A resolvent-based methodology is employed to obtain spatiotemporal estimates of turbulent pipe flow from probe measurements of wall shear-stress fluctuations. Direct numerical simulations (DNSs) and large-eddy simulations (LESs) of turbulent pipe flow at a friction Reynolds number of 550 are used as databases. We consider a DNS database as the true spatiotemporal flow field, from which wall shear-stress fluctuations are extracted and considered as measurements. A resolvent-based estimator is built following our earlier work [Amaral et al., J. Fluid Mech. 927, A17 (2021)], requiring a model for the nonlinear (or forcing) terms of the Navier-Stokes equations system, which are obtained from another DNS database, as in our earlier work, and from a series of computationally cheaper LES databases with coarser grids; the underlying idea is that LESs may provide accurate statistics of nonlinear terms related to large-scale structures at a low computational cost. Comparisons between the DNS and the estimates indicate that sufficiently accurate results can be achieved with estimators built with statistics from LESs with an order of magnitude fewer grid points than the DNSs, with estimates closely matching the reference DNS results up to the buffer layer and reasonable agreement up to the beginning of the log layer.

A circular cylindrical segment is a sharp-crested weir with a circular downstream curve profile. Overflow characteristics of circular cylindrical and circular-crested weirs have been studied extensively over the past century. Meanwhile, the available literature on the circular cylindrical segment is comparatively limited. Previous studies have often employed the potential flow theory to predict the mean velocities, pressure, and discharge coefficient, which may not be able to accurately predict the flow characteristics for a circular cylindrical segment. The aim of the present study is to experimentally investigate turbulent flows over circular cylindrical segments and to provide equations that can predict the mean velocities along the weir. Three upstream face angles $\alpha ={90}^{\circ }, {45}^{\circ }$, and ${30}^{\circ }$, and three water depths over the crest $D_c/h=0.7$, 0.4, and 0.2, were tested to simultaneously characterize the effects of both the upstream face angle and water depth. The instantaneous velocities were measured using a planar particle image velocimetry system in an open recirculating water channel. The results showed the presence of a recirculation bubble at the crest of the weir for all test conditions. The size of this recirculation zone decreases as the water depth or the upstream face angle decreases. At a far enough distance from the recirculation zone, the mean angular momentum varied linearly in the circumferential direction. Meanwhile, a rigid-body rotation region was detected near the free surface, which grows thicker in the circumferential direction.

In this study, we consider the buoyancy-driven flow of a non-Newtonian fluid over an inclined flat plate immersed in a thermally stratified medium. Using the Carreau model, we determine the base flow profiles and associated linear stability results for both pseudoplastic and dilatant fluids. For steady basic flow, the shear-thinning behavior enhances the convection and heat transfer characteristics while it is opposite for shear-thickening flow. Based on linear stability analysis, the effects of Prandtl number, tile angle, and power-law index on the transverse traveling Tolmien-Schlichting waves, the stationary longitudinal rolls and the oblique rolls are investigated. Different from the Newtonian fluids, under appropriate parameters, a new oblique rolls mode appears in dilatant fluids. Furthermore, it is shown that both the TS mode and OR mode are destabilized and stabilized for shear-thinning and shear-thickening fluids, respectively. However, non-Newtonian effects always stabilize the SL mode. These results reveal that the nature of the stability depends on the rheological properties significantly.

We combine experiments and numerical computations to examine underlying fluid mechanical processes associated with bioaerosol generation during violent respiratory maneuvers, such as coughing or sneezing. Analogous experiments performed in a cough machine—consisting of a strong shearing airflow over a thin liquid film—allow us to illustrate the changes in film topology as it disintegrates into small droplets. We identify that aerosol generation during the shearing of the liquid film is mediated by the formation of inflated baglike structures. The breakup of these bags is triggered by the appearance of retracting holes that puncture the bag surface. Consequently, the cascade from inflated bags to droplets is primarily controlled by the dynamics and stability of liquid rims bounding these retracting holes. We also reveal the key role of fluid viscosity in the overall fragmentation process. It is shown that more viscous films when sheared produce smaller droplets.

