Drag mitigation by passive surfaces with engineered material properties has gained significant attention in low-speed flows. The present work investigates the skin friction drag mitigation caused by flow interactions with a nonrigid surface at supersonic speeds. The nonrigid surface was formed by implanting viscoelastic rubber materials of different elastic moduli over a rigid surface. Direct measurements of the skin friction coefficient ($C_f$) were made along the length of the viscoelastic surfaces and compared against the corresponding values over a rigid surface. The $C_f$ over the implants employed in this work demonstrated measurable decrease compared to a rigid surface along their entire length. A maximum local decrease in $C_f$ of $30\%$ was measured at a station located 30 mm downstream of the implant leading edge, demonstrating that the boundary layer responds to the presence of the compliant surface within a short distance after encountering the surface. The mechanisms that drive the reduction in $C_f$ was investigated through a combination of turbulent statistics measurements and theoretical analysis. The results suggest that the unsteady deformations of the viscoelastic surface can affect VLSMs (very large-scale motions) as well as the near-wall burst cycles, which in turn could drive the observed $C_f$ mitigation.

We investigate states of rapidly rotating Rayleigh-Bénard convection in a cylindrical cell over a range of Rayleigh numbers $3\times {10}^5\le \text{Ra}\le 5\times {10}^9$ and Ekman numbers ${10}^{-6}\le \text{Ek}\le {10}^{-4}$ for Prandtl number $\text{Pr}=0.8$ and aspect ratios $1/5\le \mathrm{\Gamma }\le 5$ using direct numerical simulations. We characterize, for perfectly insulating sidewall boundary conditions, the first transition to convection via wall mode instability and the nonlinear growth and instability of the resulting wall mode states, including a secondary transition to time dependence. We show how the radial structure of the vertical velocity $u_z$ and the temperature $T$ is captured well by the linear eigenfunctions of the wall mode instability where the radial width of $u_z$ is ${\delta }_{u_z}\sim {\text{Ek}}^{1/3}r/H$ whereas ${\delta }_T\sim e^{-kr}$ ($k$ is the wave number of a laterally infinite wall mode state). The disparity in spatial scales for $\text{Ek}={10}^{-6}$ means that the heat transport is dominated by the radial structure of $u_z$ since $T$ varies slowly over the radial scale ${\delta }_{u_z}$. We further describe how the transition to a state of bulk convection is influenced by the presence of the wall mode states. We use temporal and spatial scales as measures of the local state of convection and the Nusselt number $\text{Nu}$ as representative of global transport. Our results elucidate the evolution of the wall state of rotating convection and confirm that wall modes are strongly linked with the boundary zonal flow being the robust remnant of nonlinear wall mode states. We also show how the heat transport ($\text{Nu}$) contributions of wall modes and bulk modes are related and discuss approaches to disentangling their relative contributions.

In this work rectilinear collisions of spheres coated in a thin viscous liquid film are considered, where the surface roughness of the spheres was varied. Experiments were performed using a Newton's cradle apparatus and the collision dynamics was measured using particle tracking velocimetry. The experiments showed that the dry and wet coefficient of restitution decreases as the roughness increases. Experimental collisions are compared with numerical simulations to examine criteria that limit the viscous force. We show that a model in which the liquid undergoes a glass transition is in excellent agreement with experimental measurements for smooth spheres, i.e., when the roughness of the spheres is less than the glass transition length. For rough particles, a constant minimum separation distance is more accurate than the glass transition model, which is consistent with the idea that contact occurs on the roughness elements. Furthermore, smoothed particle hydrodynamics (SPH) simulations were used to examine the viscous flow in detail. The SPH simulations accurately predicted the collision outcome for smooth spheres and showed that the maximum pressure was greater than the glass transition pressure used for the discrete element method simulations, supporting the feasibility of the glass transition model. The SPH simulations of rough particles indicate that during a collision the interstitial liquid flows through microchannels between roughness elements as a mechanism to alleviate pressure buildup, and reduce the viscous force consistent with the experimental observations.

