Volatile viscous fluids on partially wetting solid substrates can exhibit interesting interfacial instabilities and pattern formation. We study the dynamics of vapor condensation and fluid evaporation governed by a one-sided model in a low-Reynolds-number lubrication approximation incorporating surface tension, intermolecular effects, and evaporative fluxes. Parameter ranges for evaporation-dominated and condensation-dominated regimes and a critical case are identified. Interfacial instabilities driven by the competition between the disjoining pressure and evaporative effects are studied via linear stability analysis. Transient pattern formation in nearly flat evolving films in the critical case is investigated. In the weak evaporation limit unstable modes of finite-amplitude nonuniform steady states lead to rich droplet dynamics, including flattening, symmetry breaking, and droplet merging. Numerical simulations show that long-time behaviors leading to evaporation or condensation are sensitive to transitions between filmwise and dropwise dynamics.

The goal of the present study is threefold: (i) to demonstrate the two-dimensional nature of the elasto-inertial instability in elasto-inertial turbulence (EIT), (ii) to identify the role of the bidimensional instability in three-dimensional EIT flows, and (iii) to establish the role of the small elastic scales in the mechanism of self-sustained EIT. Direct numerical simulations of viscoelastic fluid flows are performed in both two- and three-dimensional straight periodic channels using the Peterlin finitely extensible nonlinear elastic model (FENE-P). The Reynolds number is set to ${\mathrm{Re}}_{\tau }=85$, which is subcritical for two-dimensional flows but beyond the transition for three-dimensional ones. The polymer properties selected correspond to those of typical dilute polymer solutions, and two moderate Weissenberg numbers, ${\mathrm{Wi}}_{\tau }=40,100$, are considered. The simulation results show that sustained turbulence can be observed in two-dimensional subcritical flows, confirming the existence of a bidimensional elasto-inertial instability. The same type of instability is also observed in three-dimensional simulations where both Newtonian and elasto-inertial turbulent structures coexist. Depending on the $\mathrm{Wi}$ number, one type of structure can dominate and drive the flow. For large $\mathrm{Wi}$ values, the elasto-inertial instability tends to prevail over the Newtonian turbulence. This statement is supported by (i) the absence of typical Newtonian near-wall vortices and (ii) strong similarities between two- and three-dimensional flows when considering larger $\mathrm{Wi}$ numbers. The role of small elastic scales is investigated by introducing global artificial diffusion (GAD) in the hyperbolic transport equation for polymers. The aim is to measure how the flow reacts when the smallest elastic scales are progressively filtered out. The study results show that the introduction of large polymer diffusion in the system strongly damps a significant part of the elastic scales that are necessary to feed turbulence, eventually leading to flow laminarization. A sufficiently high Schmidt number (weakly diffusive polymers) is necessary to allow self-sustained turbulence to settle. Although EIT can withstand a low amount of diffusion and remains in a nonlaminar chaotic state, adding a finite amount of GAD in the system can have an impact on the dynamics and lead to important quantitative changes, even for Schmidt numbers as large as ${10}^2$. The use of GAD should therefore be avoided in viscoelastic flow simulations.

Many transitional shear flows show a regime of complex spatiotemporal dynamics that has been linked to directed percolation. Using direct numerical simulations of plane-Poiseuille flow, we identify a state of sparse oblique turbulent bands that exists in a Reynolds number range between 660 and 800, below the anticipated directed percolation transition. The localized turbulent bands will increase steadily in length in sufficiently large domains, or will sustain themselves in a cycle of band extension and breakup in periodic domains. The spreading process is not sensitive to random perturbations, and the width and tilt angle of the band are statistically invariant during the extension. The results show that at least in the case of plane-Poiseuille flow a possible transition in the directed percolation class is preceded by the formation of robust oblique turbulent bands.

We present the results of an integrated experimental and theoretical investigation of the promenade mode, a bound state formed by a pair of droplets walking side by side on the surface of a vibrating fluid bath. Particular attention is given to characterizing the dependence of the promenading behavior on the vibrational forcing for drops of a given size. We also enumerate the different instabilities that may arise, including transitions to smaller promenade modes or orbiting pairs. Our theoretical developments highlight the importance of the vertical bouncing dynamics on the stability characteristics. Specifically, quantitative comparison between experiment and theory prompts further refinement of the stroboscopic model [A. U. Oza et al., J. Fluid Mech. 737, 552 (2013)] through inclusion of phase adaptation and reveals the critical role that impact phase variations play in the stability of the promenading pairs.

