A bi-frequency open-loop control strategy aiming to combine both high- and low-frequency forcing effects is used to experimentally reduce the drag of a simplified car model at a slight yaw angle of $5^{\circ }$. The unforced mean wake features a lateral asymmetry which induces a low base pressure footprint close to the leeward side and increases drag compared to the aligned model. Forcing is performed with pulsed jets along the windward trailing edge. High-frequency forcing acts as a time-invariant flap. The fluidic flap effect deviates the windward shear layer towards the leeward side and reduces the wake bluffness, but the lateral asymmetry of the near wake is still observed. The drag reduction related to this high-frequency forcing is about 6% with a high actuation efficiency. A modulation of the high-frequency forcing with a low-frequency component is then introduced in order to modify the mass and momentum exchange in the separating shear layer at the windward trailing edge. We find that the modulated forcing provides the ability to manipulate the mean wake orientation while maintaining the fluidic flap effect. Among all wake orientations, those reducing drag are the ones having a mean symmetric wake. The bi-frequency control strategy leads to a maximum drag reduction of 7% for the best choice of frequencies. Importantly, the bi-frequency control is more efficient than the single high-frequency forcing, the actuator requiring only half the actuation energy and presenting an actuation efficiency multiplied by 3. Finally, the physical mechanisms related to drag reduction are carefully analyzed. In particular, we show that the wake symmetrization reduces the global production of turbulent kinetic energy in the shear layers. These results open up opportunities for closed-loop control of wake asymmetries.

We study the interaction between capillary forces and deformation in the context of a deformable capillary adhesive: a clamped, tense membrane is adhered to a rigid substrate by the surface tension of a liquid droplet. We find that the equilibrium adhesive force for this elasto-capillary adhesive is significantly enhanced in comparison to the capillary adhesion between rigid plates. In particular, the equilibrium adhesion force is orders of magnitude greater when the membrane is sufficiently deformed to contact the substrate. From a dynamic perspective, however, the formation of a fluid-filled dimple slows this approach to contact and means that stable attachment is only achieved if adhesion is maintained for a minimum time. The inclusion of a variable membrane tension (as a means of modifying the deformability) gives additional control over the system, allowing new detachment strategies to be explored.

The collapse, or reduction in size to zero volume, of bubbles injected into incipiently fluidized beds was studied using rapid magnetic resonance imaging. The collapse of a smaller lower bubble trailing a larger upper bubble and the collapse of one bubble when two bubbles rose side by side were found to occur. Under the same conditions with the use of finer particles or the injection of an isolated bubble, no collapse occurred. Thus, results indicate that gas leakage into the particulate phase of coarse particles and bubble interaction promote bubble collapse. Furthermore, injection of larger bubbles also resulted in bubbles rising to the bed surface instead of collapsing, indicating that bubbles must be below a critical size in order to collapse. For side-by-side bubbles, bubble collapse is attributed to gas flow channeling to the larger bubble; for consecutive bubbles, bubble collapse is attributed to increased gas leakage in a dilated bubble wake.

There has been much debate over the past decade or so over the scaling of the thickness of the turbulent/nonturbulent (TNT) interface for turbulent shear flows. It is generally considered to consist of the outer viscous superlayer, in which viscous processes are significant, and an inner turbulent sublayer which is dominated by inertial processes. Various authors have stated that the interface thickness scales with the Taylor length scale $\lambda$ while others state that it scales with the Kolmogorov length scale $\eta$ [Buxton et al., Phys. Fluids 23, 061704 (2011)]. Frequently, only self-similar turbulent flows are considered in which a single value of either $\lambda$ or $\eta$ is sufficient to scale various phenomena, including the thickness of the TNT interface. In this paper we show that for flows which are not self-similar the local Kolmogorov length scale increases quite significantly as one moves closer to the boundary between the turbulent and nonturbulent fluid. We find that the variation of this local Kolmogorov length scale with normal distance from the TNT boundary may be collapsed by the local Kolmogorov length scale computed from the TNT boundary itself. We subsequently show that this variation in local Kolmogorov length scale occurs concurrently with an increase in the small-scale anisotropy in the TNT interface. This anisotropy peaks at the boundary between the viscous superlayer and the turbulent sublayer, suggesting that these two sublayers are in fact quite distinct from one another. We show that these results hold for a number of different TNT interfaces from various flows and with the bulk turbulence being in a variety of states of development. The local viscous scaling that we obtain, along with an increase in anisotropy primarily driven by an increased magnitude of velocity gradients in the TNT-boundary-normal direction, leads us to draw an analogy between TNT interfaces and the wall in wall-bounded turbulence.