The dynamics of the axisymmetric jets originated from the bursting of bubbles in a liquid of density $\rho$, viscosity $\mu$, and interfacial tension coefficient $\sigma$ can be rationalized as a two-stage process in which, initially, the pressure jump $\sim \sigma /R_b$ accelerates the liquid towards the axis of symmetry, inducing a far-field flow rate per unit length $Q_{\infty }\propto V_c{R}_b$, with $R_b$ and $V_c=\sqrt{\sigma /\left(\rho R_b\right)}$ indicating the radius of the bubble and the capillary velocity, respectively. The second stage, during which a fast jet of radius $R_{\mathrm{jet}}\left(T\right)\ll R_b$ and velocity $V_{\mathrm{jet}}\left(T\right)\gg V_c$ is ejected, is driven by the far-field radial velocity field established initially, which forces the collapse of the cavity walls while keeping $Q_{\infty }$ practically constant in time because liquid inertia and mass conservation prevent appreciable changes of this quantity during the very short timescale characterizing the ejection of the jet. Our theoretical predictions for $R_{\mathrm{jet}}\left(T\right)$ and $V_{\mathrm{jet}}\left(T\right)$ reproduce fairly well the time evolution of the jet width and of the jet velocity for over three decades in time, obtaining good agreement with numerical simulations from the instant of jet inception until $R_{\mathrm{jet}}\sim R_b$. The analytical expressions for the jet width and for the jet velocity provided here constitute the initial conditions for the explicit solution of the ballistic equations deduced in Gekle and Gordillo [J. Fluid Mech. 663, 293 (2010)], which, hence, can be straightforwardly used in order to quantify the size and velocity of the first drop ejected and the fluxes of mass, momentum, and energy transferred from the ocean into the atmosphere. In addition, motivated by the results obtained for the particular case of bubble bursting jets, we also present here a unified theoretical framework aimed at quantifying the dynamics of the type of generic jets produced by the collapse of axisymmetric gas cavities of arbitrary shape when their implosion is forced by the radial velocity induced by a far-field boundary condition expressing that the dimensionless liquid flow rate per unit length directed towards the axis of symmetry, $q_{\infty }$, remains constant in time. Making use of theory and of full numerical simulations, we first analyze the case of the collapse of a conical bubble with a half-opening angle $\beta$ finding that, when the value of $q_{\infty }$ is fixed to a constant, this type of axisymmetric jets converge towards a purely inertial $\beta$-dependent self-similar solution of the inviscid Navier-Stokes equations, described here for the first time, which is characterized by the fact that the jet width and velocity are respectively given, in the limit $\beta \ll 1$, by $r_{\mathrm{jet}}\approx 2.25tan\beta \sqrt{q_{\infty }\tau }$ and $v_{\mathrm{jet}}\approx 3q_{\infty }/(2tan\beta \sqrt{q_{\infty }\tau })$, with $\tau$ indicating the dimensionless time after the jet is ejected. For the case of parabolic cavities with a dimensionless radius of curvature at the plane of symmetry $r_c$, our theory predicts that $r_{\mathrm{jet}}\propto {\left(2r_c\right)}^{-1/2}{\left(q_{\infty }\tau \right)}^{3/4}$ and $v_{\mathrm{jet}}\propto q_{\infty }{\left(2r_c\right)}^{1/2}{\left(q_{\infty }\tau \right)}^{-3/4}$, a result which is also in good agreement with full numerical simulations. The present results might also find applications in the description of the very fast jets, with velocities reaching up to 1000 m ${\mathrm{s}}^{-1}$, produced after a bubble cavitates very close to a wall and in the quantification of the so-called bazooka effect.