In this paper, we investigate the exit dynamics of a sphere launched underneath a liquid bath surface at a prescribed impact velocity. Spheres with radii approximate or smaller than the capillary length are considered. Following our previous work of a ligament drawn of a liquid bath [J. Fluid Mech. 922, A14 (2021)], a two-dimensional model is applied to describe the liquid dynamics, and the whole exit dynamics up to the descent or the pinch-off moments is considered. The process can be sequenced into a partial exit stage that forms a coated layer and a full exit stage with an attached ligament. A bouncing-off regime, a lower pinch-off penetration regime, and an upper pinch-off penetration regime are identified, separating by a penetration Weber number and a switching Weber number. The phase diagram is revealed, where the two critical Weber numbers are functions of the Bond number. By considering the energy evolutions, we show that the impact energy is mainly converted into the surface energy and the gravitational potential energy for the low- and large-gravity cases, respectively. The coated layer is mainly formed in the partial exit stage, whose maximum volume increases with the impact velocity but decreases with gravity effect. Stretching motion is shown to have negligible influence on the local pinch-off behavior, while it determines the appearance and the location of pinch-off. Our results can help to understand the exit behaviors of aquatic animals, and the design of microamphibious aircraft or energy collection devices.

A comprehensive approach, combining theoretical analysis and large-eddy simulation, is employed in this study to investigate the influence of temperature gradient on the stability phenomenon of the von Kármán boundary layer in a rotor-stator cavity. Further from previous studies, a temperature term is introduced to account for centrifugal buoyancy within the cavity. The focus is on analyzing the transitional behavior and the effects of centrifugal buoyancy on the boundary layer of the rotating disk under operating conditions characterized by a Reynolds number $\text{Re}={\mathrm{\Omega }}_D{b}^2/\nu =4\times {10}^5$. The findings highlight that a temperature gradient between the stationary and rotating disks establishes enhanced flow circulation within the cavity. Consequently, this temperature gradient significantly influences the base flow and alters the critical Reynolds numbers governing the rotating-disk boundary layer transition. Specifically, in the rotating-disk boundary layer, centrifugal buoyancy causes the premature breakdown of some inviscid modes, leading to an earlier transition to turbulence at lower Reynolds numbers. However, there exists a minimum critical Reynolds number in the rotating-disk boundary layer, beyond which the increase in centrifugal buoyancy does not further reduce the critical Reynolds number. This research emphasizes the importance of considering temperature variations in rotor-stator cavities for improved control of the stability within the rotating-disk boundary layer flow.

For wall-bounded turbulent flows, Townsend's attached eddy hypothesis proposes that the logarithmic layer is populated by a set of energetic and geometrically self-similar eddies. These eddies scale with a single length scale, their distance to the wall, while their velocity scale remains constant across all self-similar structures. To investigate the existence of such structures in fully developed turbulent pipe flow, stereoscopic particle image velocimetry measurements were performed in two parallel cross-sectional planes, spaced apart by a varying distance from 0 to $9.97R$, where $R$ is the radius of the pipe, for friction Reynolds numbers ${\text{Re}}_{\tau }=1310$, 2430, and 3810. The instantaneous turbulence structures are sorted by width using an azimuthal Fourier decomposition and then azimuthally aligned to create a set of average eddy velocity profiles. The profiles exhibit geometric self-similar behavior in the azimuthal plane for eddies with spanwise length scales (${\lambda }_{\theta }/R$) spanning from 1.03 to 0.175. The streamwise similarity is then investigated using two-point correlations, where the structures exhibit a self-similar behavior with length scales (${\lambda }_{\theta }/R$) ranging from approximately 0.88 to 0.203. The candidate structures thereby establish full three-dimensional geometric self-similarity. In addition, the characteristic velocity magnitudes exhibit self-similarity within these ranges, using a velocity scale that is proportional to eddy size. This unexpected result is reconciled with the attached eddy hypothesis in terms of sampling probabilities.