While data-based approaches were found to be useful for subgrid scale (SGS) modeling in Reynolds-averaged Navier-Stokes (RANS) simulations, there have not been many attempts at using machine learning techniques for wall modeling in large-eddy simulations (LESs). Large-eddy simulation differs from RANS simulation in many aspects. For one thing, LES is scale resolving. For another, LES is in and of itself a high-fidelity tool. Because data sets of higher fidelity are in general not frequently accessible or available, this poses additional challenges to data-based modeling in LES. Further, SGS modeling usually needs flow information at only large scales, in contrast with wall modeling, which needs to account for both near-wall small scales and large scales above the wall. In this work we discuss how the above-noted challenges may be addressed when taking a data-based approach for wall modeling. We also show the necessity of incorporating physical insights in model inputs, i.e., using inputs that are inspired by the vertically integrated thin-boundary-layer equations and the eddy population density scalings. We show that the inclusion of the above physics-based considerations would enhance extrapolation capabilities of a neural network to flow conditions that are not within the train data. Being cheap to evaluate and using only channel flow data at ${\mathrm{Re}}_{\tau }=1000$, the trained networks are found to capture the law of the wall at arbitrary Reynolds numbers and outperform the conventional equilibrium model in a nonequilibrium flow.

Elastic stress concentration at the tips of long slender objects moving in viscoelastic fluids has been observed in numerical simulations, but despite the prevalence of flagellated motion in complex fluids in many biological functions, the physics of stress accumulation near the tips has not been analyzed. Here, we theoretically investigate elastic stress development at the tips of slender objects by computing the leading-order viscoelastic correction to the equilibrium viscous flow around long cylinders, using the weak-coupling limit. In this limit, nonlinearities in the fluid are retained, allowing us to study the biologically relevant parameter regime of high Weissenberg number. We calculate a stretch rate from the viscous flow around cylinders to predict when large elastic stress develops at the tips, find thresholds for large stress development depending on orientation, and calculate greater stress accumulation near the tips of cylinders oriented parallel to the motion over perpendicular.

We consider the effect of heat-flux boundary conditions, replacing the previously studied isothermal wall conditions, on the Rayleigh-Bénard instability in a rarefied gas. The problem is investigated in the limit of small Knudsen numbers, by means of a linear stability analysis of a slip flow model, and the direct simulation Monte Carlo method. In the latter, a noniterative algorithm is applied to implement the heat-flux conditions. The results delineate the instability domain in the parameters plane of the Knudsen number (Kn), Froude number (Fr), and walls reference temperature ratio. The heat-flux conditions result in a significant destabilizing effect, extending instability to larger Knudsen numbers. At large Fr, the Boussinesq limit is recovered, and transition to instability is governed by a critical value of the Rayleigh number. With decreasing Fr, gas compressibility becomes dominant, confining the convection layer to the vicinity of the upper cold wall. Asymptotic analysis of the low-Fr limit is carried out, to highlight the impact of difference in thermal conditions. The Monte Carlo scheme is applied to investigate system instability at supercritical states, where walls heat-flux conditions lead to elevated shear stresses. Nonmonotonic variations in the walls shear stress with Kn are observed and discussed.