We study steady flows that are optimal for heat transfer in a two-dimensional periodic domain. The flows maximize heat transfer under the constraints of incompressibility and a given energy budget (i.e., mean viscous power dissipation). Using an unconstrained optimization approach, we compute optima starting from 30–50 random initializations across several decades of Pe, the energy budget parameter. At Pe between ${10}^{4.5}$ and ${10}^{4.75}$, convective rolls with U-shaped branching near the walls emerge. They exceed the heat transfer of the simple convective roll optimum at Pe between ${10}^5$ and ${10}^{5.25}$. At larger Pe, multiple layers of branching occur in the optima and become increasingly elongated, asymmetrical, and heterogeneous. The rate of heat transfer scales as ${\mathrm{Pe}}^{0.575}$, which, in this range of Pe, is very close to the ${\mathrm{Pe}}^{2/3}{(ln\mathrm{Pe})}^{-4/3}$ behavior of self-similar branching solutions proposed earlier. Compared to the simple convective roll, the branching flows have lower maximum speeds and thinner boundary layers but nearly the same maximum power density.

The effects of density and viscosity fluctuations on the total stress balance are identified and used to create a mean velocity transformation for compressible boundary layers. This work is enabled by an extensive database of direct numerical simulations that incorporate wall-cooling, semilocal Reynolds numbers ranging from 800 to 34 000, and Mach numbers up to 12. The role, significance, and physical mechanisms connecting density and viscosity fluctuations to the momentum balance and to the viscous, turbulent, and total stresses are presented, allowing the creation of generalized formulations. We identify the significant properties that thus far have been neglected in the derivation of velocity transformations: (1) the Mach invariance of the near-wall momentum balance for the generalized total stress and (2) the Mach invariance of the relative contributions from the generalized viscous and Reynolds stresses to the total stress. The proposed velocity transformation integrates both properties into a single transformation equation and successfully demonstrates a collapsing of all currently considered compressible cases onto the incompressible law of the wall, within the bounds of reported slope and intercept for incompressible data. Based on the physics embedded in the two scaling properties, the success of the proposed transformation is attributed to considering the effects of the viscous stress and turbulent stresses as well as mean and fluctuating density viscosity in a single transformation form.

Particles such as microplastics and phytoplankton suspended in the water column in the natural environment are often subject to the action of surface gravity waves. By modeling such anisotropic particles as small spheroids that slowly settle (or rise) in a wavy environment, we consider how the particle shape and buoyancy couple to the background wave-driven flow to influence the particle orientation, drift, and dispersion. A multiscale expansion allows the wave-induced oscillations to be separated from the wave-averaged particle motion. Using the wave-averaged equations of particle motion, we demonstrate that spheroidal particles have a wave-induced preferential orientation with different stable solutions for prolate and oblate particles. The resulting preferential orientation positions particles with their longest axis pointing in the direction of wave propagation and upwards against gravity. The angle at which the longest axis points upwards is a function of particle aspect ratio. In this orientation, particles drift in the direction opposite to wave propagation, weakening and potentially even reversing their Stokes drift. The wave-induced stable orientation also results in a reduced settling velocity relative to a random (isotropic) orientation. The dispersion of a particle cloud is controlled by the distribution of orientations. For a cloud of particles released together with random (isotropic) orientation, the initial cloud growth rate is ballistic in all directions. Wave action acts to suppress the vertical dispersion but enhances horizontal dispersion into a super-ballistic state when the Stokes drift shear acts on a particle cloud that has expanded in the vertical direction.

In confined rotating convection, a strong zonal flow can develop close to the side wall with a modal structure that precesses anticyclonically (counter to the applied rotation) along the side wall. It is surmised that this is a robust nonlinear evolution of the wall modes observed before the onset of bulk convection. Here, we perform direct numerical simulations of cylindrically confined rotating convection at high rotation rates and strong turbulent forcing. Through comparison with earlier work, we find a fit-parameter-free relation that links the angular drift frequency of the robust wall mode observed far into the turbulent regime with the critical wall mode frequency at onset, firmly substantiating the connection between the observed boundary zonal flow and the wall modes. Deviations from this relation at stronger turbulent forcing suggest early signs of the bulk turbulence starting to hamper the development of the wall mode. Furthermore, by studying the interactive flow between the robust wall mode and the bulk turbulence, we identify radial jets penetrating from the wall mode into the bulk. These jets induce a large-scale multipolar vortex structure in the bulk turbulence, dependent on the wave number of the wall mode. In a narrow cylinder the entire bulk flow is dominated by a quadrupolar vortex driven by the radial jets, while in a wider cylinder the jets are found to have a finite penetration length and the vortices do not cover the entire bulk. We also identify the role of Reynolds stresses in the generation of zonal flows in the region near the sidewall.