We investigate the evolution of passive scalar statistics in a spatially developing turbulence using direct numerical simulation. Turbulence is generated by a square grid element, which is heated continuously, and the passive scalar is temperature. The square element is the fundamental building block for both regular and fractal grids. We trace the dominant mechanisms responsible for the dynamical evolution of scalar-variance and its dissipation along the bar and grid-element centerlines. The scalar-variance is generated predominantly by the action of the mean scalar gradient behind the bar and is transported laterally by turbulent fluctuations to the grid-element centerline. The scalar-variance dissipation (proportional to the scalar-gradient variance) is produced primarily by the compression of the fluctuating scalar-gradient vector by the turbulent strain rate, while the contribution of mean velocity and scalar fields is negligible. Close to the grid element the scalar spectrum exhibits a well-defined $-5/3$ power-law, even though the basic premises of the Kolmogorov-Obukhov-Corrsin theory are not satisfied (the fluctuating scalar field is highly intermittent, inhomogeneous, and anisotropic, and the local Corrsin-microscale-Péclet number is small). At this location, the PDF of scalar gradient production is only slightly skewed towards positive, and the fluctuating scalar-gradient vector aligns only with the compressive strain-rate eigenvector. The scalar-gradient vector is stretched or compressed stronger than the vorticity vector by turbulent strain rate throughout the grid-element centerline. However, the alignment of the former changes much earlier in space than that of the latter, resulting in scalar-variance dissipation to decay earlier along the grid-element centerline compared to the turbulent kinetic energy dissipation. The universal alignment behavior of the scalar-gradient vector is found far downstream, although the local Reynolds and Péclet numbers (based on the Taylor and Corrsin length scales, respectively) are low.

Experiments are reported on the performance of a pitching and heaving two-dimensional foil in a water channel in either continuous or intermittent motion. We find that the thrust and power are independent of the mean free-stream velocity for twofold changes in the mean velocity (fourfold in the dynamic pressure) and for oscillations in the velocity up to 38% of the mean, where the oscillations are intended to mimic those of freely swimming motions where the thrust varies during the flapping cycle. We demonstrate that the correct velocity scale is not the flow velocity but the mean velocity of the trailing edge. We also find little or no impact of streamwise velocity change on the wake characteristics such as vortex organization, vortex strength, and time-averaged velocity profile development—the wake is both qualitatively and quantitatively unchanged. Our results suggest that constant velocity studies can be used to make robust conclusions about swimming performance without a need to explore the free-swimming condition.

We investigate experimentally the local erosion of a granular bed near a fixed vertical cylinder that emerges from the bed. The onset of erosion arising at the base of the cylinder and usually ascribed to the wrapping horseshoe vortex is determined and rationalized by a flow contraction effect. We report another erosion pattern visible downstream of the cylinder that consists of two side-by-side elongated holes. This pattern is observed for flow regimes close to the horseshoe scour onset, whose growth usually inhibits its spatiotemporal development.

Direct numerical simulations of channel flow up to $\mathrm{R}{\mathrm{e}}_{\tau }=8000$ have been performed to determine the existence of a logarithmic region in channel flow at high-Reynolds number. It is notable that the logarithmic variations both in the mean velocity, $U^{+}=\left(1/\phantom{1\kappa }\kappa \right)ln\left(y^{+}\right)+B$ and the streamwise Reynolds stress, $\overline{u^{+}{u}^{+}}=B_1-A_{1}ln(y/h)$ are first confirmed for $\mathrm{R}{\mathrm{e}}_{\tau }=8000$, with $\kappa =0.387,B=4.21$ and $A_1=1.65,B_1=1.23$, where $y$ is the distance from the wall and $h$ is the channel half-height. The logarithmic region of $U^{+}$ locates between $300<y^{+}<1100$ ($y/h=0.14$) and that of $\overline{u^{+}{u}^{+}}$ locates between $1200\left(y/h=0.15\right)<y^{+}<2000(y/h=0.25)$. Therefore, these logarithmic regions do not overlap with each other. Furthermore, the region of ${k_x}^{-1}$ law is studied without using the frozen turbulence hypothesis in logarithmic regions of the mean velocity and the streamwise Reynolds stress.

