise modeling efforts. Recent work has shown that the nonlinear effects responsible for the two-point coherence of wave packets must be correctly accounted for if accurate sound prediction is to be achieved for subsonic turbulent jets. We therefore consider the same Mach 0.4 turbulent jet studied by Cavalieri et al. [Cavalieri et al., J. Fluid Mech. 730, 559 (2013)], but this time using two independent but synchronized, time-resolved stereo particle-image velocimetry systems. Each system can be moved independently, allowing simultaneous measurement of velocity in two, axially separated, crossflow planes, enabling eduction of the two-point coherence of wave packets. This and the associated length scales and phase speeds are studied and compared with those of the energy-containing turbulent eddies. The study illustrates how the two-point behavior of wave packets is fundamentally different from that of the more usually studied bulk two-point behavior, suggesting that sound-source modeling efforts should be reconsidered in the framework of wave packets. The study furthermore identifies two families of two-point-coherence behavior, respectively upstream and downstream of the end of the potential core, regions where linear theory is, respectively, successful and unsuccessful in predicting the axial evolution of wave-packets fluctuation energy.

This study addresses the flow structure and unsteady loading arising over a pitching low-aspect-ratio rectangular wing under low-Reynolds-number conditions of interest in small unmanned aerial vehicle operation and gust interactions. Simulations are performed employing a high-fidelity computational approach capable of accurately capturing the complex unsteady transitional flows. The wing is pitched about its quarter-chord axis to a maximum incidence of ${45}^{\circ }$ over time intervals ranging from four to 16 convective time scales. The Reynolds number based on the wing chord varied from ${10}^3$ to $4\times {10}^4$. For the highest pitch rate, good agreement between the computed three-dimensional (3D) flow structure and recent experimental measurements is demonstrated. The 3D dynamic stall process is characterized by the formation of an initially spanwise-oriented leading-edge vortex which evolves into an arch-type structure with legs anchored to the wing surface. The normal vorticity in the arch vortex legs establishes a low-pressure region and swirling pattern on the wing surface. A distinct characteristic of the arch vortex is its upstream propagation and persistence over the wing, postulated to be the result of the self-induced velocity of the vortex and its image underneath the plate. Increasing either pitch rate or Reynolds number promotes a more coherent arch vortex and circulation pattern, and delays the onset of stall to a higher angle of attack. Even for the lowest pitch rate considered, a significant increase in maximum lift is achieved relative to the static situation.

Measurements of the surface diffusivity of colloidal spheres translating along a vapor-liquid interface show an unexpected decrease in diffusivity, or increase in surface drag (from the Stokes-Einstein relation), when the particles situate further into the vapor phase. However, direct measurements of the surface drag from the colloid velocity due to an external force find the expected decrease with deeper immersion into the vapor. We perform molecular dynamics simulations of the diffusivity and force experiments for a nanoparticle with a small surface roughness at a vapor-liquid interface to examine the effect of contact line fluctuations. The drag calculated from both calculations agree and decrease as the particle positions further into the vapor. The surface drag is smaller than the bulk liquid drag due to the partial submersion into the liquid and the finite thickness of the interfacial zone relative to the nanoparticle size. We observe weak contact line fluctuations and transient pinning events, but these do not give rise to an anomalous increase in drag in this system.

This paper reveals and explains the flow topology and instability hidden in an experimental study by Tsai et al. [Tsai et al., Phys. Rev. E 92, 031002(R) (2015)]. Water and soybean oil fill a sealed vertical cylindrical container. The rotating top disk induces the meridional circulation and swirl of both fluids. The experiment shows a flattop interface shape and vortex breakdown in the oil flow developing as the rotation strength $\mathrm{R}{\mathrm{e}}_o$ increases. Our numerical study shows that vortex breakdown occurs in the water flow at $\mathrm{R}{\mathrm{e}}_o=300$ and in the oil flow at $\mathrm{R}{\mathrm{e}}_o=941$. As $\mathrm{R}{\mathrm{e}}_o$ increases, the vortex breakdown cell occupies most of the water domain and approaches the interface at $\mathrm{R}{\mathrm{e}}_o$ around 600. The rest of the (countercirculating) water separates from the axis as the vortex breakdown cells in the oil and water meet at the interface-axis intersection. This topological transformation of water flow significantly contributes to the development of the flattop shape. It is also shown that the steady axisymmetric flow suffers from shear-layer instability, which emerges in the water domain at $\mathrm{R}{\mathrm{e}}_o=810$.