Capillary-driven self-assembly is a common fabrication method that consists of placing floating particles onto a liquid-air interface. The attractive interaction between particles is due to the local deformations of the interface and is often described via so-called capillary charges. This approach holds for similar particles far from each other. When particles are close together or when they differ in size, their contact lines become tilted. By using different spherical particles, we show evidence experimentally that the capillary interaction becomes far more complex. We propose to consider induced capillary dipoles to model the menisci, therefore providing an extra attraction at short distances. This effect is enhanced for particles of different sizes such that binary self-assemblies reveal unusual local ordering.

The leading-edge vortex (LEV) formation on the caudal fin (CF) has been identified as playing a key role in efficient lift-based thrust production of fish-like propulsion. The enhancement of the CF LEV through its interaction with vortices formed upstream due to a median fin with a distinct shape is the focus of this paper. High-speed, high-fidelity videos and particle imaging velocimetry (PIV) were obtained from rainbow trout during steady forward swimming to visualize the undulatory kinematics and two-dimensional flow behavior. Body kinematics are quantified using a traveling-wave formulation that is used to prescribe the motion of a high-fidelity three-dimensional surface model of the fish body for a computational fluid dynamics (CFD) study. The pressure field of the CFD result is compared and validated with the PIV result from the experiment. Using CFD, the vortex forming and shedding behaviors of the anal fin (AF) and their capturing and interaction with the trunk (TK) and the CF are visualized and examined. Coherent AF-bound LEVs are found to form periodically, leading to thrust production of the AF. The vortices subsequently shed from the AF are found to help stabilize and reinforce the LEV formation on the CF by aiding LEV initiation at stroke reversal and enhancing LEV during a tail stroke, which leads to enhancement of lift-based thrust production. The CF is found to shed vortex tubes (VTs) that create backward-facing jets, and the ventral-side VT and the associated backward jets are both strengthened by vortices shed by the AF. An additional benefit of the AF is found to be reduction of body drag by reducing the lateral crossflow that leads to loss of beneficial pressure gradient across the body. Through varying AF-CF spacing and AF height, we find that CF thrust enhancement and TK drag reduction due to the AF are both affected by the position and size of the AF. The position and area of the AF that led to the most hydrodynamic benefit are found to be the original, anatomically accurate position and size. In this paper, we demonstrate the important effect of vortex interaction among propulsive surfaces in fish-like propulsion.

We propose an electrohydrodynamics model to describe the dynamic evolution of a slender drop containing a dilute ionic surfactant on a naturally wettable surface, with a varying external electric field. This unified model reproduces fundamental microfluidic operations controlled by electrical signals, including dewetting, rewetting, and droplet shifting. In this paper, lubrication theory analysis and numerical simulations illustrate how to electrically control the wettability of surface via the charged surfactant. Our numerical results show that electric field promotes dewetting by attracting ionic surfactants onto the transition thin-film region and promotes rewetting by attracting them away from the region.

The total force experienced by a droplet embedded in a uniform oscillating flow can be divided into four contributions: steady drag force, inertial or pressure gradient force, added-mass force, and Basset-Boussinesq history force. The effect of the history force is often neglected, due to numerical difficulties for its time integration, but also because no analytic expression is available in the time domain for droplets. The contribution of the history force acting on a spherical droplet in an oscillatory flow is determined using direct numerical simulation. Variation of the viscosity ratio makes the analysis relevant to bubbles, droplets, and solid particles. By changing the flow oscillation frequency, we can determine the range of physical parameters for which the contribution of the history force is significant. Additionally, the relevance of the kernel expression recently proposed by Legendre et al. [Phys. Rev. Fluids 4, 073603 (2019)] is discussed and compared to theoretical predictions in the frequency domain. We demonstrate that this kernel can be used to model history effects for droplets, especially since the contribution of the history force to the total force is important. The proposed history force expression provides a significant improvement for droplet trajectory prediction when the history force contribution cannot be neglected.

