The effect of Coriolis forces on the turbulent flow in an elliptical pipe subjected to spanwise rotation about the major axis has been studied using direct numerical simulations (DNS). In response to the system rotation, large-scale secondary flows appear in the cross-stream plane as a pair of counterrotating vortices, which significantly impact the turbulence statistics and structures of the flow. To capture the most energetic turbulent eddy motions in the streamwise direction, the pipe length has been extended to $L_z=20\pi b$ (here, $b$ is the minor semiaxis of the elliptical pipe), which is the longest in the current literature for the study of elliptical pipe flows. Laminarization occurs on the suction side of the flow and propagates toward the pressure side as the speed of the system rotation increases. The system rotation imposed radically alters the budget balance of Reynolds stresses through its effects on the mean and turbulent flow fields and through the Coriolis term. At a moderate rotation number, the Coriolis term starts to dominate the energy transfer from $\langle w^{\prime }{w}^{\prime }\rangle$ to $\langle v^{\prime }{v}^{\prime }\rangle$, and also acts on $\langle v^{\prime }{w}^{\prime }\rangle$ as an additional source term. This mechanism far surpasses the role of the pressure-strain term, which undergoes a significant reduction in response to the system rotation. The characteristics of the turbulence field is investigated in both physical and spectral spaces through analyses of the first- and second-order statistical moments, as well as the budget balance of the Reynolds stress transport equation and coherent flow structures.

In suspended falling films, i.e., films on the underside of a bounding wall with arbitrary inclination, the surface film topology evolves towards a distinct spanwise structuring of the flow into rivulets, which is potentially accompanied by dripping events. Experimental data suggest a connection between long-term spanwise structuring and primary instabilities of the film surface. However, available experimental data regarding this connection remain nonconclusive. Hence, the present study aims at elucidating the evolution of a suspended falling film from varying imposed initial conditions to the emergence of spanwise modulations and rivulet formation. The study is carried out by means of extended numerical simulations employing a weighted residual integral boundary layer model for falling liquid films. The investigated parameter space covers recent experimental data on the topic. Varying imposed initial conditions, Reynolds number, Kapitza number, as well as wall inclination, several possible causes for a deviation of observed spanwise wavelengths from the one predicted by the primary Rayleigh-Taylor mechanism, are identified. This includes a distinct influence of initial conditions, asynchronous destabilization of consecutive wavefronts, competing short wave capillary instabilities, and rivulet interaction.

Polymer retention from the flow of a polymer solution through porous media results in substantial decrease of the permeability; however, the underlying physics of this effect is unknown. While the polymer retention leads to a decrease in pore volume, here we show that this cannot cause the full reduction in permeability. Instead, to determine the origin of this anomalous decrease in permeability, we use confocal microscopy to measure the pore-level velocities in an index-matched model porous medium. We show that they exhibit an exponential distribution and, upon polymer retention, this distribution is broadened yet retains the same exponential form. Surprisingly, the velocity distributions are scaled by the inverse square root of the permeabilities. We combine experiment and simulation to show these changes result from diversion of flow in the random porous-medium network rather than reduction in pore volume upon polymer retention.

We experimentally and theoretically study the dynamics of a low-Reynolds number helical swimmer moving across viscosity gradients. Experimentally, a double-layer viscosity is generated by superposing two miscible fluids with similar densities but different dynamic viscosities. A synthetic helical magnetically driven swimmer is then made to move across the viscosity gradients along four different configurations: either head-first (pusher swimmer) or tail-first (puller), and through either positive (i.e., going from low to high viscosity) or negative viscosity gradients. We observe qualitative differences in the penetration dynamics for each case. We find that the swimming speed can either increase or decrease while swimming across the viscosity interface, which results from the fact that the head and the tail of the swimmer can be in environments in which the local viscosity leads to different relative amounts of drag and thrust. In order to rationalize the experimental measurements, we next develop a theoretical hydrodynamic model. We assume that the classical resistive-force theory of slender filaments is locally valid along the helical propeller and use it to calculate the swimming speed as a function of the position of the swimmer relative to the fluid-fluid interface. The predictions of the model agree well with experiments for the case of positive viscosity gradients. When crossing across a negative gradient, gravitational forces in the experiment become important, and we modify the model to include buoyancy, which agrees with experiments. In general our results show that it is harder for a pusher swimmer to cross from low to high viscosity, whereas for a puller swimmer it is the opposite. Our model is also extended to the case of a swimmer crossing a continuous viscosity gradient.

