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The clustering of debris floating on liquid interfaces such as water surfaces is a complex phenomenon that finds its applications in numerous examples from industrial processing and environmental systems. The recent paper by Shin & Coletti (J. Fluid Mech. , vol. 984, 2024, R7) presents an experimental campaign investigating the three effects of turbulence, particle interactions and interfacial effects, to elucidate how the three force scales drag, capillary forces and lubrication give rise to three distinct regimes of clustering in dense suspensions. The study, hence, provides a useful systematic to categorize the clustering mechanisms. As an important finding, it is shown that, depending on volume fraction and non-dimensional turbulent shear, particles either tend to cluster into aggregate sizes larger than the Kolmogorov scale or can break into pieces that are as small as the primary particle size. [ABSTRACT FROM AUTHOR]

Small finite-size particles suspended in fluid flow through an enclosed curved duct can focus to points or periodic orbits in the two-dimensional duct cross-section. This particle focusing is due to a balance between inertial lift forces arising from axial flow and drag forces arising from cross-sectional vortices. The inertial particle focusing phenomenon has been exploited in various industrial and medical applications to passively separate particles by size using purely hydrodynamic effects. A fixed size particle in a circular duct with a uniform rectangular cross-section can have a variety of particle attractors, such as stable nodes/spirals or limit cycles, depending on the radius of curvature of the duct. Bifurcations occur at different radii of curvature, such as pitchfork, saddle-node and saddle-node infinite period (SNIPER), which result in variations in the location, number and nature of these particle attractors. By using a quasi-steady approximation, we extend the theoretical model of Harding et al. (J. Fluid Mech. , vol. 875, 2019, pp. 1–43) developed for the particle dynamics in circular ducts to spiral duct geometries with slowly varying curvature, and numerically explore the particle dynamics within. Bifurcations of particle attractors with respect to radius of curvature can be traversed within spiral ducts and give rise to a rich nonlinear particle dynamics and various types of tipping phenomena, such as bifurcation-induced tipping (B-tipping), rate-induced tipping (R-tipping) and a combination of both, which we explore in detail. We discuss implications of these unsteady dynamical behaviours for particle separation and propose novel mechanisms to separate particles by size in a non-equilibrium manner. [ABSTRACT FROM AUTHOR]

The initial flow past an impulsively started rotating and translating circular cylinder is asymptotically analysed using a Brinkman penalization method on the Navier-Stokes equation. In our previous study (J. Fluid Mech., vol. 929, 2021, A31), the asymptotic solution was obtained within the second approximation with respect to the small parameter, ϵ, that is of the order of 1/λ. Here, λ is the penalization parameter. In addition, the Reynolds number based on the cylinder radius and the translating velocity is assumed to be of the order of ϵ. The previous study asymptotically analysed the initial flow past an impulsively started translating circular cylinder and investigated the influence of the penalization parameter λ on the drag coefficient. It was concluded that the drag coefficient calculated from the integration of the penalization term exhibits a half-value of the results of Bar-Lev & Yang (J. Fluid Mech., vol. 72, 1975, pp. 625-647) as λ→∞. Furthermore, the derivative of vorticity in the normal direction was found to be discontinuous on the cylinder surface, which is caused by the tangential gradient of the pressure on the cylinder surface. The present study hence aims to investigate the variance on the drag coefficient against the result of Bar-Lev & Yang (1975). First, we investigate the problem of an impulsively started rotating circular cylinder. In this situation, the moment coefficient is independent of the pressure on the cylinder surface so that we can elucidate the role of the pressure to the hydrodynamic coefficients. Then, the problem of an impulsively started rotating and translating circular cylinder is investigated. In this situation, the pressure force induced by the unsteady flow far from the cylinder is found to play a key role on the drag force for the agreement with the result of Bar-Lev & Yang (1975), whereas the variance still exists on the lift force. To resolve the variance, an alternative formula to calculate the hydrodynamic force is derived, assuming that there is the pressure jump between the outside and inside of the cylinder surface. The pressure jump is obtained in this analysis asymptotically. Of particular interest is the fact that this pressure jump can cause the variance on the lift force calculated by the integration of the penalization term. [ABSTRACT FROM AUTHOR]

The force and torque on a solid body in a viscous potential flow are often taken to be independent of viscosity. Joseph et al. (Eur. J. Mech. B/Fluids, vol. 12, 1993, pp. 97-106; J. Fluid Mech., vol. 265, 1994, pp. 1-23) proved that this holds for (i) the force (not the torque) in any two-dimensional flow, and (ii) the drag force experienced by a purely translating three-dimensional body. The remaining components of the force and torque, along with general three-dimensional flows, were not considered. Importantly, the flow was assumed to be unbounded and irrotational everywhere. We eliminate this rarely satisfied assumption and consider the viscous force and torque experienced by any closed surface where the flow is irrotational locally; this can include a body's surface. Any vorticity distribution is permitted away from the closed irrotational surface. In so doing, we complete the analysis of Joseph et al. for all components of the viscous force and torque in two and three dimensions and enable application to real flows that inevitably contain regions of vorticity. [ABSTRACT FROM AUTHOR]

We investigate the three-dimensional (3-D) flow around and through a porous screen for various porosities at high Reynolds number Re = O(104). Historically, the study of this problem has been focused on two-dimensional cases and for screens spanning completely or partially a channel. Since many recent problems have involved a porous object in a 3-D free flow, we present a 3-D model initially based on Koo & James (J. Fluid Mech., vol. 60, 1973, pp. 513-538) and Steiros & Hultmark (J. Fluid Mech., vol. 853, 2018 pp. 1-11) for screens of arbitrary shapes. In addition, we include an empirical viscous correction factor accounting for viscous effects in the vicinity of the screen. We characterize experimentally the aerodynamic drag coefficient for a porous square screen composed of fibres, immersed in a laminar air flow with various solidities and different angles of attack. We test various fibre diameters to explore the effect of the space between the pores on the drag force. Using PIV and hot wire probe measurements, we visualize the flow around and through the screen, and in particular measure the proportion of fluid that is deviated around the screen. The predictions from the model for drag coefficient, flow velocities and streamlines are in good agreement with our experimental results. In particular, we show that local viscous effects are important: at the same solidity and with the same air flow, the drag coefficient and the flow deviations strongly depend on the Reynolds number based on the fibre diameter. The model, taking into account 3-D effects and the shape of the porous screen, and including an empirical viscous correction factor that is valid for fibrous screens may have many applications including the prediction of water collection efficiency for fog harvesters. [ABSTRACT FROM AUTHOR]

Birds employ rapid pitch-up motions close to the ground for different purposes: perching birds use this motion to decelerate and come to a complete stop while hunting birds, such as bald eagles, employ it to catch prey and swiftly fly away. Motivated by these observations, our study investigates how natural flyers accomplish diverse flying objectives by rapidly pitching their wings while decelerating near ground. We conducted experimental and analytical investigations focusing on rapidly pitching plates during deceleration in close proximity to the ground to explore the impact of ground proximity on the unsteady dynamics. Initially, we executed synchronous pitch-up motion, where both pitching and deceleration have the same motion duration, at different ground heights. Experimental results demonstrate that as the pitching wing approaches the ground, the instantaneous lift increases by approximately 38% compared with a far-from-ground case, while the initial peak drag force remains relatively unchanged. Our analytical model conforms to this trend, predicting an increase in lift force as the wing approaches the ground, indicating enhanced added mass and circulatory lift force due to the ground effect. Next, we examined asynchronous pitch-up motion cases, where rapid pitching motions were initiated at different stages of deceleration. The results reveal that initiating the wing pitch early in the deceleration leads to the formation of larger counter-rotating vortices at the early stage of the manoeuvre. These vortices generate stronger dipole jets that orient backward in the later stages of the manoeuvre after impinging with the ground surface, which hunting birds utilize to accelerate after catching prey. Conversely, when the wing pitch is delayed, smaller vortices form, but their growth is postponed until late in the manoeuvre. This delayed vortex growth produces lift and drag force at the end phase of the manoeuvre that facilitates a smooth landing or perching. Thus, through strategic tuning of a rapid pitch-up motion with deceleration, natural flyers, such as birds, achieve diverse flying objectives. [ABSTRACT FROM AUTHOR]