Tidal flow over oceanic topography generates internal waves when the natural frequency $N$ of the water is greater than the tidal frequency $\omega$. When $N<\omega$, evanescent waves are generated. Although the amplitude and kinetic energy of evanescent waves decay rapidly, if the wave reaches a turning depth, where $N=\omega$, and moves into a region where $N>\omega$, the evanescent wave becomes an internal wave. This work expands upon previous research of varying stratifications by investigating the kinetic energy density in internal waves generated by evanescent waves passing through a turning depth. An analytical model is presented and compared to synthetic schlieren experiments of two Gaussian-shaped topographies. The model and experiments both indicate that the kinetic energy density of internal waves increases with decreasing topographic slope, when the distance between the topography and the turning depth decreases and when the average Froude number in the evanescent region is close to one. The model is used to estimate the normalized kinetic energy density of internal waves generated from an oceanic feature located within an evanescent region.

Evaporative loss of a volatile solvent can induce concentration inhomogeneities that give rise to spatial gradients in surface tension and subsequent solutocapillary Marangoni flows. This phenomenon is studied in the context of ultrathin liquid films resting atop curved convex substrates in contact with a fluid reservoir. Experiments are conducted with low-molecular-weight polydimethylsiloxane (silicone oil) mixtures composed of a volatile solvent and trace amounts of a nonvolatile solute. A theoretical model based on the thin-film approximation is developed, incorporating the effects of evaporative mass loss, gravity, capillarity, van der Waals forces, species diffusion, and Marangoni stresses. The spatiotemporal evolution of this system is studied by modulating the rate of evaporation of the volatile species and the bulk solute volume fraction in the mixture. The experiments and accompanying numerical simulations reveal that both Marangoni stresses and stabilizing van der Waals interactions between the substrate and the free surface can induce flow reversal and film regeneration. Their relative contribution is modulated by the solutocapillary Marangoni number, which is proportional to the bulk concentration of nonvolatile species in the mixture. Furthermore, it is revealed that increasing the rate of evaporation enhances the volumetric flow rate from thicker, solvent-rich areas towards thinner, solute-rich regions of the film. Although quantitative differences between the theory and the experiments are observed within certain ranges of the controlled parameters, the model qualitatively reproduces the flow regimes observed in the experiments and elucidates the complex interplay among the various physical forces.

Instabilities of reactive miscible flows in homogeneous porous media are investigated in the presence of nanocatalysts undergoing $A+B+n\to C+n$ reaction. The analysis is conducted under both isothermal and nonisothermal conditions resulting from the heat of reaction. Ignoring double diffusive effects of the different components, a new set of conditions is introduced to predict the instability of the isothermal case based on the species mobility ratios. Validated with nonlinear simulations, these conditions predict well the instability of the system and how the chemical product develops after the reaction. Examination of flows that account for the heat of reaction with no effect on the mobility ratios reveals that these conditions are no longer valid. This result is in contrast with nanocatalyst-free flows. In these systems the stability condition is unaffected by the heat of reactions that has neutral effects on mobility ratios. This difference is attributed to the nanocatalysts transport phenomena and in particular to thermophoretic effects arising from the temperature gradients in the flow. These effects are analyzed for both exothermic and endothermic chemical reactions.

In forward flight, high advance ratio rotors encounter a large region of reverse flow on their retreating side. The reverse flow region is the cause of significant separation in sharp-trailing edge rotor blades and is believed to be dominated by a flow structure called the reverse flow dynamic stall vortex (RFDSV). This vortex incurs large, unsteady torsional loads that are not well-predicted by modern comprehensive rotorcraft codes. To gain a physical understanding of the impact of yaw on the RFDSV, a subscale, NACA0012 model rotor blade has been experimentally tested at two reverse flow yaw angles, ${\mathrm{\Lambda }}_{\mathrm{rev}}=0^{\circ }$ (unyawed) and ${\mathrm{\Lambda }}_{\mathrm{rev}}={30}^{\circ }$ (yawed), over a range of reduced frequencies, $0.160<k<0.450$. Pressure time histories were obtained from surface-mounted unsteady pressure transducers, and three-component velocity fields were obtained using stereoscopic particle image velocimetry at the midspan. The present work focuses on the impact of yaw on the strength, number, and behavior of vortices shed for a given set of pitch kinematics. In cases where the unyawed blade shed multiple vortices, the presence of yaw was found to suppress secondary flow structures, including the trailing-edge vortex, and thus delay the breakup of the RFDSV to later times in the pitch cycle. The suppression of secondary flow structures was consistent across multiple kinematic scalings of the flow field, suggesting that the flow at ${\mathrm{\Lambda }}_{\mathrm{rev}}={30}^{\circ }$ is subject to physical mechanisms not present at ${\mathrm{\Lambda }}_{\mathrm{rev}}=0^{\circ }$. This work proposes that spanwise flow, which was found to substantially increase at ${\mathrm{\Lambda }}_{\mathrm{rev}}={30}^{\circ }$, amplifies small spanwise vorticity gradients in the flow field and results in the net transport of vorticity along the blade span. The transport of vorticity, particularly in three-dimensional flows, is the subject of ongoing experimental efforts, and the current work represents a first step in understanding its role in reverse flow aerodynamics.