This study explores the problem of optimal spatial placement of microjet actuators for flow control in a canonical bluff body of relevance to the aerodynamics community, namely, the slanted cylinder with a slant angle of ${45}^{\circ }$. The solution found by a genetic algorithm whose goal function is to reduce aerodynamic drag (achieving 10.6% reduction at ${\text{Re}}_D=100000$) challenges the intuitive and, to date, most commonly followed de facto standard of using line arrays of steady microjet actuators to control a flow field. This study provides strong evidence that line arrays are not the optimal approach for active flow control of this bluff body wake, since most of the jets in the line array were neutrally, or even negatively, contributing to the goal function of drag reduction. Further observations of the flow physics with surface flow visualization and particle image velocimetry unveil two key mechanisms that were leveraged by this automated approach: First, a shrinkage of the separation bubble at the leading edge of the slanted surface appears to be strongly related to the very strong energization of the boundary layer just upstream of the separation due to microjets in crossflow being applied in tandem. Second, a wavelike perturbation that appears to be related to an increased wandering of the vortex pair formed in the far field of this wake is also observed. Although this study employed steady microjet actuators, the lessons learned can potentially be extended to other actuation mechanisms commonly used for active flow control. The results obtained demonstrate the spatial sensitivity problem is one that, despite its complexity and challenges in physical implementation, is worthwhile considering in active flow control studies.

We have investigated the effects of the wall permeability on the isothermal-wall supersonic channel flow turbulence. The study is conducted via large-eddy simulations (LES) based on the sub-grid-scale closure proposed by Vreman [Phys. Fluids 16, 3670 (2004)]. The effects of the wall porosity are modeled via the application of a time-domain impedance boundary condition (TDIBC), which accurately imposes the complex acoustic wall impedance. Bulk Mach numbers of $M_b=1.50$ and 3.50 are selected, with bulk Reynolds numbers chosen to ensure the same semilocal friction Reynolds number of ${\text{Re}}_{\tau }^{*}\approx 220$. A three-parameter impedance model is used with resonating frequency tuned to the time scales of the energy containing eddies, with wall acoustic resistances $R=0.50,1.00,\infty$, ranging from the most permeable to impermeable, respectively. It is found that only cases with $R=0.50$ yield significant changes in the near-wall turbulence structures, which include a deviation from the linear relation of mean velocity and normalized wall distance in viscous sublayer, and increase in the mean wall-shear stress, as well as a strong increase in both turbulent kinetic energy (TKE) production and dissipation near the wall primarily due to large contribution coming from the instability waves triggered by the permeability. Such waves are found to be confined in the first $10\%$ of the channel half-height near the impedance boundary, creating local circulation zones separated by regions of flow entrainment. It is found that for a given $R$, the waves are more confined as the Mach number increases. For pressure-related terms, the complex impedance wall effects changes the role of pressure diffusion term in the budget the most, making it responsible for the transport toward the wall, opposite to what is observed in impermeable wall cases. The confined waves also enhance the sink/source effect of the pressure strain term in budget of Reynolds normal stresses, leading to a redistribution of normal stresses.

Rough surfaces are common in engineering applications, where a priori estimations of drag for a given flow are needed based on knowledge of the surface topography. It is likely that length-scale information is required, in addition to standard statistical quantities such as solidity or effective slope, root-mean-square height and skewness. In this work we consider a set of rough surfaces that are derived from a physical scan of a grid-blasted rough surface. Different surfaces are generated by applying Fourier band-pass filters to the surface scan, including complementary cases, for example, where a midrange of wave numbers are included or excluded. This enables comparisons as to how the roughness spectral content affects the mean flow and turbulence properties. In total, turbulent flow over five surfaces with different wave-number spectra is investigated by direct numerical simulation, with resulting variations in the roughness function of over a factor of 3. It is found that, except for the low-pass filtered surface which has very small effective slope, the roughness function scaled by the viscous proportion of total drag remains remarkably constant, while the pressure counterpart is largest for high-pass filtered surfaces. Existing correlations for the roughness function are found, at best, to reproduce only the qualitative effects, suggesting that the correlations would benefit from introducing additional parameters to account for the wave-number spectrum of the rough surfaces. Besides the friction effect, it is also of interest to determine the extent to which the turbulence in the roughness layer is influenced by the spectral characteristics of the surface. The location of the peak streamwise velocity fluctuations moves outwards in wall units as the roughness function increases, whereas wall-normal and spanwise velocity fluctuations are found to be insensitive to the surface filtering, down to a region below the maximum roughness height. A trend towards spanwise organization of the mean flow is observed for low-pass filtered surfaces, but otherwise the effect of the roughness wave-number spectrum appears to vanish rapidly above the maximum roughness elevation. Instead, significant differences are found in the profiles of the various dispersive stresses which are highly dependent on (local) topographical features of the roughness; for some quantities differences between surfaces persist well into the log layer.