The presence of a dispersed phase can significantly modulate the drag in turbulent systems. We derived a conserved quantity that characterizes the radial transport of azimuthal momentum in the fluid–fluid two-phase Taylor–Couette turbulence. This quantity consists of contributions from advection, diffusion and two-phase interface, which are closely related to density, viscosity and interfacial tension, respectively. We found from interface-resolved direct numerical simulations that the presence of the two-phase interface consistently produces a positive contribution to the momentum transport and leads to drag enhancement, while decreasing the density and viscosity ratios of the dispersed phase to the continuous phase reduces the contribution of local advection and diffusion terms to the momentum transport, respectively, resulting in drag reduction. Therefore, we concluded that the decreased density ratio and the decreased viscosity ratio work together to compete with the presence of a two-phase interface for achieving drag modulation in fluid–fluid two-phase turbulence. [ABSTRACT FROM AUTHOR]

An experimental investigation identifying the effects of surface roughness on the drag coefficient ($C_{D}$) of freely rolling spheres is reported. Although lubrication theory predicts an infinite drag force for an ideally smooth sphere in contact with a smooth wall, finite drag coefficients are obtained in experiments. It is proposed that surface roughness provides a finite effective gap ($G$) between the sphere and panel, resulting in a finite drag force while also allowing physical contact between the sphere and plane. The measured surface roughnesses of both the sphere and panel are combined to give a total relative roughness ($\xi$). The measured $C_{D}$ increases with decreasing $\xi$ , in agreement with analytical predictions. Furthermore, the measured $C_{D}$ is also in good agreement with the combined analytical and numerical predictions for a smooth sphere and wall, with a gap approximately equal to the root-mean-square roughness ($R_q$). The accuracy of these predictions decreases for low mean Reynolds numbers ($\overline {Re}$), due to the existence of multiple scales of surface roughness that are not effectively captured by $R_{q}$. Experimental flow visualisations have been used to identify critical flow transitions that have been previously predicted numerically. Path tracking of spheres rolling on two panels with different surface roughnesses indicates that surface roughness does not significantly affect the sphere path or oscillations. Analysis of sphere Strouhal number ($St$) highlights that wake shedding and sphere oscillations are coupled at low $\overline {Re}$ but with increasing $\overline {Re}$ , the influence of wake shedding on the sphere path diminishes. [ABSTRACT FROM AUTHOR]

Wall-based spanwise forcing has been experimentally used with success by Auteri et al. (Phys. Fluids, vol. 22, 2010, 115103) to obtain large reductions of turbulent skin-friction drag and considerable energy savings in a pipe flow. The spatial distribution of the azimuthal wall velocity used in the experiment was not continuous, but piecewise constant. The present study is a numerical replica of the experiment, based on a set of direct numerical simulations (DNS); its goal is the identification of the effects of spatially discrete forcing, as opposed to the idealized sinusoidal forcing considered in the majority of numerical studies. Regardless of the discretization, with DNS the maximum drag reduction is found to be larger: the flow easily reaches complete relaminarization, whereas the experiment was capped at 33% drag reduction. However, the key result stems from the observation that, for the piecewise-constant forcing, the apparent irregularities of the experimental data appear in the simulation data too. They derive from the rich harmonic content of the discontinuous travelling wave, which alters the drag reduction of the sinusoidal forcing. A detailed understanding of the contribution of each harmonic reveals that, whenever for example technological limitations constrain one to work far from the optimal forcing parameters, a discrete forcing may perform very differently from the corresponding ideal sinusoid, and in principle can outperform it. However, care should be exercised in comparison, as discrete and continuous forcing have different energy requirements. [ABSTRACT FROM AUTHOR]

We investigate the effect of particle inertia on the merger of co-rotating dusty vortex pairs at semi-dilute concentrations. In a particle-free flow, the merger is triggered once the ratio of vortex core size to vortex separation reaches a critical value. The vortex pair separation then decreases monotonically until the two cores merge together. Using Eulerian-Lagrangian simulations of co-rotating particle-laden vortices, we show substantial departure from the vortex dynamics previously established in particle-free flows. Most strikingly, we find that disperse particles with moderate inertia cause the vortex pair to push apart to a separation nearly twice as large as the initial separation. During this stage, the drag force exerted by particles ejected out of the vortex cores on the fluid results in a net repulsive force that pushes the two cores apart. Eventually, the two dusty vortices merge into a single vortex with most particles accumulating outside the core, similar to the dusty Lamb-Oseen vortex described in Shuai & Kasbaoui (J. Fluid Mech., vol 936, 2022, p. A8). For weakly inertial particles, we find that the merger dynamics follows the same mechanics as that of a single-phase flow, albeit with a density that must be adjusted to match the mixture density. For highly inertial particles, the feedback force exerted by the particles on the fluid may stretch the two cores during the merger to a point where each core splits into two, resulting in inner and outer vortex pairs. In this case, the merger occurs in two stages where the inner vortices merge first, followed by the outer ones. [ABSTRACT FROM AUTHOR]

Experimental and theoretical studies on millimetre-sized droplets suggest that at low Reynolds number the difference between the drag force on a circulating water droplet and that on a rigid sphere is very small (less than 1 %) (LeClair et al., J. Atmos. Sci., vol. 29, 1972, pp. 728-740). While the drag force on a spherical liquid droplet at high viscosity ratios (of the liquid to the gas), is approximately the same as that on a rigid sphere of the same size, the other quantities of interest (e.g. the temperature) in the case of a rarefied gas flow over a liquid droplet differ from the same quantities in the case of a rarefied gas flow over a rigid sphere. The goal of this article is to study the effects of internal motion within a spherical microdroplet/nanodroplet - such that its diameter is comparable to the mean free path of the surrounding gas - on the drag force and its overall dynamics. To this end, the problem of a slow rarefied gas flowing over an incompressible liquid droplet is investigated analytically by considering the internal motion of the liquid inside the droplet and also by accounting for kinetic effects in the gas. Detailed results for different values of the Knudsen number, the ratio of the thermal conductivities and the ratio of viscosities are presented for the pressure and temperature profiles inside and outside the liquid droplet. The results for the drag force obtained in the present work are in good agreement with the theoretical and experimental results existing in the literature. [ABSTRACT FROM AUTHOR]

The free-surface channel flow around a square cylinder is analysed, over a wide range of blocking ratios, using three-dimensional simulations. The state of the flow is characterised in terms of the Froude number upstream and downstream of the square cylinder. The simulations confirm the presence of the subcritical and choked states, and provide new insight into the supercritical state and band-gap through an analysis of how the momentum flux varies with Froude number along the channel. The influence of the blocking ratio on the flow state and drag force is analysed and shows the significant rise of drag in the choked regime. [ABSTRACT FROM AUTHOR]