We characterize microfluidic flows of jammed suspensions of soft microgels (Carbopol) behaving as yield-stress fluids. We quantify the wall slip friction, i.e., the slip velocity $V$ versus the tangential stress at the wall ${\sigma }_w$. We demonstrate a transition in slip regimes, from a nonlinear behavior ($V\propto {\sigma }_w^2$) to a linear one, as the stress at the wall is increased, as expected from scaling arguments. Using fluorescent imaging to characterize the microgel size, we rationalize the two friction regimes for various samples by estimating viscous and elastic forces at the scale of the microgel particle. Only local arguments are thus necessary to predict wall slip friction, in contrast to other complex flow features such as fluidity or shear banding where bulk and surface properties appear to be strongly related.

Using direct numerical simulation (DNS), we investigate how gravity modifies the multiscale dispersion of bidisperse inertial particles in isotropic turbulence. The DNS has a Taylor Reynolds number $R_{\lambda }=398$, and we simulate Stokes numbers (based on the Kolmogorov timescale) in the range $\text{St}\le 3$ and consider Froude numbers $\text{Fr}=0.052$ and $\infty$, corresponding to strong gravity and no gravity, respectively. The degree of bidispersity is quantified by the difference in the Stokes number of the particles, $\left|\mathrm{\Delta }\text{St}\right|$. We first consider the mean-square separation of bidisperse particle pairs and find that, without gravity (i.e., $\text{Fr}=\infty$), bidispersity leads to an enhancement of the the mean-square separation over a significant range of scales. When $\left|\mathrm{\Delta }\text{St}\right|\ge O\left(1\right)$, the relative dispersion is further enhanced by gravity due to the large difference in the settling velocities of the two particles. However, when $\left|\mathrm{\Delta }\text{St}\right|\ll 1$, gravity suppresses the relative dispersion as the settling velocity contribution is small, and gravity suppresses the nonlocal contribution to the particle dynamics. In order to gain further insights, we consider separately the relative dispersion in the vertical (parallel to gravity) and horizontal directions. As expected, the vertical relative dispersion can be strongly enhanced by gravity due to differences in the settling velocities of the two particles. However, a key finding of our study is that gravity can also significantly enhance the horizontal relative dispersion. This nontrivial effect occurs because fast settling particles experience rapid fluctuations in the fluid velocity field along their trajectory, leading to enhanced particle accelerations and relative velocities. For sufficiently large initial particle separations, however, gravity can lead to a suppression of the horizontal relative dispersion. We also compute the probability density function (PDF) of the particle-pair dispersion. Our results for these PDFs show that even when $\text{Fr}\ll 1$ and $\left|\mathrm{\Delta }\text{St}\right|\ge O\left(1\right)$, the vertical relative dispersion of the particles can be strongly affected by turbulence. This occurs because although the settling velocity contribution to the relative motion is much larger than the “typical” velocities of the turbulence when $\text{Fr}\ll 1$ and $\left|\mathrm{\Delta }\text{St}\right|\ge O\left(1\right)$, due to intermittency, there are significant regions of the flow where the turbulent velocities are of the same order as the settling velocity. These findings imply that in many applications where $R_{\lambda }⋙1$ the effect of turbulence on the vertical relative dispersion of settling bidisperse particles may never be ignored, even if the particles are settling rapidly.