This paper presents a comprehensive theoretical study of oblique shock wave reflection in water. The study identifies wedge angles in a structure that can alter the reflection characteristics of shock waves of different strengths. Utilizing the shock polar diagrams for both incident and reflected shock, the domain of regular and irregular reflection is identified. The effect of phase transition of water on reflection characteristics and its subsequent effect on the domain of regular and irregular reflection are also investigated theoretically. Results are compared between two equations of state, and it is observed that they give similar results for low-pressure regimes; however, reflection characteristics are significantly different for high-pressure regimes where phase transition of water has been reported to be observed. The implications of these theoretical observations are substantial for designing experimental devices and can be utilized to benchmark numerical simulations.

The ability for high-frequency, low-amplitude forcing to delay the onset of unsteady separation due to bursting of a small laminar separation bubble is considered through the use of large-eddy simulation. The study begins with the static flow over a NACA 0012 airfoil at $\alpha =8^{\circ }$ and ${\text{Re}}_c=2\times {10}^5$. The ability for the laminar separation bubble to act as a spatial amplifier of select frequencies is documented. Sinusoidal or pulsed forcing within this frequency range is shown to reduce the length of the separated region. Boundary-layer transition is shown to occur due to a short-wavelength secondary instability, the behavior of which is sensitive to the properties of the shed vortex structures. Control is then applied to the case of a constant-rate pitch-up motion to evaluate the potential for delay of dynamic stall onset. During the pitch-up motion the most amplified shear-layer frequency increases due to flow acceleration and reduced separation length scale. The most effective control scenarios using sinusoidal, pulsed, or variable frequency approaches are shown to continually energize the laminar separation bubble throughout the pitching motion until turbulent separation propagates to the leading edge.

Miniaturized, self-propelled locomotors use chemo-mechanical transduction mechanisms to convert fuel in the environment to autonomous motion. Recent experimental and theoretical studies demonstrate that these autonomous engines can passively follow the contours of solid boundaries they encounter. Boundary guidance, however, is not necessarily stable: Mechanical disturbances can cause the motor to hydrodynamically depart from the passively guided pathway. Furthermore, given the scaled-down size of micromotors (typically 100 nm $\text{to}10\mu \mathrm{m}$), Brownian thermal fluctuation forces are necessarily important, and these stochastic forces can randomize passively steered trajectories. Here we examine theoretically the stability of boundary-guided motion of micromotors along infinite planar walls to mechanical disturbances and to Brownian forces. Our aim is to understand under what conditions this passively guided motion is stable. We choose a locomotor design in which spherical colloids are partially coated with a catalytic cap that reacts with solute to produce a product. The product is repelled from the particle surface, causing the particle to move with the inert face at the front (autonomous motion via self-diffusiophoresis). When propelled towards a planar wall, deterministic hydrodynamic studies demonstrate that these locomotors can exhibit, for large enough cap sizes, steady trajectories in which the particle either skims unidirectionally along the surface at a constant distance from the wall or becomes stationary. We first investigate the linear hydrodynamic stability of these states by expanding the equations of motion about the states, and we find that linear perturbations decay exponentially in time. We then study the effects of thermal fluctuations by formulating a Langevin equation for the particle motion which includes the Brownian stochastic force. The Péclet number scales the ratio of deterministic to Brownian forces, where $\mathrm{Pe}=\pi \mu a^2{\tilde{v}}_c/k_{B}T$ and $a$ denotes the colloid radius, $\mu$ the continuous phase viscosity, ${\tilde{v}}_c$ the characteristic diffusiophoretic velocity, and $k_{B}T$ the thermal energy. The skimming and stationary states are found to persist for $\mathrm{Pe}$ above ${10}^3$. At $\mathrm{Pe}$ below 200, the trajectory of a locomotor approaching the wall is unpredictable. We present representative individual trajectories along with probability distributions for statistical ensembles of particles, quantifying the effects of thermal fluctuations and illustrating the transition from unpredictable to passively guided motion.