We investigate the global Cauchy problem for a two–phase flow model consisting of the pressureless Euler equations coupled with the isentropic compressible Navier–Stokes equations through a drag forcing term. This model was first derived by Choi–Kwon [J. Differential Equations, 261(1) (2016), pp. 654–711] by taking the hydrodynamic limit of the Vlasov/compressible Navier–Stokes equations. Under the assumption that the initial perturbation is sufficiently small, Choi–Kwon [J. Differential Equations, 261(1) (2016), pp. 654–711] established the global well–posedness and large time behaviour for the three dimensional periodic domain $\mathbb {T}^3$. However, up to now, the global well–posedness and large time behaviour for the three dimensional Cauchy problem still remain unsolved. In this paper, we resolve this problem by proving the global existence and optimal decay rates of classic solutions for the three dimensional Cauchy problem when the initial data is near its equilibrium. One of key observations here is that to overcome the difficulties arising from the absence of pressure in the Euler equations, we make full use of the drag forcing term and the dissipative structure of the Navier–Stokes equations to closure the energy estimates of the variables for the pressureless Euler equations. [ABSTRACT FROM AUTHOR]

We revisit the problem of a solid sphere rising slowly in a rotating short container filled with a slightly viscous fluid, with emphasis on the drag force. The data of the classical experiments of Maxworthy (J. Fluid Mech., vol. 31, 1968, pp. 643–655) and recent experiments of Kozlov et al. (Fluids, vol. 8 (2), 2023, paper 49), and the available geostrophic and quasi-geostrophic theories, are subjected to a novel scrutiny by combined reprocessing and comparisons. The measured drag is, consistently, about 20 % lower than the geostrophic prediction (assuming that flow is dominated by the Ekman layers, while in the inviscid cores the Coriolis acceleration is supported by the pressure gradient). The major objective is the interpretation and improvement of the gap between data and predictions. We show that the data cover a small range of relevant parameters (in particular the Taylor number T and the height ratio H of cylinder to particle diameter) that precludes a thorough and reliable assessment of the theories. However, some useful insights and improvements can be derived. The hypothesis that the discrepancy between data and the geostrophic prediction is due to inertial effects (not sufficiently small Rossby number Ro in the experiments) is dismissed. We show that the major reason for the discrepancy is the presence of relatively thick Stewartson layers about the cylinder (Taylor column) attached to the sphere. The 1/3 layer displaces the boundary condition of the angular velocity (ω = 0) outside the radius of the particle. This observation suggests a semi-empirical correction to the theoretical quasi-geostrophic predictions (which takes into account the Ekman layers and the 1/4 Stewartson layers); the corrected drag is in fair agreement with the data. We demonstrate that the inertial terms are negligible for Ro T1/2 < 0.4. We consider curve-fit approximations, and point out some persistent gaps of knowledge that require further experiments and simulations. [ABSTRACT FROM AUTHOR]

Clustering of externally and evenly heated particles is enhanced by the increased viscosity of heated fluid in the vicinity of these clusters – a phenomenon known as viscous capturing (VC). Herein we study, via direct numerical simulations of decaying turbulence, the effect of temperature-driven viscosity on clustering with different particle loading densities. We employ a two-way momentum and energy coupling, and gas viscosity is modelled by a power law to understand the role of the increased drag and particle back-reaction force on the clustering intensity. For the continuum and dispersed phases, Eulerian and Lagrangian point particle schemes have been used, neglecting inter-particle collisions. We found that the enhanced viscosity-driven clustering is a strong function of particle loading density, as the increase in particle number density enables the formation of large uneven clusters before heating, which is the main condition for VC to take effect. Higher number density should result in greater turbulence modulation and negate local temperature-based viscous effects leading to VC. However, due to higher local particle number density in the clusters and interphase heat transfer, increased drag force prevails in such cases and delivers excessive clustering. By sampling conditionally the particle velocity and temperature inside the clusters, it is found that the thermodynamic and kinematic properties of the particles in the clusters are highly correlated, and this correlation increases with the particle loading density. Therefore, based on the particle number density, temperature-based viscosity can enhance considerably the clustering of heated particles and alter the effect of particles on the underlying turbulence. [ABSTRACT FROM AUTHOR]

Many of the cell membrane’s vital functions are achieved by the self-organization of the proteins and biopolymers embedded in it. The protein dynamics is in part determined by its drag. A large number of these proteins can polymerize to form filaments. In vitro studies of protein–membrane interactions often involve using rigid beads coated with lipid bilayers, as a model for the cell membrane. Motivated by this, we use slender-body theory to compute the translational and rotational resistance of a single filamentous protein embedded in the outer layer of a supported bilayer membrane and surrounded on the exterior by a Newtonian fluid. We first consider the regime where the two layers are strongly coupled through their inter-leaflet friction. We find that the drag along the parallel direction grows linearly with the filament’s length and quadratically with the length for the perpendicular and rotational drag coefficients. These findings are explained using scaling arguments and by analysing the velocity fields around the moving filament. We then present and discuss the qualitative differences between the drag of a filament moving in a freely suspended bilayer and a supported membrane as a function of the membrane’s inter-leaflet friction. Finally, we briefly discuss how these findings can be used in experiments to determine membrane rheology. In summary, we present a formulation that allows computation of the effects of membrane properties (its curvature, viscosity and inter-leaflet friction), and the exterior and interior three-dimensional fluids’ depth and viscosity on the drag of a rod-like/filamentous protein, all in a unified theoretical framework. [ABSTRACT FROM AUTHOR]

The unsteady hydrodynamic drag exerted on an oscillating sphere near a planar wall is addressed experimentally, theoretically and numerically. The experiments are performed by using colloidal-probe atomic force microscopy in thermal noise mode. The resonance frequencies and quality factors are extracted from the measurement of the power spectrum density of the probe oscillation for a broad range of gap distances and Womersley numbers. The shift in the resonance frequency of the colloidal probe as the probe goes close to a solid wall infers the wall-induced variations of the effective mass of the probe. Interestingly, a crossover from a positive to a negative shift is observed as the Womersley number increases. In order to rationalize the results, the confined unsteady Stokes equation is solved numerically using a finite-element method, as well as asymptotic calculations. The in-phase and out-of-phase terms of the hydrodynamic drag acting on the sphere are obtained and agree well with the experimental results. All together, the experimental, theoretical and numerical results show that the hydrodynamic force felt by an immersed sphere oscillating near a wall is highly dependent on the Womersley number. [ABSTRACT FROM AUTHOR]

When inertial particles are dispersed in a turbulent flow at sufficiently high concentrations, the continuous and dispersed phases are two-way coupled. Here, we show via laboratory measurements how, as the suspended particles modify the turbulence, their behaviour is also profoundly changed. In particular, we investigate the spatial distribution and motion of sub-Kolmogorov particles falling in homogeneous air turbulence. We focus on the regime considered in Hassaini & Coletti (J. Fluid Mech., vol. 949, 2022, A30), where the turbulent kinetic energy and dissipation rate were found to increase as the particle volume fraction increases from 10-6 to 5 x 10-5. This leads to strong intensification of the clustering, encompassing a larger fraction of the particles and over a wider range of scales. The settling rate is approximately doubled over the considered range of concentrations, with particles in large clusters falling even faster. The settling enhancement is due in comparable measure to the predominantly downward fluid velocity at the particle location (attributed to the collective drag effect) and to the larger slip velocity between the particles and the fluid. With increasing loading, the particles become less able to respond to the fluid fluctuations, and the random uncorrelated component of their motion grows. Taken together, the results indicate that the concentrated particles possess an effectively higher Stokes number, which is a consequence of the amplified dissipation induced by two-way coupling. The larger relative velocities and accelerations due to the increased fall speed may have far-reaching consequences for the inter-particle collision probability. [ABSTRACT FROM AUTHOR]

Vertically vibrating a liquid bath may allow a self-propelled wave-particle entity to move on its free surface. The horizontal dynamics of this walking droplet, under the constraint of an external drag force, can be described adequately by an integro-differential trajectory equation. For a sinusoidal wave field, this equation is equivalent to a closed three-dimensional system of nonlinear ODEs. We explicitly define a stability boundary for the system and a quantised criterion for its partial integrability in the meromorphic category. [ABSTRACT FROM AUTHOR]