A core attribute of any turbulent flow is the rate at which it dissipates energy $\varepsilon$. In his classic study from 1935, Taylor invoked rotational symmetry to transform the original cumbersome expression for $\varepsilon$ into a remarkably simple formula but for which it would be practically impossible to compute $\varepsilon$ in most experiments. Taylor's analysis, though ingenious, leaves it unclear if the formula truly conforms with rotational symmetry. We use the rigorous approach of Lie groups and show that Taylor's formula indeed holds for rotational symmetry. Further, we find that the formula is surprisingly robust—it holds, as is, for a distinctly different symmetry: reflectional symmetry. Additionally, we highlight that the widely used tests for identifying flow symmetries can yield misleading results. With rigor, precision, and clarity, the machinery of Lie groups delineates the underlying symmetries that dictate turbulent flows.

The relaxation dynamics of a fluid-filled blister between an elastic sheet and a porous substrate are controlled by the deformation of the elastic sheet, the viscous stresses in the pores, and the capillary pressure at the liquid-air interface due to imbibition. We develop a mathematical model to study the effects of varying the permeability of the porous substrate, the bending stiffness of the elastic sheet, and the blister size on the relaxation dynamics. Experiments are conducted by injecting a finite volume of viscous fluid between a porous substrate and an elastic sheet, where fluid first invades the pores, and subsequently, as the pressure in the fluid increases, the elastic sheet is peeled and uplifted from the substrate to form a fluid-filled blister. After injection is stopped, the fracture front is static, and the elastic stresses in the overlying sheet and the capillary pressure at the liquid-air interface drive the drainage of the blister into the pores. We identify two regimes of drainage. For thick sheets and more permeable substrates, drainage is primarily due to the stresses in the deformed elastic sheet. For thin sheets and less permeable substrates, drainage is driven by the imbibition of the liquid into the pore space. Our model and experiments are relevant to the drainage of fluid-driven fractures in porous media.

Rigid platelike particles displaying interfacial slip can attain a constant orientation in a shear flow when the slip length is sufficiently large. But actual thin particles such as single-layer graphene are flexible and prone to bending deformations when exposed to shear stress. To study the effect of bending deformation on the dynamics of flexible platelike particles with large interfacial slip in a shear flow, we develop a two-dimensional (2D) fluid-structure interaction model. Our model is based on coupling the Euler-Bernoulli beam equation with a boundary integral method to solve the hydrodynamic stress at the particle surface. Emphasis is placed on resolving accurately the stress distribution at the edges of the particle. We find that (i) a stable alignment occurs even for relatively flexible particles and that (ii) edges effects on the shape of the plate are important for values of the length-to-thickness aspect ratio as large as 100. Our results are particularly relevant in view of recent research on the hydrodynamics of suspended flexible sheets made of 2D nanomaterials.

A droplet exposed to a high-speed gas flow is subject to a rapid and violent fragmentation, dominated by a widespread mist of multiscale structures that introduce significant complexities in numerical studies. The present work focuses on capturing all stages of the aerodynamic breakup of a waterlike droplet imposed by three different intensity shock waves, with Mach numbers of 1.21, 1.46, and 2.64, under the shear-induced entrainment regime. The numerical investigation is conducted within a physically consistent and computationally efficient multiscale framework, using the Σ-Υ two-fluid model with dynamic local topology detection. Overall, the breakup of the deforming droplet and the subsequent dispersion of the produced mist show good agreement with available experimental studies in the literature. The major features and physical mechanisms of breakup, including the incident shock wave dynamics and the vortices development, are discussed, and verified against the experiments and the theory. While the experimental visualizations inside the dense mist are restricted by the capabilities of the diagnostic methods, the multiscale two-fluid approach provides insight into the mist dynamics and the distribution of the secondary droplets under different postshock conditions.