Supersonic pretransitional boundary layers flowing over porous flat and concave surfaces are studied using numerical and asymptotic methods. The porous wall is composed of thin equally spaced cylindrical microcavities. The flow is perturbed by small-amplitude, free-stream vortical disturbances of the convected gust type. From the proximity of the leading edge, these external agents generate the compressible Klebanoff modes, i.e., low-frequency disturbances of the kinematic and thermal kind that grow algebraically downstream. For Klebanoff modes with a spanwise wavelength comparable with the boundary-layer thickness, the porous surface has a negligible effect on their growth. When the spanwise wavelength is instead larger than the boundary-layer thickness, these disturbances are effectively attenuated by the porous surface. For a specified set of frequency and wavelengths, the Klebanoff modes evolve into oblique Tollmien-Schlichting waves through a leading-edge-adjustment receptivity mechanism. The wave number of these waves is only slightly modified over the porous surface, while the growth rate increases, thus confirming previous experimental results. An asymptotic analysis based on the triple-deck theory confirms these numerical findings. When the wall is concave, the amplitude of the Klebanoff modes is enhanced by the wall curvature and is attenuated by the wall porosity during the initial development.

When a fluid in turbulent motion is tagged by a nonuniform concentration of ideal tracers, the mean velocity of the tracers may not match with the mean velocity of the fluid flow. This implies that conventional particle tracking velocimetry will not produce the mean flow of a turbulent flow unless the particle seeding is homogeneous. In this work, we consider the problem of mean flow estimation from a set of particle tracks obtained in a situation of nonhomogeneous seeding. To compensate the bias caused by the nonhomogeneous particle seeding, we propose a modified particle tracking velocimetry method. This method is called a time-delayed velocity and considers the velocity trajectory of a given particle shifted in time with respect to its position. We first introduce our method for an ideal advection–diffusion model and then we implement it for a turbulent channel and a turbulent jet. For both situations, we find that the velocity bias caused by the nonhomogeneous tracer concentration is reduced with a time delay introduced between position and velocity of the tracer trajectories. For the turbulent channel, the error on the mean flow estimation monotonically decreases for increasing time delays. For the turbulent jet, the error on the mean flow estimation also reduces with positive time delays but the time delay should not be too large. We interpret this limitation as a consequence of the spatial dependence of the mean flow. For the turbulent channel, this limitation does not appear because the velocity for the mean flow streamlines is constant. For both flows, the optimal time delay for the velocity bias compensation is consistent with the Lagrangian timescales of the flow. This method gives promising elements to take into account inhomogeneous seedings in velocity fields measurements for all kinds of turbulent flows and interesting perspectives to understand how Lagrangian trajectories from various sources build an Eulerian mean field.

To get a deeper understanding of our laboratory experiments [Q. Kriaa et al., Phys. Rev. Fluids 7, 124302 (2022)], we numerically model settling clouds produced by localized instantaneous releases of heavy particles in a quiescent fluid. By modeling particles as a field of mass concentration in an equilibrium Eulerian approach, our two-way coupling simulations recover our original experimental observation of a maximum growth rate for clouds laden with particles of finite Rouse number $\mathcal{R}\approx 0.22$, where $\mathcal{R}$ is the ratio of the individual particle settling velocity to the typical cloud velocity based on its initial radius and total buoyancy. Consistent with the literature on buoyant vortex rings, our clouds verify the relation $\alpha \propto {\mathrm{\Gamma }}_{\infty }^{-2}$ between the clouds' growth rate $\alpha$, as firstly defined by Morton et al. [Proc. R. Soc. London A 234, 1 (1956)], and their eventually constant circulation ${\mathrm{\Gamma }}_{\infty }$. As the Rouse number approaches $\mathcal{R}\approx 0.22$, the baroclinic forcing of the circulation reduces down to a minimum, thus optimizing the cloud growth rate $\alpha$. This analysis highlights the role of the mean flow in the enhanced entrainment of ambient fluid by negatively buoyant clouds. Our results also validate, on the basis of direct comparison with experimental results, the use of a one-fluid two-way coupling numerical model to simulate particle clouds in the limit of weak particle inertia.