We investigate experimentally the nonlinear structures that develop from interacting vortex rings induced by a sinusoidally oscillating ellipsoidal disk in fluid at rest. We vary the scaled amplitude or Keulegan-Carpenter number $0.3<N_{\text{KC}}=2\pi A/c<1.5$, where $A$ is the oscillation amplitude and $c$ is the major diameter of the disk, and the scaled frequency or Stokes number $100<\beta =f{c}^2/\nu <1200$, where $f$ is the frequency of oscillation and $\nu$ is the kinematic viscosity. Broadly consistent with global linear stability analyses, highly organized nonlinear structures with clear azimuthal wave number emerge as sequential vortex rings are shed from the disk. These organized structures exhibit wave numbers ranging from $m=2$ to $m=9$ and can be further divided into two distinct classes, distinguished by the phase and symmetry properties above and below the disk. We find some discrepancies between experiments and linear stability analysis, due to the inherent nonlinear mechanisms in the experiments, particulary on the boundary between the two branches, presenting unevenly distributed flow structures along the azimuthal direction.

The coating of discrete objects having surface topography is an important step in the manufacturing of a broad variety of products. To develop a fundamental understanding of this problem, we study liquid-film flow on rotating cylinders patterned with sinusoidal topographical features. The Stokes equations, augmented with a term accounting for centrifugal forces, are solved in a rotating reference frame using the Galerkin finite-element method (GFEM). A nonlinear evolution equation for the film thickness based on lubrication theory is also solved numerically and its predictions are compared to those from the GFEM calculations. When gravitational effects are negligible and the rotation rate is sufficiently low, liquid accumulates over the pattern troughs before merging to form multiple larger drops (located over troughs) whose number at steady state depends on the topography wavelength and rotation rate. When the rotation rate is sufficiently high, similar merging events occur, but liquid accumulates over the pattern crests at steady state. When gravitational forces become significant, it is possible to obtain a coating that closely conforms to the surface topography. The GFEM calculations are in agreement with predictions from the lubrication model provided the free-surface curvatures are sufficiently small. For sufficiently large pattern amplitude and film thickness, the GFEM calculations show that recirculation regions inside the troughs can appear and vanish as the cylinder rotates due to the variation of gravitational forces around the cylinder surface. This phenomenon, along with flow reversal over the crests, may strongly influence mixing, mass transport, and heat transport.

The computational efficiency of Brownian dynamics (BD) simulation of the constrained model of a polymeric chain (bead-rod) with $n$ beads and in the presence of hydrodynamic interaction (HI) is reduced to the order of $n^2$ via an efficient algorithm which utilizes the conjugate-gradient (CG) method within a Picard iteration scheme. Moreover, the utility of the Barnes and Hut (BH) multipole method in BD simulation of polymeric solutions in the presence of HI, with regard to computational cost, scaling, and accuracy, is discussed. Overall, it is determined that this approach leads to a scaling of $O\left(n^{1.2}\right)$. Furthermore, a stress algorithm is developed which accurately captures the transient stress growth in the startup of flow for the bead-rod model with HI and excluded volume (EV) interaction. Rheological properties of the chains up to $n=350$ in the presence of EV and HI are computed via the former algorithm. The result depicts qualitative differences in shear thinning behavior of the polymeric solutions in the intermediate values of the Weissenburg number ($10<\text{Wi}<300$) when compared to ideal chains with HI. Moreover, the reduction of root mean square end-to-end distance, $r_e$, at high $\text{Wi}$ under shear flow is shown to be the consequence of frozen folded state in the third (neutral) direction for systems with HI and EV. The uniaxial extensional flow of polymeric solutions has also been investigated and it is shown that the critical strain rates scales with $n^{1.6}$, which is also commensurate with the scaling of the longest relaxation time for systems with HI and EV.