Two-way momentum-coupled direct numerical simulations of a particle-laden turbulent channel flow are addressed to investigate the effect of the particle Stokes number and of the particle-to-fluid density ratio on the turbulence modification. The exact regularised point-particle method is used to model the interphase momentum exchange in presence of solid boundaries, allowing the exploration of an extensive region of the parameter space. Results show that the particles increase the friction drag in the parameter space region considered, namely the Stokes number $St_+ \in [2,80]$ , and the particle-to-fluid density ratio $\rho _p/\rho _f \in [90,5760]$ at a fixed mass loading $\phi =0.4$. It is noteworthy that the highest drag occurs for small Stokes number particles. A measurable drag increase occurs for all particle-to-fluid density ratios, the effect being reduced significantly only at the highest value of $\rho _p/\rho _f$. The modified stress budget and turbulent kinetic energy equation provide the rationale behind the observed behaviour. The particles' extra stress causes an additional momentum flux towards the wall that modifies the structure of the buffer and of the viscous sublayer where the streamwise and wall-normal velocity fluctuations are increased. Indeed, in the viscous sublayer, additional turbulent kinetic energy is produced by the particles' back-reaction, resulting in a strong augmentation of the spatial energy flux towards the wall where the energy is ultimately dissipated. This behaviour explains the increase of friction drag in particle-laden wall-bounded flows. [ABSTRACT FROM AUTHOR]

We investigate steady and oscillatory flow through a hexagonal close-packed arrangement of spheres in the framework of the volume-averaged momentum equation. We quantify the friction and pressure drag based on a direct numerical simulation dataset. Using the pressure decomposition of Graham (J. Fluid Mech. , vol. 881, 2019), the pressure drag can be further split up into an accelerative, a viscous and a convective contribution. For the accelerative pressure, a closed-form expression can be given in terms of the potential flow solution. We investigate the contributions of the different drag components to the volume-averaged momentum budget and their Reynolds number scaling. For steady flow, we find that the friction and viscous pressure drag are proportional to $Re$ at low Reynolds numbers and scale with $Re^{1.4}$ for high Reynolds numbers. This is close to the steady laminar boundary layer scaling. For the convective pressure drag, we find a cubic scaling at low and a quadratic scaling at high Reynolds numbers. The Reynolds stresses have a minor contribution to the momentum budget. For oscillatory flow at low and medium Womersley numbers, the amplitudes of the drag components are similar to the steady cases at the same Reynolds number. At high Womersley numbers, the drag components behave quite differently and the friction and viscous pressure drag are relatively insignificant. The drag components are not in phase with the forcing and the superficial velocity; the phase lag increases with the Womersley number. This suggests that new models beyond the current quasisteady approaches need to be developed. [ABSTRACT FROM AUTHOR]

Wake interaction of two rotationally oscillating cylinders in side-by-side configuration is studied experimentally at a Reynolds number of 150. Five spacing ratios, $T/D$ (ratio of centre-to-centre spacing to cylinder diameter), are considered, namely, 1.4, 1.8, 2.5, 4.0 and 7.5. Both in-phase and antiphase forcing are investigated. Oscillation amplitude is varied from ${\rm \pi} /8$ to ${\rm \pi}$ , and forcing frequency, $FR$ (ratio of the oscillation frequency to the vortex-shedding frequency of a stationary cylinder) is varied from 0 to 5. The experimental investigation is done using laser-induced fluorescence, hot film anemometry and particle-image velocimetry (PIV). The interaction between the two cylinders under forcing results in new wake modes and vortex structures and a comprehensive study from the wake visualisations is conducted. Quantitative results are presented in terms of streamwise and cross-stream mean velocity profiles, centreline velocity recovery, peak velocity deficit, wake width, fluctuation intensity, circulation, vorticity contours and drag coefficient. The magnitude of streamwise velocity deficit and cross-stream velocity variation is strongly affected by the presence of second cylinder. The recirculation region behind the cylinders is found to extend further downstream with increase in the forcing. Scaling analysis is carried out to express the peak velocity deficit variation with forcing. It is observed that the relative strength of the vortices shed from inner and outer shear layers depends on the phase of oscillation. An experimental set-up for direct force measurement is designed and the drag force acting on the oscillating cylinders assembly is directly measured and the effect of forcing on the variation of ${C}_{d}$ is studied. An estimate for drag coefficient is also made from the PIV data following a detailed control volume analysis. It is observed that the set of forcing parameters that correspond to maximum and minimum drag also yield extrema in the values of circulation and fluctuation intensity. [ABSTRACT FROM AUTHOR]

Effects of the spanwise wavelength (λ) of a sinusoidal wavy cylinder with elliptic cross-section on wake structures and fluid forces are numerically investigated at a Reynolds number Re  = 100. A wide range of the wavelength, $0.43 \le \lambda /{D_m} \le 8.59$ , is considered with a wave amplitude of a / Dm  = 0.048, where Dm is the hydraulic diameter of the wavy cylinder. Based on vortical structures, Strouhal number (St) and wake closure length (Lc), fluid forces, streamline topologies and spatio-temporal evolutions of the near wake, five distinct flow patterns (I–V) are identified depending on λ / Dm. The drag force reaches its minimum in pattern III, the fluctuating lift force is zero in flow patterns III and IV. Distinct from the classical flow where alternate vortex shedding occurs synchronously over the entire cylinder span, flow pattern IV has alternate vortex shedding over a one half-wavelength of the wavy elliptic cylinder, antiphased with that over the other half-wavelength, thus leading to zero fluctuating lift over one complete wavelength. A thorough comparison of the wakes is made between the wavy elliptic cylinder and wavy circular or square cylinder, distinguishing the underlying flow physics behind the salient behaviours observed. [ABSTRACT FROM AUTHOR]

This paper discusses how the submergence ratio, defined as the ratio between the flow depth, D, and the height, h, of the solid rigid cylinders forming the array affects flow and turbulence structure inside and around a rectangular array of cylinders placed adjacent to one of the channel sidewalls. As the array becomes submerged, a vertical shear layer develops in between the top face of the array and the free surface, which strongly increases flow three-dimensionality and modifies how the momentum exchange between the array and the surrounding open water regions occurs with respect to the case of an emerged array where only a horizontal shear layer forms as part of the incoming flow approaching the array is deflected laterally. Eddy-resolving simulations are conducted for several values of the solid volume fraction, ϕ, and of the submergence ratio, 1.0 ≤ D/h ≤ 4.0. Similar to the limiting case of an emerged array (D/h = 1.0), the width- and depth-averaged streamwise velocity inside the array reaches a constant value after an initial adjustment region in the submerged-array cases. For D/h ≥ 1.33, the mean normal velocities through the top and side faces of the array do not become equal to zero downstream of the initial adjustment region. The flow inside the array reaches an equilibrium regime where the local flux of fluid leaving the array through its side face is balanced by the local flux of fluid entering the array through its top face. This regime is observed until close to the end of the array. For D/h ≥ 2.0, the horizontal shear layer vortices do not generate successive regions of high and low streamwise velocity and bed friction velocity inside the array, as is observed in the emerged cases. With respect to the emerged case, the size of the shear layer vortices and the shear layer width increase for low submergence ratios before decreasing rapidly for D/h ≥ 1.33. Significant three-dimensional effects are present inside the array and the horizontal shear layer for cases with both emerged and submerged arrays. In the ϕ = 0.08 cases, strong upwelling and downwelling motions are observed inside the array for D/h ≥ 1.33, while the circulation of the streamwise-oriented cell of secondary flow forming close to the lateral face of the array peaks when the submergence ratio is close to 1.33. For constant ϕ, the total streamwise drag force normalized with the height and width of the array increases with increasing submergence ratio. As the array submergence increases, the cylinders near the front of the array contribute less to the total force acting on the cylinders forming the array. For constant D/h, the total streamwise drag force acting on the array increases with ϕ for the submerged and emerged cases. [ABSTRACT FROM AUTHOR]