Turbulent Rayleigh-Bénard convection was investigated within a liquid metal layer, Prandtl number $\mathrm{Pr}=0.03$, in a square vessel having a moderate aspect ratio, $\mathrm{\Gamma }=5$. Laboratory experiments were performed at moderate Rayleigh numbers, $7.9\times {10}^3<\mathrm{Ra}<3.5\times {10}^5$. Ultrasonic velocity profiling was used to visualize the spatiotemporal flow structure in two horizontal planes, while temperature fluctuations were monitored simultaneously in the fluid layer. By using multiple ultrasonic sensors, a grid of orthogonal measurement lines was created. This configuration enabled the identification of coherent flow structures showing periodic oscillations. In particular, oscillatory roll-like structures were observed for $\mathrm{Ra}\lesssim 6\times {10}^4$, while the transition to a new-found, fully three-dimensional cellular structure occurs around $\mathrm{Ra}=7\times {10}^4$. The Fourier analysis of the temperature fluctuations indicates that the convection reaches the developed state of thermal turbulence at this $\mathrm{Ra}$ number. This cellular structure of the flow field is recognized as a representation of the large-scale circulation in thermal turbulence for the specific situation of confined convection in the rectangular vessel. The transition from laminar convection to thermal turbulence manifests itself in the occurrence of unstable intermediate regimes accompanied by a stepwise increment in the horizontal scale. We suggest scaling laws for the characteristic velocity and the dominating oscillation frequency and based on that for the horizontal length scale as a function of the Ra number. The comparison to corresponding values of characteristic length scales published for thermal convection in air in larger aspect ratios $[\mathrm{Pr}=0.7$, T. Hartlep et al., Phys. Rev. Lett. 91, 064501 (2003), A. Pandey et al., Nat. Commun. 9, 2118 (2018), and D. E. Fitzjarrald, J. Fluid Mech. 73, 693 (1976)] reveals a different $\mathrm{Ra}$ number dependence of the horizontal wave number.

The wake characteristics and force production of an aspect-ratio-8 flat plate rectangular wing starting from rest at a high angle of attack ($\alpha ={45}^{\circ }$) were examined. The first portion of this paper presents experimental measurements that focus on circulation production at the leading edge of the wing. Circulation production is shown to be coupled to both the wing kinematics and the wake state. The second portion of the paper reviews the implementation of several pertinent potential flow models from the literature and compares the results of these models to the experimental results. Quasisteady and fixed-wake models were found to be poor predictors of both force and circulation. A similarity-solution-based model was found to make accurate predictions only at very short times. An unsteady strength two-vortex model predicted the circulation production during the acceleration portion of the kinematics, but did not predict the force. A multiple-discrete-vortex model was found to predict both the force and circulation production well, but had difficulty after the shedding of the first leading-edge vortex.

Probability density functions (PDFs) give well-rounded statistical descriptions of stochastic quantities and therefore are fundamental to turbulence. Wall-bounded turbulent flows are of particular interest given their prevalence in a vast array of applications, but for these flows the scaling of velocity probability distribution is still far from being well founded. By exploiting the self-similarity in wall-bounded turbulent flows and modeling velocity fluctuations as results of self-repeating processes, we present a theoretical argument, supported by empirical evidence, for a universal velocity PDF scaling in high-Reynolds-number wall turbulence.

The aerodynamic loads on a static airfoil are modified below its stall margin by deliberate formation and regulation of trapped vorticity on the suction and pressure surfaces near the trailing edge. Vorticity accumulation and shedding are effected using a hybrid actuator comprising a miniature two-dimensional passive protuberance having a cross-stream scale that is nominally commensurate with the local boundary layer thickness, and the vorticity flux is regulated using integrated spanwise arrays of equally spaced high aspect ratio synthetic jet actuators. The aerodynamic loads are varied by independent differential control of flux of opposite sense vorticity from both sides of the airfoil that are characterized using measurements of the force/torque, surface pressure, and particle image velocimetry over the suction surface and in the airfoil's near wake. The induced changes in circulation and lift and in the pitching moment are traced to complex transitory changes in vorticity flux associated with the onset and termination of the actuation. These changes are characterized by transitory variations in the balance of flux and shedding of clockwise and counterclockwise vorticities that are triggered, respectively, by actuation on the pressure or suction surfaces. These investigations indicate that hybrid flow control by trapped vorticity, which has the potential to manipulate prestall aerodynamic loads without mechanical control surfaces, may enable novel wing designs.