We investigate experimentally the jet formed by the collapse of a cavity created by the impact of a drop on a pool of the same aqueous liquid. We show that jets can emerge with very different shapes and velocities, depending on the impact parameters, thus generating droplets with various initial sizes and velocities. After presenting the jet velocity and top drop radius variation as a function of the impact parameters, we discuss the influence of the liquid parameters on the jet velocity. This allows us to define two different regimes: the singular jet and the cavity jet regimes, where the mechanisms leading to the cavity retraction and subsequent jet dynamics are drastically different. In particular, we demonstrate that in the first regime, a singular capillary wave collapse sparks the whole jet dynamics, making the jet's fast, thin, liquid parameters dependent and barely reproducible. On the contrary, in the cavity jet regime, defined for higher impact Froude numbers, the jets are fat and slow. We show that jet velocity is simply proportional to the capillary velocity $\sqrt{\gamma /{\rho }_l{D}_d}$, where $\gamma$ is the liquid surface tension, ${\rho }_l$ the liquid density, and $D_d$ the impacting drop diameter, and it is in particular independent of viscosity, impact velocity, and gravity, even though the cavity is larger than the capillary length. Finally, we demonstrate that capillary wave collapse and cavity retraction are correlated in the singular regime and decorrelated in the cavity jet regime.

The effect of rotation upon the classical Rayleigh-Taylor instability is investigated. We consider a two-layer system with an axis of rotation that is perpendicular to the interface between the layers. In general, we find that a wave mode's growth rate may be reduced by rotation. We further show that in some cases, unstable axisymmetric wave modes may be stabilized by rotating the system above a critical rotation rate associated with the mode's wavelength, the Atwood number, and the flow's aspect ratio.

Shocklet statistics in compressible isotropic turbulence are studied by using numerical simulations with solenoidal forcing, at the turbulent Mach number $M_t$ ranging from 0.5 up to 1.0 and at the Taylor Reynolds number ${\text{Re}}_{\lambda }$ ranging from 110 to 250. A power-law region of the probability density function (PDF) of the shocklet strength $M_n-1$ ($M_n$ is the normal shock Mach number) is observed. The magnitude of the power-law exponent is found to decrease with the increase of $M_t$. We show that the most probable shocklet strength is proportional to $M_t^3$, and the shocklet thickness corresponding to the most probable shock Mach number is proportional to $M_t^{-2}$ in our numerical simulations. The PDFs of the jumps of the velocity and thermodynamic variables across a shocklet exhibit a similar power-law scaling. The statistics of the jumps of the velocity and thermodynamic variables are further investigated by conditioned average. Nonlinear models for the conditional average of the jumps of the velocity and thermodynamic variables are developed and verified.

An analytical-based method is utilized to follow the evolution of localized initially Gaussian disturbances in flows with homogeneous shear, in which the base velocity components are at most linear functions of the coordinates, including hyperbolic, elliptic, and simple shear. Coherent structures, including counterrotating vortex pairs (CVPs) and hairpin vortices, are formed for the cases where the streamlines of the base flow are open (hyperbolic and simple shear). For hyperbolic base flows, the dominance of shear over rotation leads to elongation of the localized disturbance along the outlet asymptote and formation of CVPs. For simple shear CVPs are formed from linear and nonlinear disturbances, whereas hairpins are observed only for highly nonlinear disturbances. For elliptic base flows CVPs, hairpins and vortex loops form initially, however they do not last and break into various vortical structures that spread in the spanwise direction. The effect of the disturbance's initial amplitude and orientation is examined and the optimal orientation achieving maximal growth is identified.

We consider the flow of thixotropic yield stress fluids between two concentric cylinders. To account for the fluid thixotropy, we use Houška's model [Houška, Ph.D. thesis, Czech Technical University, Prague, 1981] with a single structural parameter driven by a kinetic equation. Because of the yield stress and the geometric inhomogeneity of the stress, only a part of the material in the gap may flow. Depending on the breakdown rate of the structural parameter, the constitutive relation can lead to a nonmonotonic flow curve. This nonmonotonic behavior is known to induce a discontinuity in the slope of the velocity profile within the flowing material, called shear banding. Thus, for fragile structures, a shear-banded flow characterized by a very sharp transition between the flowing and the static regions may be observed. For stronger structures, the discontinuity disappears and a smooth transition between the flowing and the static regions is observed. The consequences of the thixotropy on the linear stability of the azimuthal flow are studied in a large range of parameters. Although the thixotropy allows shear banding in the base flow, it does not modify fundamentally the linear stability of the Couette flow compared to a simple yield stress fluid. The apparent shear-thinning behavior depends on the thixotropic parameters of the fluid and the results about the onset of the Taylor vortices in shear-thinning fluids are retrieved. Nevertheless, the shear banding modifies the stratification of the viscosity in the flowing zone such that the critical conditions are mainly driven by the width of the flowing region.