Flow and turbulent structures generated by the interaction of forced incoming oscillatory flow with a circular, vertical cylinder placed in an open channel with a horizontal bed are investigated using eddy-resolving simulations. Validation simulations performed with a Keulegan–Carpenter (KC) number of 20 and multiple-mode forcing corresponding to the laboratory experiment of Sumer et al. (J. Fluid Mech. , vol. 332, 1997, pp. 41–70) show that detached eddy simulation (DES) predicts more accurately the amplification of the bed shear stress beneath the horseshoe vortex system (upstream side of the cylinder) and the maximum magnitude of the bed shear stress at the downstream (wake) side of the cylinder compared with unsteady Reynolds-averaged Navier–Stokes simulations. High-Reynolds-number DES simulations are then conducted with 1.5 ≤  KC  ≤ 30.8 and one-mode sinusoidal forcing of the streamwise velocity in the approaching flow to investigate the changes in the wake vortex-flow regimes, the coherence of the horseshoe vortices and the generation of other near-bed coherent structures in the wake during the oscillatory cycle. The flow is periodic, no horseshoe vortices form and no vortices are shed in the wake for KC  = 1.5. By contrast, for KC  ≥ 8 horseshoe vortices are present over part of the oscillatory cycle and up to three wake vortices are shed over each half-cycle as KC is increased to 30.8. For an intermediate range of KC numbers, one (KC  = 15.4) or two (KC  = 8) of the vortices forming at the back of the cylinder during each half-cycle are washed around it when the flow reverses. The main horseshoe vortex and other horizontal near-bed vortices have a large capacity to amplify the bed shear stresses when the incoming velocity magnitude is significantly less than its peak value. Assuming the depth-averaged velocity in the incoming (undisturbed) oscillatory flow is the same in simulations conducted with different KC numbers, the peak values of the sediment entrainment potential measured by the mean (cycle-averaged) volumetric flux of sediment entrained from the bed over one oscillatory cycle occur for 8 ≤  KC  ≤ 15.4. For all KC numbers, the in-line force variation over the oscillatory cycle is fairly well approximated by the Morison equation. For KC  = 1.5, the in-line force is only due to inertia effects. For KC  = 30.8, the maximum and minimum values of the phase-averaged in-line force are approximatively in phase with those of the incoming flow velocity. For KC  ≥ 15, the phase-averaged in-line force coefficients vary between 0.8 and 1.1 during most of the oscillatory cycle (e.g. when the incoming flow velocity is not close to zero). This is different from cases with KC  ≤ 8 where the in-line force coefficient is equal to zero twice during the oscillatory cycle as the in-line force becomes equal to zero for non-zero values of the incoming velocity. The largest cycle-to-cycle variations of the in-line force coefficient and in-line force are observed around KC  = 8. For KC  = 8 and 15.4, the cylinder is subject to relatively large phase-averaged spanwise drag forces that are comparable to the peak phase-averaged streamwise drag forces. As KC is increased to 30.8, the phase-averaged spanwise drag force becomes zero over the whole oscillatory cycle but the cylinder is still subject to large instantaneous spanwise forces over part of the oscillatory cycle. [ABSTRACT FROM AUTHOR]

While large-scale seafloor features (e.g. continental slopes, mid-ocean ridges) help shape the broad patterns of ocean circulation, small-scale rough topography (e.g. seamounts, abyssal hills) can also impact the large-scale dynamics in two significant ways. First, they impact the momentum budget through flow steering, flow blocking and drag force, non-local momentum transfer via the generation of radiating internal waves and momentum dissipation by topographically induced turbulence. Second, they impact the density budget. Turbulence induced by flow–topography interactions facilitates ocean overturning circulation by upwelling dense, deep waters which form in polar oceans and sink to the abyss. Rough topography and its associated dynamics are of subgrid scale in Earth systems models (ESMs) and need parameterization for the foreseeable future. A parameterization of the intertwined impacts of flow–topography interactions on momentum and density budgets is currently non-existent, although its importance is well established. Radko (J. Fluid Mech. , vol. 961, 2023, A24) provides a novel analytical model for representing the impact of rough seafloor on larger-scale flows, spanning slow to fast flow-speed regimes in homogeneous and multilayer models. The proposed 'closure' is in remarkable agreement with high-resolution numerical simulations and provides a crucial step forward in parameterizing the impact of rough topography in coarse-resolution ocean models. Extending the model to the full Navier–Stokes equations, linking it to the density budget and considering more realistic ocean topography are three critical future steps towards implementing Radko's theory in operational ESMs. [ABSTRACT FROM AUTHOR]

Drag force acting on a particle is vital for the accurate simulation of turbulent multiphase flows, but the robust drag model is still an open issue. Fully resolved direct numerical simulation (DNS) with an immersed boundary method is performed to investigate the drag force on saltating particles in wall turbulence over a sediment bed. Results show that, for saltating particles, the drag force along the particle trajectories cannot be estimated accurately by traditional drag models originally developed for an isolated particle that depends on the particle-wall separation distance or local volume fraction in addition to the particle Reynolds number. The errors between the models and DNS are especially clear during the descending phase of the particles. Through simple theoretical analysis and DNS data fitting, we present a corrected factor using the classical, particle Reynolds number dependent drag force model as the benchmark model. The new drag model, which takes the particle vertical velocity into account, can reasonably predict the mean drag force obtained by DNS along a particle trajectory. [ABSTRACT FROM AUTHOR]

This study conducts direct numerical simulations of free-streaming turbulence passing over individual fixed particles and particle arrays of different number densities. The purpose is to investigate the changes in the mean particle drag due to turbulent environments and the responsible mechanisms. It is confirmed that turbulent environments significantly enhance the particle drag relative to the standard drag in a uniform flow, and the nonlinear dependency of the drag force on the instantaneous incoming flow velocity is insufficient to explain the enhancement. Two mechanisms of particle–turbulence interactions are found to be responsible for the particle drag enhancements. The first mechanism is the enlarged pressure drops on the particle surface, mainly governed by the large scales in turbulent flows. The second mechanism is the increased viscous stresses on the particle surface, dominated by the small scales that enhance the mixing of the low- and high-speed fluids across the particle boundary layer. In terms of quantitative drag enhancement predictions, more general models accounting for the anisotropy of the turbulence are proposed, which fit well with both the simulation data generated in this study and those reported in the literature. Finally, by measuring the drag forces of laminar and turbulent flows passing over arrays of particles, it is found that the overall particle drag increases with decreasing particle–particle relative gap distance. However, the relative enhancement due to turbulence decreases with the particle–particle relative gap distance. [ABSTRACT FROM AUTHOR]