Plastic pollution has been observed throughout the world's oceans and estuaries, whether floating at the surface, settled in bottom sediments, washed up on beaches, or ingested by marine life. However, the vast majority of discarded plastics are unaccounted for. The problem of predicting the fate of discarded plastics has spurred fundamental research into fluid-particle interactions in previously unexplored regimes. Through talks and focused discussion groups taking place during a February 2022 online workshop hosted by the Banff International Research Station, theorists, experimentalists, numerical modelers, and observational oceanographers presented recent advances and identified outstanding problems in predicting plastic transport in the ocean, focusing on the role of fluid dynamics. The outcomes of this meeting and discussions that followed are reported upon here.

We present experimental results describing the behavior of a bubble placed within a horizontal high-speed solid-body rotating flow. We focus on the stretching and breakup of the bubble that happens in this situation and on the effect that a surfactant introduced in the liquid has on this. In order to explore the effects of surfactants on the bubble we have used two solutions of tetradecyltrimethylammoniumbromide (TTAB), one whose concentration is lower than the critical micelle concentration (0.33 CMC) and one with a concentration larger than the CMC (2 CMC). The results show that, as expected, the deformation of the bubble is larger in both surfactant solutions than in water and can be modeled by the model of Rosenthal 1962 in the case of both solutions. In the case of the 0.33 CMC solution, the bubble behaves as if it were seeing an effective surface tension equal to that in the saturated solution. We observed that the bubble could break up at certain rotational speeds for large bubble sizes. We show that this breakup occurs through a resonance mechanism when the rotational velocity of the tank becomes of the order of the eigenfrequency of the bubble.

Reactive flow control has been shown to be a promising tool to improve, among other aspects, the aerodynamic characteristics of an aircraft. This paper focuses on the use of reactive flow control to attenuate Tollmien-Schlichting (TS) waves over a wing profile. TS waves are an instability mechanism that is one of the first stages of boundary layer transition to turbulence. The Wiener-Hopf technique was used in this work for the experimental boundary layer control. The approach improves previous wave-cancellation techniques that, by constructing control kernels in the frequency domain, lead to control kernels with a noncausal part, i.e., actuation would need future sensor information to be constructed. In practical applications, it is unfeasible to access this type of information. Ignoring the noncausal part of the kernel leads to suboptimal solutions that might significantly degrade the performance of the controller. The Wiener-Hopf formalism allows us to take into account causality constraints in the formulation of the control problem, leading to an optimal realistic solution and a control kernel that is causal by construction. Moreover, it is possible to construct the control strategy based only on the power and cross-spectra obtained experimentally in a data-driven approach. The present work shows how to apply experimentally the Wiener-Hopf resolvent-based formalism using signals from a wind tunnel experiment, demonstrating that the TS waves can be effectively attenuated via a Wiener-Hopf-based controller, which yielded better results than a typical wave-cancellation approach.

Ionic liquids (ILs), molten salts at low temperatures, are nonionizing, thermally stable, and with low vapor pressure, thereby offering promising applications for lubrication, cooling, and combustion, where drop impact on a heated surface plays a vital role. Drop impact on heated surfaces has been extensively investigated with molecular liquid drops, such as water and ethanol, but rarely explored with ILs. We experimentally investigate the impact dynamics of three types of IL drops onto a heated flat surface under broad ranges of impact velocity ($0.18\le U\le 4.22$ m/s) and surface temperature ($18\le T_s\le 455{}^{\circ }\text{C}$). The impact events observed with the ILs include spreading, spreading with bubbling, and splashing with bubbling. However, the dynamic Leidenfrost effect with an insulating vapor film causing droplet rebound, typically recorded for molecular liquid drops under an initial impact velocity, is not observed for the IL liquids under similar Weber number ($\text{We}\approx 2)$ and surface temperature (at $T_s=350{}^{\circ }\text{C}$). This suppression is attributed to the low gas pressure underneath the IL droplet, induced by evaporation and thermal decomposition of ILs, and can significantly benefit various thermal applications such as cooling and coating. Finally, the maximum spreading factor of the IL drops is modeled using an energy conservation concept and is consistent with experimental results.