The surface shear rheology of many insoluble surfactants depends strongly on the surface pressure (or concentration) of that surfactant. Here we highlight the dramatic consequences that surface-pressure-dependent surface viscosities have on interfacially dominant flows, by considering lubrication-style geometries within high Boussinesq (Bo) number flows. As with three-dimensional lubrication, high-Bo surfactant flows through thin gaps give high surface pressures, which in turn increase the local surface viscosity, further amplifying lubrication stresses and surface pressures. Despite their strong nonlinearity, the governing equations are separable, so that results from two-dimensional Newtonian lubrication analyses may be immediately adapted to treat surfactant monolayers with a general functional form of ${\eta }_s\left(\mathrm{\Pi }\right)$. Three paradigmatic systems are analyzed to reveal qualitatively new features: a maximum, self-limiting value for surfactant fluxes and particle migration velocities appears for $\mathrm{\Pi }$-thickening surfactants, and kinematic reversibility is broken for the journal bearing and for suspensions more generally.

We investigate the incompressible turbulent jet formed when buoyant fluid is steadily ejected horizontally from a circular source into an otherwise quiescent uniform environment. As our primary focus, we introduce a horizontal boundary beneath the source. For sufficiently small separations, the jet attaches and clings to the boundary, herein the “clinging jet,” before, farther downstream, the jet is pulled away from the boundary by the buoyancy force. For larger source-boundary separations, the buoyant jet is free to rise under the action of the buoyancy force, herein the “free jet.” Based on measurements of saline jets in freshwater surroundings we deduce the conditions required for a jet to cling. We present a data set that spans a broad range of source conditions for the variation in volume flux (indicative of entrainment), jet perimeter, and jet centerline for both “clinging” and “free” jets. For source Froude numbers ${\text{Fr}}_0\ge 12$ the data collapse when scaled, displaying universal behaviors for both clinging and free jets. Our results for the variation in the volume flux across horizontal planes, $\pi Q_{\mathit{jet}}$, show that within a few jet lengths of the source, $\pi Q_{\mathit{jet}}$ for the clinging jet exceeds that of a free jet with identical source conditions. However, when examined in a coordinate following the jet centerline $\pi Q_{\mathit{jet}}$ for free jets is greater. Finally, we propose a new parametrization for an existing integral model which agrees well with our experimental data as well as with data from other studies. Our findings offer the potential to tailor the dilution of horizontal buoyant jets by altering the distance at which they are released from a boundary.

Turbulent flows laden with inertial particles present multiple open questions and are a subject of great interest in current research. Due to their higher density compared to the carrier fluid, inertial particles tend to form high-concentration regions, i.e., clusters, and low-concentration regions, i.e., voids, due to the interaction with the turbulence. In this work we present an experimental investigation of the clustering phenomenon of heavy sub-Kolmogorov particles in homogeneous isotropic turbulent flows. Three control parameters are varied over significant ranges: ${\text{Re}}_{\lambda }\in [170–450], \text{St}\in [0.1–5]$, and volume fraction ${\varphi }_v\in [(2\times {10}^{-6})–(2\times {10}^{-5})]$. The scaling of clustering characteristics, such as the distribution of Voronoi areas and the dimensions of cluster and void regions, with the three parameters is discussed. In particular, for the polydispersed size distributions considered here, clustering is found to be enhanced strongly (quasilinearly) by ${\text{Re}}_{\lambda }$ and noticeably (with a square-root dependence) with ${\varphi }_v$, while the cluster and void sizes, scaled with the Kolmogorov length scale $\eta$, are driven primarily by ${\text{Re}}_{\lambda }$. Cluster characteristic size $\sqrt{\langle A_c\rangle }$ scales up to $\approx 100\eta$, measured at the highest ${\text{Re}}_{\lambda }$, while void sizes $\sqrt{\langle A_v\rangle }$, scaled also with $\eta$, are typically twice as large as clusters at the same ${\text{Re}}_{\lambda }\left(\approx 200\eta \right)$. The lack of sensitivity of the above characteristics to the Stokes number lends support to the sweep-stick particle accumulation scenario. The non-negligible influence of the volume fraction, however, is not considered by that model and can be connected with collective effects.