We analyze the scraping of a thin layer of viscoplastic fluid residing on a horizontal surface by a translating rigid scraper. This motion generates a mound of fluid upstream of the scraper and a residual layer behind it, both of which are modelled using a shallow layer theory for a Bingham or Herschel-Bulkley fluid. The flows ahead of and behind the scraper are coupled by the motion in the gap under the scraper, which is driven both by the translation of the scraper and by the induced pressure gradient due to the difference in flow thickness upstream and downstream. When the gap between the scraper and the underlying surface is sufficiently small, we find that a steady state emerges after a relatively long transient and that en route to this state, the unsteady dynamics exhibit a variety of regimes that are self-similar to leading order. We construct these solutions explicitly and derive key scalings for the temporal development of the flowing viscoplastic layer, as well as identifying the timescales at which there are transitions between the regimes. These predictions are confirmed by comparison with results from the numerical integration of the full system. Finally, we report results from preliminary laboratory experiments, which are compared with predictions from the shallow-layer theory, obtaining reasonable agreement once a slip boundary condition is included in the model, as motivated by experimental observations.

Simulations employing the continuum model of T. Gao et al [ Phys. Rev. Fluids 2, 093302 (2017)] are used to study the transport of an object in a closed two-dimensional container by a suspension of contractile active agents. For parameters that generally yield nematic alignment, the initial flow and object motion is typically characterized by chaotically interacting $m=\pm \frac{1}{2}$ defects in its nematic structure, which form in oppositely signed pairs or on the container wall or on the object. Those that form on the object also make an oppositely signed contribution to the $m_{\circ }$ nematic structure associated with the object. However, in many cases, the chaotic flow does not persist. It instead ends up in one of two states, which are studied in detail for a circular object in a circular container. One is a fixed point, associated with an $m_{\circ }=+1$ object with radial nematic ordering. The suspension flows but with the object stationary near the container wall. A sharply aligned nematic model confirms that its position is maintained by a (nearly) hydrostatic balance and that a related circumferential $m_{\circ }=+1$ configuration, which is not observed, would indeed be unstable. The second terminal behavior, which can occur for the same physical parameters as the fixed-point behavior, is associated with an $m_{\circ }=0$ object. It is a limit-cycle oscillation in which the object cyclically traverses the container, spawning transient $m=-\frac{1}{2}$ defect pairs each half cycle. Both of these configurations are analyzed in detail and are potential related to simple biological tasks. It is shown that they also occur in square and elliptical containers, with the ellipse displaying a particularly rich phenomenology that includes switching between them.

We present a numerical study of a thin elastic sheet with small extensibility freely sedimenting in a viscous fluid. Two scenarios are investigated: sedimentation in free space and near an infinite wall, where the wall may be vertical or tilted. Elastic sheets with a rest shape of a square are modeled with a finite-element-based continuum model that accounts for in-plane stretching and out-of-plane bending. The fluid motion is computed by the method of regularized Stokeslets in free space and regularized Blakelets near a wall. During sedimentation, the interplay between gravity and the elastic response of sheets gives rise to complex deformation and reorientation dynamics, measured by a dimensionless elastogravitational number $\left({\mathrm{E}}_{\mathrm{G}}\right)$. In free space, sheets attain a stable orientation by aligning perpendicular to gravity. Sheets with larger deformability adopt more compact conformations and experience smaller hydrodynamic drag, thereby sedimenting faster. A sheet with a random initial orientation reorients to align perpendicular to gravity, accompanied by lateral drift due to the symmetry-breaking in conformations. We identified two reorientation mechanisms depending on flexibility. When a sheet is placed near an infinite wall, sedimentation is hindered compared to that in free space due to wall-induced hydrodynamic drag. Near a vertical wall, sheets exhibit asymmetric conformations that cause the sheet to drift, with the drifting dynamics determined by ${\mathrm{E}}_{\mathrm{G}}$. The difference in flexibility leads to a nonmonotonic trend in the evolution of wall-normal distance. Near a tilted wall, sheets show qualitatively different dynamics when the wall angle is large: they either deposit on or slide along the wall with a fixed wall-normal distance.