Wet high-shear granulation consists in vigorously mixing grains and a liquid binder to create agglomerates of various sizes. The process results from a balance between cohesion of the wet granular agglomerates and fragmentation due to the high mixing. By performing a simple test with glass beads and various liquids, we first focus on the static cohesion of wet granular media. Contrary to previous works, we extend the study to larger values of the liquid fraction $w$. After the well-documented plateau, the cohesive strength increases again with $w$, a behavior we capture by a simple model. We then focus on the dynamical cohesion of the media and we design an agglomeration process that consists in vibrating a bead/liquid mixture at a large amplitude. The vibrations induce not only the fluidization of the wet granular material but also the formation of aggregates. As expected, their size is affected by the liquid content, the frequency, and the amplitude of the vibrations, similarly to high-shear granulation data. However, the number of beads in an agglomerate does not depend on the bead size, showing a self-similar mechanism of agglomeration. The role of the static cohesion strength in this dynamical process remains therefore ambiguous.

Coherent vortex structures are tracked in simulations of massively-separated and turbulent flows. Topological Lagrangian saddle points are found using intersections of the positive and negative finite-time Lyapunov exponent ridges, and these points are then followed in order to track individual coherent structure motion both in a complex interacting three-dimensional flow (turbulent channel) and during vortex formation (two-dimensional bluff body shedding). For a simulation of wall-bounded turbulence in a channel flow, tracking Lagrangian saddles shows that the average structure convection speed exhibits a similar trend as a previously published result based on velocity and pressure correlations, giving validity to the method. When this tracking method is applied in a study of a circular cylinder in cross-flow it shows that Lagrangian saddles rapidly accelerate away from the cylinder surface as the vortex sheds. This saddle behavior is compared with the time-resolved static pressure distribution on the circular cylinder, yielding locations on a cylinder surface where common sensors could detect this phenomenon, which is not available from force measurements or vortex circulation calculations. The current method of tracking coherent structures yields insight into the behavior of the coherent structures in both of the diverse flows presented, highlighting the breadth of its potential application.

We investigate flow instability created by an oblique shock wave impinging on a Mach 5.92 laminar boundary layer at a transitional Reynolds number. The adverse pressure gradient of the oblique shock causes the boundary layer to separate from the wall, resulting in the formation of a recirculation bubble. For sufficiently large oblique shock angles, the recirculation bubble is unstable to three-dimensional perturbations and the flow bifurcates from its original laminar state. We utilize direct numerical simulation (DNS) and global stability analysis to show that this first occurs at a critical shock angle of $\theta =12.9^{\circ }$. At bifurcation, the least-stable global mode is nonoscillatory and it takes place at a spanwise wave number $\beta =0.25$, in good agreement with DNS results. Examination of the critical global mode reveals that it originates from an interaction between small spanwise corrugations at the base of the incident shock, streamwise vortices inside the recirculation bubble, and spanwise modulation of the bubble strength. The global mode drives the formation of long streamwise streaks downstream of the bubble. While the streaks may be amplified by either the lift-up effect or by Görtler instability, we show that centrifugal instability plays no role in the upstream self-sustaining mechanism of the global mode. We employ an adjoint solver to corroborate our physical interpretation by showing that the critical global mode is most sensitive to base flow modifications that are entirely contained inside the recirculation bubble.

Bingham fluids behave like solids below a von Mises stress threshold, the yield stress, while above it they behave like Newtonian fluids. They are characterized by a dimensionless parameter, Bingham number (Bn), which is the ratio of the yield stress to a characteristic viscous stress. In this study, the noninertial steady motion of a finite-size gas bubble in both a plane two-dimensional (2D) channel and an axisymmetric tube filled by a Bingham fluid has been studied numerically. The Bingham number, Bn, is in the range $0\le \mathrm{Bn}\le 3$, where $\mathrm{Bn}=0$ is the Newtonian case, while the capillary number, which is the ratio of a characteristic viscous force to the surface tension, has values $\mathrm{Ca}=0.05,0.10$, and 0.25. The volume of all axisymmetric and 2D bubbles has been chosen to be identical for all parameter choices and large enough for the bubbles to be long compared to the channel, tube height, and diameter. The Bingham fluid constitutive equation is approximated by a regularized equation. During the motion, the bubble interface is separated from the wall by a static liquid film. The film thickness scaled by the tube radius (axisymmetric) and half of the channel height (2D) is the dimensionless film thickness, $h$. The results show that increasing Bn initially leads to an increase in $h$; however, the profile $h$ versus Bn can be monotonic or nonmonotonic depending on Ca values and 2D or axisymmetric configurations. The yield stress also alters the shape of the front and rear of the bubble and suppresses the capillary waves at the rear of the bubble. The yield stress increases the magnitude of the wall shear stress and its gradient and therefore increases the potential for epithelial cell injuries in applications to lung airway mucus plugs. The topology of the yield surfaces as well as the flow pattern in the bubble frame of reference varies significantly by Ca and Bn.