An approach to designing passive devices for control of unsteady flows is presented. The method requires only snapshots of the flow to be controlled as inputs. A temporal correlation based on proper orthogonal decomposition of both fluctuating velocity and nonlinear forcing serves to identify the spatial locations in which the forcing drives the different unsteady flow features. The installation of a passive device in these spatial locations inhibits the fluctuating motion. The potential of the methodology is demonstrated via the suppression of vortex shedding in flow past a square cylinder, paving the way to the control of more complex flows using passive devices. Connections in agreement with previous studies targeting the same flow using different passive flow control strategies are provided.

In this paper we consider the effects of adding high-frequency, low-amplitude perturbations to a smooth sinusoidal base input signal for a heaving panel in a closed loop flow tank. Specifically, 0.1 cm amplitude sinusoidal perturbation waves with frequency $f_p$ ranging from 0.5 to 13.0 Hz are added to 1 cm heave sinusoids with base frequencies, $f_b$, ranging from 0.5 to 3.0 Hz. Two thin foils with different flexural stiffness are heaved with the combined input signals in addition to both the high-heave and low-heave signals independently. In all cases, the foils are heaved in a recirculating water channel with an incoming velocity of $V_x=10\text{cm/s}$ and a Reynolds number based on the chord length of $\text{Re}=17300$. Results demonstrate that perturbations increase the net axial force, in the streamwise direction, in most cases tested (with the exception of some poor performing flexible foil cases). Most significantly, for a base frequency of 1 Hz, perturbations at 9 Hz result in a 780.7% increase in net streamwise force production. Generally, the higher the perturbation frequency, $f_p$ the more axial force generated. However, for the stiffer foil, a clear peak in net force exists at $f_p=9\mathrm{Hz}$, regardless of the base frequency. For the stiffer foil, swimming efficiency at a 1 Hz flapping frequency is increased dramatically with the addition of a perturbation, with reduced efficiency increases at higher flapping frequencies. Likewise, for the flexible foil, swimming efficiency gains are greatest at the lower flapping frequencies. Perturbations alter the wake structure by increasing the vorticity magnitude and increasing the vortex shedding frequency; i.e., more, stronger vortices are produced in each flapping cycle.

Back-and-forth oscillations of a container filled with fluid often result in spilling as the gravest mode gets excited, a well-known phenomenon experienced in everyday life and of particular importance in industry. Our understanding of sloshing is largely restricted to linear response, and existing extensions mostly focus on nonlinear coupling between modes. Linear theory is expected to correctly model the dynamics of the system as long as the amplitude of the mode remains small compared to another length scale, so far unknown. Using a fluid in the vicinity of its critical point, we demonstrate that in perfect wetting this length scale is neither the wavelength nor the capillary length but a much shorter one, the thickness of the boundary layer. Above this crossover length scale, the resonance frequency remains roughly constant while dissipation significantly increases. We also show that dynamical wetting is involved in both linear and nonlinear dissipative processes.

Modal and nonmodal growth of three-dimensional perturbations in a shear flow with a free surface are examined for a wide range of Froude numbers. By approximating the mean flow with a piecewise linear profile, the modal instabilities are shown to arise from the interaction of three-dimensional edge waves supported at the interfaces of density discontinuity at the surface and mean vorticity discontinuity at the edges of the shear layer. The mechanism and properties of the instability are explained in terms of the dynamics of the edge-wave interactions. Previously reported modal stability analysis restricted to two-dimensional perturbations in the plane of the flow accurately predicts the fastest growing perturbations but underestimates the range of length scales for the unstable structures. Robust nonmodal transient growth of perturbations within a few advective time units is found. For low Froude numbers or low values of the shear, three-dimensional perturbations with small horizontal scales exhibit the largest growth through a synergy between the Orr and the lift-up mechanisms and produce large streamwise streaks in the shear flow without an effect on the free surface. For large Froude numbers or large values of the shear, planar perturbations with larger horizontal scales exhibit the largest energy growth by effectively instigating the modal instability and excite surface waves at large amplitude.