We study a liquid-gas front propagation in a modulated Hele-Shaw cell by means of multiphase computational fluid mechanics based on the three-dimensional Navier-Stokes equations. In the simulations an obstacle that partially fills the gap is placed at the center of the cell, and the liquid-gas interface is driven at a constant velocity. We study the morphological differences between imbibition and drainage for a wide range of capillary numbers, and explore how the wetting properties of the constriction affect the amount of liquid that remains trapped in the draining process. We observe increasing remaining volumes with increasing capillary number and decreasing contact angle. The present CFD implementation for a single mesa defect provides insight into a wide number of practical applications.

This paper analyzes odd and even higher-order moments for longitudinal velocity increment $\mathrm{\Delta }u(x,r)$, where $x$ is the longitudinal coordinate and $r$ is the separation distance, based on the canonical and a modified normalization for skewness of longitudinal velocity derivative $\partial u/\partial x$. Two types of data were used, stably stratified turbulence data from the nocturnal atmospheric boundary layer taken during the Mountain Terrain Atmospheric Modeling and Observations field campaign and from the direct numerical simulation of homogeneous and isotropic turbulence in a box at four Reynolds numbers and four different grid resolutions. Third moment data normalized by the same moment of third order for modulus $\left|\mathrm{\Delta }u(x,r)\right|$ representing modified skewness of the velocity increment showed a better collapse at all Reynolds numbers in the inertial and viscous subranges than canonical normalized skewness with normalization parameter ${\langle {\left(\mathrm{\Delta }u(x,r)\right)}^2\rangle }^{3/2}$, where $\langle ··\rangle$ represents the ensemble average. The analysis also considered odd $p\mathrm{th}$-order classical structure functions $\langle \mathrm{\Delta }u{(x,r)}^p\rangle$ with Kolmogorov-theory based normalization $\langle \mathrm{\Delta }u{(x,r)}^p\rangle /{\left(\varepsilon r\right)}^{p/3}$ for the inertial subrange, where ε is the rate of dissipation, and a modulus-based structure function $\langle {\left|\mathrm{\Delta }u(x,r)\right|}^p\rangle /{\left(\varepsilon r\right)}^{p/3}$. Both types of structure functions of order $p=1ndash;6$ were computed using different normalizations, and corresponding scaling exponents were assessed for the inertial and viscous subranges. Scaling for modulus-based structure functions in the viscous subrange was identified as $\langle {\left|\mathrm{\Delta }u(x,r)\right|}^p\rangle \propto r^{p·(5/6)}$. In the viscous subrange, the velocity increment varied linearly with $r$ for the classical third moment $\langle \mathrm{\Delta }u{(x,r)}^3\rangle \propto r^3$ based on the velocity increment while the classical fifth moment $\langle \mathrm{\Delta }u{(x,r)}^5\rangle$ did not provide any meaningful scaling exponent. A plausible qualitative explanation linking these effects to anisotropy of nocturnal stratified turbulence is proposed.

Traveling-wave problems, due to their sizable Kolmogorov $n$-width, have brought critical challenges to conventional model reduction techniques. This study aims to provide insights into this problem by exploiting the Radon cumulative distribution transform (R-CDT) [Kolouri, Park, and Rohde, IEEE Trans. Image Process. 25, 920 (2016)], which has emerged in the sector of computer vision science. The core lies in the unique property of the nonlinear invertible R-CDT that renders both traveling and scaling components into amplitude modulations. In contrast to the physical space, a substantial model reduction is achieved in the R-CDT space while sustaining high accuracy. The method is parameter-free and data-driven and lends itself to problems regardless of the dimensions or boundary conditions. Examples start with a one-dimensional Burgers' equation subject to nonperiodic boundary conditions, where both traveling and diffusion dominate the physics. In higher-dimensional problems, we show the model reduction of traveling Gaussian solitons. In addition to foreseeable motions, the proposed method is capable of handling random traveling with a nondifferentiable trajectory.

