We investigate granular transport by a fluid flow under steady-state driving conditions, from the bed-load regime to the suspension regime, with an experimental system based on a conical rheometer. The mean granular volume fraction ${\varphi }_g$, the mean granular velocity $u_g$, and the fluid velocity $u_f$ are obtained as a function of depth inside the bed using refractive index matching and particle-tracking techniques. A torque sensor is utilized to measure the applied shear stress to complement estimates obtained from measured strain rates high above the bed where ${\varphi }_g\approx 0$. The flow is found to be transitional at the onset of transport and the shear stress required to transport grains rises sharply as grains are increasingly entrained by the fluid flow. A significant slip velocity between the fluid and the granular phases is observed at the bed surface before the onset of transport as well as in the bed-load transport regime. We show that $u_g$ decays exponentially deep into the bed for ${\varphi }_g>0.45$ with a decay constant which is described by a nonlocal rheology model of granular flow that neglects fluid stress. Further, we show that $u_f$ and $u_g$ can be described using the applied shear stress and the Krieger-Dougherty model for the effective viscosity in the suspension regime, where $0<{\varphi }_g<0.45$ and where $u_g\approx u_f$.

How droplets grow rapidly from 10 to 50 $\mu \mathrm{m}$ is an outstanding question in cloud physics. We show theoretically and numerically that caustics, locations of multivalued droplet velocity, of small droplets near a single planar steady vortex offer one route through this bottleneck. Such a vortex serves as a simple model for the more complicated turbulence field existing in clouds. Within a special radial distance $r_c$ from the vortex center, droplets closer to the vortex can centrifugally overtake those farther out and coalesce. Small polydispersity increases $r_c$ dramatically, enabling repeated collisions at short time intervals and formation of large droplets. Our results show that caustics brought about in a polydisperse suspension could offer a mechanistic explanation of accelerated rain initiation.

Particle sedimentation under a turbulent flow is a fundamental problem that has numerous applications in natural and industrial processes. In particular, the motion of anisotropic particles yields complex dynamics whose features are not completely understood in the presence of inertia. While inertia is generally introduced through a finite particle response time, many processes involve particles with a low response time but a finite particle Reynolds number. In this case, theoretical models are rather sparse, and their validity has never been tested against controlled experiments. This work precisely proposes a careful testing of fiber sedimentation and advection models at finite particle Reynolds number against well-controlled two-dimensional experiments. We show that the slender body limit model has strong limitations at finite aspect ratio and Reynolds number, and we identify the main corrections that need to be incorporated into this basic model by expanding on the work of Khayat and Cox [J. Fluid Mech. 209, 435 (1989)]. Additionally, we present the different models under a uniform framework, providing a simpler and clearer use. Using the validated inertial model, we show the importance of the ratio between the settling speed and the typical flow velocity for describing the fiber motion.

We present simulations of the effects of insoluble surfactant on drops rising in unstratified media and density-stratified media. We consider an oil drop rising in water, and we track surfactant concentration on the drop surface. We first consider a drop coated with insoluble surfactant rising through an unstratified ambient. The drop speed is computed for various Marangoni numbers, and inertial and surface diffusion effects are also examined. In the second setup, we compare clean and contaminated drops rising through a linear density-stratified fluid. The entrained buoyancy is computed for various density gradients, and the effects of inertia and Marangoni number are characterized. We find that the entrained fluid slows the drop in a manner comparable to a vertical shift in the ambient density gradient.

Reynolds-averaged Navier-Stokes (RANS) models represent the workhorse for predicting turbulent flows in complex industrial applications. However, RANS closures introduce a significant degree of epistemic uncertainty in predictions due to the potential lack of validity of the assumptions utilized in model formulation. Estimating this uncertainty is a fundamental requirement for building confidence in such predictions. We outline a methodology to estimate this structural uncertainty, incorporating perturbations to the eigenvalues and the eigenvectors of the modeled Reynolds stress tensor. The mathematical foundations of this framework are derived and explicated. Thence, this framework is applied to a set of separated turbulent flows, while compared to numerical and experimental data and contrasted against the predictions of the eigenvalue-only perturbation methodology. It is exhibited that for separated flows, this framework is able to yield significant enhancement over the established eigenvalue perturbation methodology in explaining the discrepancy against experimental observations and high-fidelity simulations. Furthermore, uncertainty bounds of potential engineering utility can be estimated by performing five specific RANS simulations, reducing the computational expenditure on such an exercise.

Numerical simulations of the G.O. Roberts dynamo are presented. Dynamos both with and without a significant mean field are obtained. Exact bounds are derived for the total energy which conform with the Kolmogorov phenomenology of turbulence. Best fits to numerical data show the same functional dependences as the inequalities obtained from optimum theory.

Direct numerical simulations (DNS) of plane Poiseuille flow are performed in an extended domain at friction Reynolds numbers ranging from 70 to 100. In minimal domains, turbulence in this Reynolds number range displays substantial intermittency that is associated with chaotic movement of turbulent trajectories between lower and upper branch invariant solutions known as exact coherent states (ECS). The present work aims to address the relationship between temporal dynamics in minimal channels and spatiotemporal dynamics in extended domains. Both temporal and spatial analyses of the turbulent velocity fields are performed, the latter using image analysis methods. These analyses partition the flow characteristics into low-, intermediate- and high-drag classes; we present the differences between flows fields in these classes in terms of simple quantities like mean velocity, wall shear stress, and flow structures. The temporal and spatial analysis methods, although completely independent of one another, yield very similar results for both low- and high-drag regions. In particular, the conditional mean profiles in regions of low drag closely resemble those found in low-drag temporal intervals in the minimal channel. Finally, we address the possibility of similarities between turbulence and exact coherent states in two ways: (1) comparing wall shear stress in localized patches the size of minimal channels in large domains with those in actual minimal channel and (2) comparing conditional mean velocity profiles during low-drag events with mean profiles from lower branch ECS. These analyses show that both the local near-wall flow structure in the low-drag patches of the large domain and the conditional mean profiles in the region $y^{+}\lesssim 30$ resemble those of a lower branch minimal domain ECS. In summary, the results presented here suggest that spatiotemporal intermittency in transitional channel flow turbulence is related to temporal intermittency, and by extension to the state space structure, in the minimal channel.

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.