We present a series of experiments on a one-degree-of-freedom circular cylinder allowed to exhibit pure translational motion in the streamwise direction. Our displacement measurements confirm the existence of two nonzero amplitude regions in the amplitude response: one at lower reduced velocities, which is accompanied by a symmetric shedding, and one at higher reduced velocities, which is accompanied by asymmetric shedding. Besides the typical displacement measurements that have been conducted in previous studies on this system, the current experiments include force measurement results for such systems. A combination of (i) synchronized displacement measurements, force measurements, and flow visualizations, (ii) a very fine reduced velocity step, and (iii) a highly controlled setup, which allows a pure inline displacement, has enabled us to (i) observe an intermediate wake mode, which occurs for reduced velocities between the range of symmetric and asymmetric reduced velocities, and (ii) relate the wake transition to the fine changes in the ratio of fluctuating lift to fluctuating drag. We call the wake mode that we have identified the alternating-symmetric mode, since in this mode two vortices of opposite signs are shed per cycle of oscillations, but their sizes relative to one another alternate for every cycle.

A numerical investigation of electrohydrodynamics of an initially spherical droplet suspended in a continuous fluid subjected to shear flow in the presence of an electric field is presented. The numerical framework is based on coupling of a multicomponent lattice Boltzmann method with a leaky dielectric model. Simulations reveal distinct deformation and breakup behavior of the droplet for a fixed channel confinement and for widely different viscosity ratio $\lambda$. For each $\lambda$, defined as ratio of droplet to outer fluid viscosity ($\lambda ={\mu }_d/{\mu }_c$), computations are performed for two specific combinations of electrical properties given by ratios of conductivity $R(={\sigma }_d/{\sigma }_c)$ and permittivity $S(={\varepsilon }_d/{\varepsilon }_c)$. Simulations show that the droplet orients toward the direction of shearing motion for $R<S$, whereas it orients along the direction of applied electric field when $R>S$. For $R>S$, the droplet elongation increases with an increase in electric field and breakup of the droplet into smaller droplets is observed beyond a threshold value. The application of electric field also results in the breakup of highly viscous droplets which otherwise are very difficult to break in shear flows. In contrast, the droplet elongation for $R<S$ is observed to be dependent upon the competing interplay of electric and shear stresses acting at the droplet interface. The cumulative effect of electric field and shear flow alters the shear stress acting at the droplet interface, thereby leading to a deviation in the droplet dynamics when $R<S$.

We report an experimental study of the instability of a nearly resonant Kelvin mode forced by precession in a cylindrical vessel. The instability is detected above a critical precession ratio via the appearance of peaks in the temporal power spectrum of pressure fluctuations measured at the end walls of the cylinder. The corresponding frequencies can be grouped into frequency sets satisfying resonance conditions with the forced Kelvin mode. We show that one set forms a triad that is associated with a parametric resonance of Kelvin modes. We observe a significant frequency variation of the unstable modes with the precession ratio, which can be explained by a detuning mechanism due to the slowdown of the background flow. By introducing a semianalytical model, we show that the departure of the flow from the solid body rotation leads to a modification of the dispersion relation of Kelvin modes and to a detuning of the resonance condition. The second frequency set includes a very low frequency and does not exhibit the properties of a parametric resonance between Kelvin modes. Interestingly, this frequency set always emerges before the occurrence of the triadic resonances, i.e., at a lower precession ratio, which implies that it may correspond to a different type of instability. We discuss the relevance of an instability of a geostrophic mode described by Kerswell [Kerswell, J. Fluid Mech. 382, 283 (1999)], although other mechanisms cannot be completely ruled out.