The splat formed after drop impact on supercooled solid surfaces sticks to it. On the contrary, a sublimating supercooled surface such as dry ice inhibits pinning and therefore efficiently rebounds drops made of a variety of liquids. While rebound is expected at lower impact velocities on dry ice, at higher impact velocities the drop fragments leave behind a trail of smaller droplets. However, it is not known whether rebound can be entirely suppressed or fragmentation can be controlled on such surfaces and if it depends on the extent of solidification inside the drop. In this paper, we report on the role played by solidification within drops in modifying the outcomes of their impact on the supercooled ultralow adhesive surface of sublimating dry ice. We show that the solidification thickness depends on the impact velocity and is the primary driver in suppression of rebound and delay in fragmentation. Our findings imply that sublimating supercooled surfaces can present a broad spectrum of outcomes from complete bouncing to no rebound, which is not seen in drop impacts on supercooled superhydrophobic surfaces. We attribute this to thermo-elastocapillarity, which considers bending of the solidified layer and is used to demarcate regime boundaries and determine the coefficient of restitution during rebound.

Lubricated textured surfaces immersed in liquid flows offer tremendous potential for reducing fluid drag, enhancing heat and mass transfer, and preventing fouling. According to current design rules, the lubricant must chemically match the surface to remain robustly trapped within the texture. However, achieving such chemical compatibility poses a significant challenge for large-scale flow systems, as it demands advanced surface treatments or severely limits the range of viable lubricants. In addition, chemically tuned surfaces often degrade over time in harsh environments. Here, we demonstrate that a lubricant-infused surface (LIS) can resist drainage in the presence of external shear flow without requiring chemical compatibility. Surfaces featuring longitudinal grooves can retain up to 50% of partially wetting lubricants in fully developed turbulent flows. The retention relies on contact-angle hysteresis, where triple-phase contact lines are pinned to substrate heterogeneities, creating capillary resistance that prevents lubricant depletion. We develop an analytical model to predict the maximum length of pinned lubricant droplets in microgrooves. This model, validated through a combination of experiments and numerical simulations, can be used to design chemistry-free LISs for applications where the external environment is continuously flowing. Our findings open up new possibilities for using functional surfaces to control transport processes in large systems.

The breaking of surface gravity waves is a key process contributing to air-sea fluxes and turbulent ocean mixing. The highly nonlinear nature of wave breaking, combined with the challenges of observing this process in a laboratory or field setting, leaves our understanding of the energetic processes underpinning wave breaking incomplete. Progress towards refining this understanding was made in a recent study [D. G. Boettger, S. R. Keating, M. L. Banner, R. P. Morison, and X. Barthelemy, An energetic signature for breaking inception in surface gravity waves, J. Fluid Mech. 959, A33 (2023)], which identified an energetic signature in the wave kinetic energy evolution that preceded breaking onset and correlated with the strength of the breaking event. In this paper, we examine the influence of wind forcing on this energetic signature. We develop a numerical wave tank that simulates wind flowing over mechanically generated waves and construct an ensemble of cases with varying wave steepness and wind forcing speed. The wind is shown to modulate the wave geometry and elevate kinetic energy at the crest tip by up to 35%. Despite these influences on the wave, the energetic inception signature was found to robustly indicate breaking inception in all cases examined. At breaking inception, a kinetic energy growth rate threshold was found to separate breaking and nonbreaking waves. Under wind forcing, the timing of the energetic inception point occurred slightly earlier than unforced breaking waves, giving advance warning of breaking 0.3 wave periods prior to breaking onset.