Bubble–particle collisions in turbulence are central to a variety of processes such as froth flotation. Despite their importance, details of the collision process have not received much attention yet. This is compounded by the sometimes counter-intuitive behaviour of bubbles and particles in turbulence, as exemplified by the fact that they segregate in space. Although bubble–particle relative behaviour is fundamentally different from that of identical particles, the existing theoretical models are nearly all extensions of theories for particle–particle collisions in turbulence. The adequacy of these theories has yet to be assessed as appropriate data remain scarce to date. In this investigation, we study the geometric collision rate by means of direct numerical simulations of bubble–particle collisions in homogeneous isotropic turbulence using the point-particle approach over a range of the relevant parameters, including the Stokes and Reynolds numbers. We analyse the spatial distribution of bubble and particles, and quantify to what extent their segregation reduces the collision rate. This effect is countered by increased approach velocities for bubble–particle compared to monodisperse pairs, which we relate to the difference in how bubbles and particles respond to fluid accelerations. We found that in the investigated parameter range, these collision statistics are not altered significantly by the inclusion of a lift force or different drag parametrisations, or when assuming infinite particle density. Furthermore, we critically examine existing models and discuss inconsistencies therein that contribute to the discrepancy. [ABSTRACT FROM AUTHOR]

Power-law shear-thinning fluid motions induced by a translating spherical bubble with sinusoidal oscillation at a high frequency are numerically studied. We focus on reducing the time-averaged drag force $D$ on the bubble owing to the oscillation-enhanced shear-thinning effect. Under the assumption of negligible convection, the unsteady Stokes equation is directly solved in a finite-difference manner over a wide parameter space of the dimensionless oscillation amplitude $A$ (corresponding to the oscillatory-to-translational velocity ratio) and the power-law index $n$ of the viscosity. The results show that, for small amplitude ($A\ll 1$), the drag reduction ratio $1-D/D_0$ (here, $D_0$ is $D$ with no oscillation) is proportional to $A^2$. In contrast, for large amplitude ($A \gg 1$), the drag ratio $D/D_0$ is proportional to $A^{n-1}$ , revealing a power-law behaviour. In the case of $A \gg 1$ for a strong shear-thinning fluid with small $n$ , the square of the vorticity over the entire domain is much smaller than that of the shear rate, and thus the bulk flow may be regarded as irrotational. To provide a fundamental perspective on the drag reduction mechanism, a theoretical model is proposed based on potential theory, and demonstrated to well capture the power-law relation between $D/D_0$ and $A$. [ABSTRACT FROM AUTHOR]

In the classical irreversible thermodynamics (CIT) framework, the Navier–Stokes–Fourier constitutive equations are obtained so as to satisfy the entropy inequality, by and large assuming that the entropy flux is equal to the heat flux over the temperature. This article is focused on the derivation of second-order constitutive equations for polyatomic gases; it takes the basis of CIT, but most importantly, allows up to quadratic nonlinearities in the entropy flux. Mathematical similarities between the proposed model and the classic Stokes–Laplace equations are exploited so as to construct analytic/semi-analytic solutions for the slow rarefied gas flow over different shapes. A set of second-order boundary conditions are formulated such that the model's prediction for the drag force is in excellent agreement with the experimental data over the whole range of Knudsen numbers. We have also computed the normal shock structure in nitrogen for Mach ${Ma} \lesssim 4$. A very good agreement was observed with the kinetic theory, as well as with the experimental data. [ABSTRACT FROM AUTHOR]

A multiscale asymptotic theory is formulated for surface gravity waves and currents in finite-depth water with a vegetation canopy that provides a drag force on both flows with known drag coefficients. It assumes that the density is uniform and the depth is uniform pro tem and that the wave frequency is fast compared to the current advective rate. It is a quasi-linear theory in which the wave dynamics is independent of current and drag to leading order but provides perturbative corrections, and in which wave nonlinear interactions are neglected while quadratic wave-averaged wave fluxes and quadratic wave-drag effects are retained. The primary surface wave is modified by drag and current interactions, and the wave-averaged current momentum balance includes a wave-augmented drag force and several vortex forces due to Earth's rotation, current vorticity, Stokes drift and drag-induced wave vorticity. The wave-averaged current equations derived here are a suitable basis for future large-eddy simulation and submesoscale circulation computational models. [ABSTRACT FROM AUTHOR]

Glacial ripping involves glaciotectonic disintegration of rock hills and extensive removal of rock at the ice-sheet bed, triggered by hydraulic jacking caused by fluctuating water pressures. Evidence from eastern Sweden shows that glacial ripping caused significant subglacial erosion during the final deglaciation of the Fennoscandian ice sheet, distinct from abrasion and plucking (quarrying). Here we analyse the ice drag forces exerted onto rock obstacles at the base of an ice sheet, and the resisting forces of such rock obstacles: glaciotectonic disintegration requires that ice drag forces exceed the resisting forces of the rock obstacle. We consider rock obstacles of different sizes, shapes and fracture patterns, informed by natural examples from eastern Sweden. Our analysis shows that limited overpressure events, unfavourable fracture patterns, low-transmissivity fractures, slow ice and streamlined rock hamper rock hill disintegration. Conversely, under fast ice flow and fluctuating water pressures, disintegration is possible if the rock hill contains subhorizontal, transmissive fractures. Rock steps on previously smooth, abraded surfaces, caused by hydraulic jacking, also enhance drag forces and can cause disintegration of a rock hill. Glacial ripping is a physically plausible erosion mechanism, under realistic glaciological conditions prevalent near ice margins. [ABSTRACT FROM AUTHOR]

Motivated by drag-based propulsion of crinoids, the shape reconfiguration of a feather-like elastic structure under both steady and unsteady translational motions is investigated. The simplified elastic structure consists of a centre rod to which numerous side flaps are attached by elastic hinges. These side flaps fold in only one direction to realize a dramatic reduction in the area of the structure during the recovery stroke. Compared with experimental measurements, analytical methods developed to couple the dynamics of the centre rod and the side flaps successfully predict the drag force and three-dimensional reconfiguration of the elastic structure during both power and recovery strokes. A dimensionless speed given by the ratio of inertial fluid force to elastic bending force is proposed for the coupled deflections of the centre rod and side flaps, and is found to determine primarily the reconfiguration of the elastic structure. A reconfiguration number defined specifically for our model provides an appropriate characterization of the effect of side-flap folding on drag force reduction. Moreover, the ratio of drag forces between the power and recovery strokes is evaluated to find model conditions for the optimal force ratio. [ABSTRACT FROM AUTHOR]

The drag force on a spherical intruder in dense granular shear flows is studied using discrete element method simulations. Three regimes of the intruder dynamics are observed depending on the magnitude of the drag force (or the corresponding intruder velocity) and the flow inertial number: a fluctuation-dominated regime for small drag forces; a viscous regime for intermediate drag forces; and an inertial (cavity formation) regime for large drag forces. The transition from the viscous regime (linear force-velocity relation) to the inertial regime (quadratic force-velocity relation) depends further on the inertial number. Despite these distinct intruder dynamics, we find a quantitative similarity between the intruder drag in granular shear flows and the Stokesian drag on a sphere in a viscous fluid for intruder Reynolds numbers spanning five orders of magnitude. Beyond this first-order description, a modified Stokes drag model is developed that accounts for the secondary dependence of the drag coefficient on the inertial number and the intruder size and density ratios. When the drag model is coupled with a segregation force model for intruders in dense granular flows, it is possible to predict the velocity of gravity-driven segregation of an intruder particle in shear flow simulations. [ABSTRACT FROM AUTHOR]