Sea spray is the main source of aerosols above the ocean. One of the pathways for sea spray production is through bubble bursting, which ejects myriads of droplets. We present a detailed description of the velocity of jets formed by bubble bursting, obtained through extensive comparison between experimental results and numerical simulations for a wide range of physical parameters. We discuss the importance of the shape of the cavity on the jet velocity and the regime of parameters for which drop ejection is observed. We present a phenomenological formula that predicts the jet velocity for the full range of parameters and compare it to a theoretical prediction based on curvature reversal. The results are then discussed in light of their fundamental applications in the understanding of the phenomena.

The dynamics of the turbulent near-wall region is known to be dominated by coherent structures. These near-wall coherent structures are observed to burst in a very intermittent fashion, exporting turbulent kinetic energy to the rest of the flow. In addition, they are closely related to invariant solutions known as exact coherent states (ECS), some of which display nonlinear critical layer dynamics (motions that are highly localized around the surface on which the streamwise velocity matches the wave speed of ECS). The present work aims to investigate temporal coherence in minimal channel flow relevant to turbulent bursting and critical layer dynamics and its connection to the instability of ECS. It is seen that the minimal channel turbulence displays frequencies very close to those displayed by an ECS family recently identified in the channel flow geometry. The frequencies of these ECS are determined by critical layer structures and thus might be described as “critical layer frequencies.” While the bursting frequency is predominant near the wall, the ECS frequencies (critical layer frequencies) become predominant over the bursting frequency at larger distances from the wall, and increasingly so as Reynolds number increases. Turbulent bursts are classified into strong and relatively weak classes with respect to an intermittent approach to a lower branch ECS. This temporally intermittent approach is closely related to an intermittent low drag event, called hibernating turbulence, found in minimal and large domains. The relationship between the strong burst and the instability of the lower branch ECS is further discussed in state space. The state-space dynamics of strong bursts is very similar to that of the unstable manifolds of the lower branch ECS. In particular, strong bursting processes are always preceded by hibernation events. This precursor dynamics to strong turbulence may aid in development of more effective control schemes by a way of anticipating dynamics such as intermittent hibernating dynamics.

We numerically investigate the flight dynamics and aerodynamics of a two-dimensional model for the jellyfishlike ornithopter recently devised by Ristroph and Childress [L. Ristroph and S. Childress, J. R. Soc. Interface 11, 20130992 (2014)]. This simplified model is composed of two rigid thin foils which are forced to pitch in antiphase fashion. The Navier-Stokes equations for the fluid and the dynamics equations for the flyer are solved together in the simulations. We first consider the constrained-flying condition where the flyer model is only allowed to move in the vertical direction. The influences of the control parameters on the hovering performance are studied. With the variations in parameter values, three different locomotion states, i.e., ascending, descending, and approximate hovering, are identified. The wake structures corresponding to these three locomotion states are explored. It is found that the approximate hovering state cannot persist due to the occurrence of wake symmetry breaking after long-time simulation. We then consider the free-flying condition where the motions in three degrees of freedom are allowed. We study the postural stability of a flyer, with its center of gravity located at the geometric center. The responses of the flyer at different locomotion states to physical and numerical perturbations are examined. Our results show that the ascending state is recoverable after the perturbation. The descending state is irrecoverable after the perturbation and a mixed fluttering and tumbling motion which resembles that of a falling card emerges. The approximate hovering state is also irrecoverable and it eventually transits to the ascending state after the perturbation. The research sheds light on the lift-producing mechanism and stability of the flyer and the results are helpful in guiding the design and optimization of the jellyfishlike flying machine.