The morphological properties of red blood cells, such as size and shape, play a crucial role in determining their flow properties. A typical abnormal shape can be found in several blood disorders, such as spherocytosis, ellipsocytosis, etc., where the cells have a spherelike or ellipselike appearance, instead of being biconcave. These shape anomalies can affect the ability of RBCs to deform and squeeze through narrow capillaries, leading to reduced blood flow and oxygen supply to tissues. This can cause tissue ischemia, which can lead to organ damage and dysfunction. We conduct numerical simulations in order to study the flow properties (such as flow rate, cell-free-layer, and RBCs hydrodynamic diffusion) by varying the shapes of the cells, from a biconcave one (healthy RBCs) to a spherical one, representing RBCs suffering spherocytosis disease. Our study highlights nontrivial effects, such as nonmonotonic behaviors of the flow rate as a function of asphericity, depending on the channel width. For example, for some channel width the usual biconcave shape is revealed to be optimal with respect to flow rate, whereas for other widths more inflated shapes are more efficient. This offers an interesting basis for the understanding of the mechanisms underlying blood flow deficiencies associated with shape anomalies, and may help evaluating the potential therapeutic strategies that might be used to alleviate the symptoms. As RBCs also serve as a classical model system for very deformable objects, our study reveals also some fundamental aspects of the flow of soft suspensions.

In this experimental study on a methane-hydrogen fired laboratory-scale pressurized annular combustor, various steady and transient operating conditions were explored. Under steady operation, the thermoacoustic stability depended strongly on the equivalence ratio, but only weakly on the mass flow rate and hydrogen power fraction. During transient equivalence-ratio ramps, the predominant instability of the system switched between standing and spinning azimuthal modes. The ramping rate influenced the thermoacoustic amplitude during the switching, as well as the onset and decay of the different modes. The strong acoustic reflection at the choked outlet produced significant harmonic content during both steady and transient operation. Nonlinear time-series analysis and clustering algorithms showed that the Jensen-Shannon complexity and the permutation entropy could accurately classify the modal dynamics in an unsupervised manner. The classification revealed that standing azimuthal modes, with several preferred orientations, dominated under steady operation. The amplitude of the heat-release-rate (HRR) oscillations around the annulus depended on the mode orientation. The energy contribution from the harmonic components was isolated via bandpass filtering, revealing that the orientation of the first harmonic ($n=2)$ followed the fundamental mode, eliminating negligible HRR oscillation regions at the pressure node of the fundamental mode. By filtering out the higher-order harmonic content, intermittent switching between high-amplitude periodicity and low-amplitude chaos in the fundamental azimuthal mode was uncovered. Tools from dynamical systems theory confirmed the existence of chaos and demonstrated that the intermittency belongs to the type-II Pomeau-Manneville class. This study provides evidence of the type-II intermittency route to chaos in an annular combustor with longitudinal and azimuthal modes.

While predicting the flow behavior for a well-defined particulate microstructure is fairly tractable, systematic tailoring of the particle properties to yield desired flows remains illusive. For example, we still do not know how to precisely control rheological response by tuning particle types and properties or how to tailor porous media for filtration applications. Here we show that the recent advances in automatic differentiation provide a platform for methodologically addressing such questions. We optimize the packing of a polydisperse system of periodically arranged circular rods to maximize flow rate in the direction of applied pressure gradient. We show that the optimum topology of the structured porous medium depends on the solid volume fraction and approaches a staggered square with the particles' diameter ratio of $\sqrt{2}-1$ as the solid volume fraction reaches $\pi /4[1+{(\sqrt{2}-1)}^2]$. Regardless of the porous medium topology, the divergence exponent of the pressure gradient is universal and is equal to $5/2$, as one finds from lubrication theory for a simple square lattice. These results are independent of the flow's Reynolds number and can provide a foundation to study inverse problems for suspension systems.