Heterogeneous roughness in the form of streamwise aligned strips is known to generate large scale secondary motions under turbulent flow conditions that can induce the intriguing feature of larger flow rates above rough than smooth surface parts. The hydrodynamical definition of a surface roughness includes a large scale separation between the roughness height and the boundary layer thickness which is directly related to the fact that the drag of a laminar flow is not altered by the presence of roughness. Existing simplified approaches for direct numerical simulation of roughness strips do not fulfil this requirement of an unmodified laminar base flow compared with a smooth wall reference. It is shown that disturbances induced in a modified laminar base flow can trigger large-scale motions with resemblance to turbulent secondary flow. We propose a simple roughness model that allows us to capture the particular features of turbulent secondary flow without impacting the laminar base flow. The roughness model is based on the prescription of a spanwise slip length, a quantity that can directly be translated into the Hama roughness function for a homogeneous rough surface. The heterogeneous application of the slip-length boundary condition results in very good agreement with existing experimental data in terms of the secondary flow topology. In addition, the proposed modelling approach allows us to quantitatively evaluate the drag increasing contribution of the secondary flow. Both the secondary flow itself and the related drag increase reveal a very small dependence on the gradient of the transition between rough and smooth surface parts only. Interestingly, the observed drag increase due to secondary flows above the modelled roughness is significantly smaller than the one previously reported for roughness resolving simulations. We hypothesise that this difference arises from the fact that roughness resolving simulations cannot truly fulfil the requirement of large scale separation. [ABSTRACT FROM AUTHOR]

A droplet under a thermal gradient is known to migrate in a preferential direction, as governed by the variation of its interfacial tension with temperature. Contradicting the outcome of reported asymptotic analysis, here we show that the calculation of the droplet migration by considering the variation of interfacial tension with the imposed thermal field alone may be fundamentally incorrect. This error is attributed to the dynamically evolving interfacial temperature field due to a two-way coupling between the thermal field and the flow field, mediated by the droplet deformation and thermal diffusion. By directly capturing an inherent nonlinear coupling between the thermal field and the flow field using explicit interface tracking in a three-dimensional space, our boundary integral based analysis reveals that a linearly decreasing temperature profile imposed along the direction of a plane Poiseuille flow enhances the migration speed of the droplet in both the axial and cross-stream directions. This is in sharp contrast to a prediction of decelerated motion of the droplet under the same imposed thermal field, as obtained from asymptotic theory.We attribute this discrepancy to an alteration of the surface tension mediated interfacial stress due to the locally evolving temperature field, and a consequent concomitant alteration in the interfacial viscous stress to realize a tangential force balance at the interface. From scaling arguments, we show that the resulting change in the viscous drag force may occur over an order of magnitude, disrupting the outcome as compared to that obtained from asymptotic analysis. These results are likely to bear significant implications in controllable separation and sorting of deformable entities in confined fluidic media. [ABSTRACT FROM AUTHOR]

The paper investigates experimentally the flow past a flat-back, taller than wide Ahmed body having rectangular base aspect ratio H/W = 1.11 in the context of ground vehicle aerodynamics. Parametric studies at Reynolds number 2.1 × 105 explore the sensitivity of the aerodynamic force and body pressure distribution with respect to varying flow conditions defined from variable ground clearance C (taken at mid-distance from the front and rear axles of the body), pitch angle α, and yaw angle β (equivalent to a crosswind). Two-dimensional parametric maps in the parametric spaces (β, C) and (β, α) are obtained for parameter ranges covering real road vehicle driving conditions. The study of the base pressure gradient reveals non-trivial and sharp transitions identified as significant changes of near wake orientation in both parametric spaces. All unsteady transitions correspond to fluctuation crises of the vertical gradient component only. These transitions are summarized in phase diagram representations. Both phase diagrams in (β, C) and (β, α) parametric spaces can be unified at large yaw in the (β, Cr) space, where the rear clearance Cr separating the lower edge of the base from the ground is a simple function of the pitch α and the clearance C. The impacts of the wake transitions are clearly identified in the base drag, drag, lift and side force coefficients. The contribution of the steady near wake z-instability (Grandemange et al., Phys. Fluids, vol. 25, 2013a, pp. 95-103) is assessed by repeating the sensitivity analysis with a rear cavity. As reported previously, the rear cavity suppresses the steady instability by symmetrizing the wake. A domain for the existence of the instability is finally proposed in the attitudes map (β, α) defined from regions where the mean lateral force coefficients are significantly decreased by the presence of the rear cavity. In addition, it is found that the steady instability forces the wake to be less unsteady for all attitudes that do not correspond to unsteady transitions. [ABSTRACT FROM AUTHOR]

We study the effect of negatively charged dust on the magnetic-field-aligned polarisation electrostatic field ($\boldsymbol {E}_{\parallel }$) using Cassini's RPWS/LP in situ measurements during the 'ring-grazing' orbits. We derive a general expression for $\boldsymbol {E}_{\parallel }$ and estimate for the first time in situ $\lVert \boldsymbol {E}_{\parallel } \rVert$ (approximately $10^{-5} \, \text {V}\, \text {m}^{-1}$) near the Janus and Epimetheus rings. We further demonstrate that the presence of the negatively charged dust close to the ring plane ($\vert \text {Z} \vert \lesssim 0.11 \, \text {R}_{s}$) amplifies $\lVert \boldsymbol {E}_{\parallel } \rVert$ by at least one order of magnitude and reverses its direction due to the effect of the charged dust gravitational and inertial forces. Such reversal confines the electrons at the magnetic equator within the dusty region, around $0.047 \, \text {R}_{s}$ above the ring plane. Furthermore, we discuss the role of the collision terms, in particular the ion–dust drag force, in amplifying $\boldsymbol {E}_{\parallel }$. These results imply that the charged dust, as small as nanometres in size, can have a significant influence on the plasma transport, in particular ambipolar diffusion along the magnetic field lines, and so their presence must be taken into account when studying such dynamical processes. [ABSTRACT FROM AUTHOR]

When Graph $U w/U c$ is large (wave-dominated cases), Graph $C D\alpha$ varies less with Graph $U w/U c$ but increases strongly with Graph $KC$, as orbital excursion increases and flow separation is more developed. At small Graph $KC$ and Graph $U w/U c$ (current-dominated), Graph $d/D$ is around 0.3 for both the strong and weak current cases, which gives the value Graph $k = 0.6$. Generally, when Graph $U w/U c$ is small (current-dominated cases), Graph $C D\alpha$ is high and there is little dependence on Graph $KC$ but a strong dependence on Graph $U w/U c$. Two contrasting cases are used to illustrate flow features for cases with different Graph $U w/U c$: a representative wave-dominated case with weak current forcing and Graph $U w = 0.3\ \textrm {m}\ \textrm {s}^{-1}$ (Graph $U w/U c = 8.6$, Graph $KC = 12$; case 4); and a representative current-dominated case with strong current forcing and Graph $U w = 0.1\ \textrm {m}\ \textrm {s}^{-1}$ (Graph $U w/U c = 0.7$, Graph $KC = 4$; case 7). Important parameters are the ratio of wave orbital velocity amplitude to current Graph $U w/U c$, the angle between waves and current and Graph $KC$. [Extracted from the article]

We consider the translation of a rigid, axisymmetric, tightly fitting object through a cylindrical elastic tube filled with viscous fluid, using a combination of theory and direct numerical simulations. The intruding object is assumed to be wider than the undeformed tube radius, forcing solid–solid contact in the absence of relative motion. The motion of the object establishes a thin fluid film that lubricates this contact. Our theory couples lubrication theory to a geometrically nonlinear membrane description of the tube's elasticity, and applies to a slender intruding object and a thin tube with negligible bending rigidity. We show using asymptotic and numerical solutions of the theory, that the thickness of the thin fluid film scales with the square root of the relative speed for small speeds, set by a balance of hoop stresses, membrane tension and fluid pressure. While membrane tension is relatively small at the entrance of the film, it dominates near the exit and produces undulations of the film thickness, even in the limit of vanishing speeds and slender objects. We find that the drag force on the intruding object depends on the slope of its surface at the entrance to the thin fluid film, and scales as the square root of the relative speed. The predictions of the lubricated membrane theory for the shape of the film and the force on the intruder are in quantitative agreement with three-dimensional direct numerical simulations of the coupled fluid–elastic problem. [ABSTRACT FROM AUTHOR]