Microorganisms navigate through fluid, often confined by complex environments, to survive and sustain life. Inspired by this fact, we consider a model system and seek to understand the wall curvature driven dynamics of a squirmer, a mathematical model for a microswimmer, using (i) lattice Boltzmann simulations and (ii) analytical theory by D. Papavassiliou and G. P. Alexander [Eur. Phys. Lett. 110, 44001 (2015)]. The instantaneous dynamics of the system is presented in terms of fluid velocity fields, and the translational and angular velocities of the microswimmer, whereas the long time dynamics is presented by plotting the squirmer trajectories near curved boundaries in physical and dynamical space, as well as characterizing them in terms of fixed points and experimentally relevant measures, namely, (i) proximity parameter, (ii) retention time, (iii) swimmer orientation and (iv) tangential velocity near the boundary, and (v) scattering angle during the collision. Our detailed analysis shows that irrespective of the type and strength, microswimmers exhibit a greater affinity towards a concave boundary due to hydrodynamic interactions compared to a convex boundary. In the presence of additional repulsive interactions with the boundary, we find that pullers (propel by forward thrust) have a slightly greater affinity towards the convex-curved walls compared to pushers (propel by backward thrust). Our study provides a comprehensive understanding of the consequence of hydrodynamic interactions in a unified framework that encompasses the dynamics of pullers, pushers, and neutral swimmers in the neighborhood of flat, concave, and convex walls. In addition, the combined effect of oppositely curved surfaces is studied by confining the squirmer in an annulus. The results presented in a unified framework and insights obtained are expected to be useful to design geometrical confinements to control and guide the motion of microswimmers in microfluidic applications.

The objective of this work is the understanding of lift forces exerted on two side-by-side intruders within a granular flow that is uniform upstream. To this end, we have performed experiments that reveal long-range attraction and repulsion depending on flow velocity and the distance between intruders. We found an interesting correlation between the asymmetry of flow velocity around the obstacles and the lift force, although the understanding of this correlation rests as an open question for future work. Additionally, a hydrodynamic model based on kinetic theory for inelastic particles was solved numerically. The model reproduces remarkably well the general qualitative features of the experiments which shows that the system behaves similarly to a pair of hot intruders immersed in a liquid of temperature-dependent viscosity. However, quantitative discrepancies suggest that better constitutive relations are needed.

The stability of a thin viscoelastic film of Oldroyd-B fluid falling down an incline is investigated. In the weak viscoelasticity limit, a reduced model is derived using the weighted residual techniques, which consists of two coupled equations for the film thickness and local flow rate. Through the normal mode analysis, temporal growth rates and neutral stability curves are calculated to explore linear stability of the film. Results show that the viscoelasticity acts to destabilize the film and decrease the phase speed of linear waves. Good agreement is found between the reduced model and full linearized equations solved by the Chebyshev spectral collocation method when viscoelastic effect is relatively weak. Nonlinear traveling waves are further determined. The speed of fast/slow-wave families is promoted/reduced in the presence of the viscoelasticity, resulting in a dispersion effect on the system; while the wave amplitudes are augmented for both fast and slow waves. Besides, the temporal evolution of surface waves is numerically resolved, which validates the linear prediction of the instability threshold. Steady permanent waves are observed in the final stage; the surface deformation and perturbation energy are enhanced by the viscoelasticity as expected.

Applying a dynamic free-slip boundary in a turbulent boundary layer has been shown recently to shift outward the near-wall transverse vorticity away from the wall and reduces the wall skin friction by more than 40%. Herein we present a local relaminarization mechanism induced by the dynamic free-slip boundary, from the perspective of energy exchange and transportation. The spatial evolution of the energy components associated with the mean motion, turbulent motion, and a shear-free oscillatory motion is presented. An analysis of the average energy exchange process in the near-wall region suggests that the energy of turbulence is transferred to the mean motion, against the canonical downward turbulent energy cascade. A considerable amount of energy is supplied to the shear-free motions, which displaces the highly turbulent and shear motions away from the wall. The relaminarization mechanism is associated with outward-shifted transverse vorticity and the depletion of the shear motions near the wall. As an effective method to manipulate the critical region for wall shear stress generation, the dynamic free-slip boundary produces a much stronger effect than the conventional relaminarization process, which can be employed for efficient drag reduction and boundary layer control.

We investigate the dynamics of millimeter-sized droplets moved on a liquid infused surface. The motion of the droplet is driven by a small spherical bead, whose trajectory is precisely controlled, which acts as a carrier. We first characterize the strength of the contact that maintains the adhesion between the droplet and the bead as a function of the ratio $R/r$ of their radii. When the bead is moved at a fixed velocity, the droplet follows its trajectory until a critical value of the velocity is reached at which the bead and the droplet lose contact. The critical velocity is rationalized as a balance between the capillary contact force and the friction acting on the droplet where it is in contact with the substrate. Experimental results are in good agreement with the model proposed. This study highlights a very efficient actuation method for millimetric droplets.