We present an asymptotic theory for solving the dynamics of slender autophoretic loops and knots. Our formulation is valid for nonintersecting three-dimensional center lines, with arbitrary chemical patterning and varying (circular) cross-sectional radius, allowing a broad class of slender active loops and knots to be studied. The theory is amenable to closed-form solutions in simpler cases, allowing us to analytically derive the swimming speed of chemically patterned tori, and the pumping strength (stresslet) of a uniformly active slender torus. Using simple numerical solutions of our asymptotic equations, we then elucidate the behavior of many exotic active particle geometries, such as a bumpy uniformly active torus that spins and a Janus trefoil knot, which rotates as it swims forwards.

Numerical simulations of Rayleigh-Bénard convection with suspended particles are described. The Rayleigh number is ${10}^7$ and the Prandtl number unity. The particles have a finite size and are individually resolved by the physalis method which combines a regular Cartesian grid with a local spectral method around each particle. Two cells are considered, a cubic one with up to 3000 particles and a quasi-two-dimensional one with aspect ratio 2 with up to 1000 particles. In both cases the maximum volume fraction is about 20%. Emphasis is placed on the key role played by particle “dunes” in the resuspension of particles after they have fallen to the ground. Dunes are structures formed on the bottom of the cell by the nearly horizontal fluid velocity field which pushes particles from the foot of the descending plume to that of the ascending one. Without this mechanism which, by its very nature, cannot be captured by point-particle models, very few particles, if any, would be resuspended. Bigger dunes, formed by more or heavier particles, are more effective than smaller ones in causing particle resuspension provided the total number and mass of particles is not too large. A small number of particles produces a modest improvement on the Nusselt number, but the effectiveness of particles as heat carriers is soon overshadowed by the weight they add to the mixture which slows down the circulation. The efficiency with which particles extract gravitational energy from the fluid reaches 20%, far higher than previous estimates in the literature which place it below 1%.

It is believed that the space-time correlation is a fundamental statistical tool for analyzing the dynamic coupling between spatial and temporal scales of the motion in turbulent flows. In this paper, by coupling the inner-outer interaction model with the attached-eddy hypothesis, the space-time correlations of both wall-shear fluctuations and the streamwise velocity fluctuations carried by wall-attached eddies at a given length scale are investigated. The present results demonstrate that the space-time correlations for the wall-shear stress fluctuation are mainly dominated by near-wall small-scale motions and the superposition effects generated by wall-attached eddies are only reflected in the weakly correlated regions with large space separations and/or time delays. Furthermore, the findings in the present study demonstrate that wall-attached eddies at a given length scale feature distinctly different space-time properties as compared to those of ensembled eddies with multiple length scales, which provides an alternative perspective for analyzing the decorrelation mechanisms in turbulence theory and developing an advanced space-time correlation model.

Here we show how Feynman's simplified model for the Josephson junction, as a macroscopic two-state coupled quantum system, has a one-to-one correspondence with the stable dynamics of two interfacial Rossby waves in piecewise linear shear flows. The conservation of electric charge and energy of the superconducting electron gas layers become, respectively, equivalent to the conservation of wave action and pseudoenergy of the Rossby waves. Quantumlike tunneling is enabled via action at a distance between the two Rossby waves. Furthermore, the quantumlike phenomena of avoided crossing between eigenstates, described by the Klein-Gordon equation, is obtained as well in the classical shear flow system. In the latter, it results from the inherent difference in pseudoenergy between the in-phase and antiphased normal modes of the interfacial waves. This provides an intuitive physical meaning to the role of the wave function's phase in the quantum system. A partial analog to the quantum collapse of the wave function is also obtained due to the existence of a separatrix between normal mode regions of influence on the phase plane, describing the system's dynamics. As for two-state quantum bits (qubits), the two-Rossby wave system solutions can be represented on a Bloch sphere, where the Hadamard gate transforms the two normal modes and eigenstates into an intuitive computational basis in which only one interface is occupied by a Rossby wave. Yet, it is a classical system which lacks exact analogs to collapse and entanglement, and thus cannot be used for quantum computation, even in principle.