The modelling of natural convection in porous media is receiving increased interest due to its significance in environmental and engineering problems. State-of-the-art simulations are based on the classic macroscopic Darcy–Oberbeck–Boussinesq (DOB) equations, which are widely accepted to capture the underlying physics of convection in porous media provided the Darcy number, $Da$ , is small. In this paper we analyse and extend the recent pore-resolved direct numerical simulations (DNS) of Gasow et al. (J. Fluid Mech, vol. 891, 2020, p. A25) and show that the macroscopic diffusion, which is neglected in DOB, is of the same order (with respect to $Da$) as the buoyancy force and the Darcy drag. Consequently, the macroscopic diffusion must be modelled even if the value of $Da$ is small. We propose a 'two-length-scale diffusion' model, in which the effect of the pore scale on the momentum transport is approximated with a macroscopic diffusion term. This term is determined by both the macroscopic length scale and the pore scale. It includes a transport coefficient that solely depends on the pore-scale geometry. Simulations of our model render a more accurate Sherwood number, root mean square (r.m.s.) of the mass concentration and r.m.s. of the velocity than simulations that employ the DOB equations. In particular, we find that the Sherwood number $Sh$ increases with decreasing porosity and with increasing Schmidt number $(Sc)$. In addition, for high values of $Ra$ and high porosities, $Sh$ scales nonlinearly. These trends agree with the DNS, but are not captured in the DOB simulations. [ABSTRACT FROM AUTHOR]

Determining physically admissible boundary conditions for higher moments in an extended continuum model is recognised as a major obstacle. Boundary conditions for the regularised 26-moment (R26) equations obtained using Maxwell's accommodation model do exist in the literature; however, we show in this article that these boundary conditions violate the second law of thermodynamics and the Onsager reciprocity relations for certain boundary value problems, and, hence, are not physically admissible. We further prove that the linearised R26 (LR26) equations possess a proper $H$ -theorem (second-law inequality) by determining a quadratic form without cross-product terms for the entropy density. The establishment of the $H$ -theorem for the LR26 equations in turn leads to a complete set of boundary conditions that are physically admissible for all processes and comply with the Onsager reciprocity relations. As an application, the problem of a slow rarefied gas flow past a spherical droplet with and without evaporation is considered and solved analytically. The results are compared with the numerical solution of the linearised Boltzmann equation, experimental results from the literature and/or other macroscopic theories to show that the LR26 theory with the physically admissible boundary conditions provides an excellent prediction up to Knudsen number $\lesssim 1$ and, consequently, provides transpicuous insights into intriguing effects, such as thermal polarisation. In particular, the analytic results for the drag force obtained in the present work are in an excellent agreement with experimental results even for very large values of the Knudsen number. [ABSTRACT FROM AUTHOR]

In this paper we study finite particle Reynolds number effects up to $Re_p=50$ on the dynamics of small spherical bubbles and solid particles in an isotropic turbulent flow. We consider direct numerical simulations of light pointwise particles with various expressions of the drag force to account for finite $Re_p$ and the type of particle. Namely, we consider the Stokes drag law, the Schiller and Neumann relation and the Mei law. We show that an effective Stokes number, based on the mean value of the drag coefficient to account for the inertial effects involved in the drag law, gives a quasi-self-similar evolution of the variances of the bubble acceleration and of the forces exerted on the particle. This allows us to provide a satisfactory prediction of these quantities using Tchen's theory at finite particle Reynolds number. Based on these relations, we can specify the conditions under which the total inertial force (sum of the added mass and the Tchen contributions) is negligible compared with the drag force. Thus, for particles of very small dimensions, the fluid inertia force is negligible, provided the density ratio is of order 1 or larger. However, when the particle inertia becomes consequential, the threshold value of the density ratio increases significantly. Although this corresponds to the limit of the validity of the model, this draws attention to the fact that, for large Stokes numbers, the added mass and fluid inertia forces could play a more important role than is usually attributed to them. [ABSTRACT FROM AUTHOR]

We present an asymptotic theory for analytical characterization of the high-Reynolds-number incompressible flow of a Newtonian fluid past a shear-free circular cylinder. The viscosity-induced modifications to this flow are localized and except in the neighbourhood of the rear stagnation point, behave like a linear perturbation of the inviscid flow. Our theory gives a highly accurate description of these modifications by including the contribution from the most significant viscous term in a correctional perturbation expansion about an inviscid base state. We derive the boundary layer equation for the flow and deduce a similarity transformation that leads to a set of infinite, shear-free-condition-incompatible, self-similar solutions. By suitably combining members from this set, we construct an all-boundary-condition-compatible solution to the boundary layer equation. We derive the governing equation for vorticity transport through the narrow wake region and determine its closed-form solution. The near and far-field forms of our wake solution are desirably consistent with the boundary layer solution and the well-known, self-similar planar wake solution, respectively. We analyse the flow in the rear stagnation region by formulating an elliptic partial integro-differential equation for the distortion streamfunction that specifically accounts for the fully nonlinear and inviscid dynamics of the viscous correctional terms. The drag force and its atypical logarithmic dependence on Reynolds number, deduced from our matched asymptotic analysis, are in remarkable agreement with the high-resolution simulation results. The logarithmic dependence gives rise to a critical Reynolds number below which the viscous correction term, counterintuitively, reduces the net dissipation in the flow field. [ABSTRACT FROM AUTHOR]

Efficiently predicting the flow field and load in aerodynamic shape optimisation remains a highly challenging and relevant task. Deep learning methods have been of particular interest for such problems, due to their success in solving inverse problems in other fields. In the present study, U-net-based deep neural network (DNN) models are trained with high-fidelity datasets to infer flow fields, and then employed as surrogate models to carry out the shape optimisation problem, i.e. to find a minimal drag profile with a fixed cross-sectional area subjected to a two-dimensional steady laminar flow. A level-set method as well as Bézier curve method are used to parameterise the shape, while trained neural networks in conjunction with automatic differentiation are utilised to calculate the gradient flow in the optimisation framework. The optimised shapes and drag force values calculated from the flow fields predicted by the DNN models agree well with reference data obtained via a Navier–Stokes solver and from the literature, which demonstrates that the DNN models are capable not only of predicting flow field but also yielding satisfactory aerodynamic forces. This is particularly promising as the DNNs were not specifically trained to infer aerodynamic forces. In conjunction with a fast runtime, the DNN-based optimisation framework shows promise for general aerodynamic design problems. [ABSTRACT FROM AUTHOR]

This paper presents the results of the time resolved flow field measurements around a realistic rowing oar blade that moves along a realistic path through water. To the authors' knowledge no prior account of this complex flow field has been given. Simultaneously with the flow field measurements, the hydrodynamic forces acting on the blade were measured. These combined measurements allow us to identify the relevant flow physics that governs rowing propulsion, and subsequently use this information to adjust the oar blade configuration to improve rowing propulsion. Analysis of the instationary flow field around the oar blade during the drive phase indicated how the initial formation, and subsequent development, of leading-edge and trailing-edge vortices are related to the generation of instationary lift and drag forces, and how these forces contribute to rowing propulsion. It is shown that the observed individual flow mechanisms are similar to the flow mechanisms observed in bird flight, but that the overall propulsive mechanism for rowing propulsion is fundamentally different. To quantify the rowing propulsion efficiency, we introduced the energetic efficiency $\eta _E$ and the impulse efficiency $\eta _J$ , where the latter can be interpreted as the alignment of the generated impulse with the propulsive direction. It is found that in the conventional oar blade configuration, the generated impulse is not aligned with the propulsive direction, indicating that the propulsion is suboptimal. By adjusting the angle at which the blade is attached to the oar, the generation of leading- and trailing-edge vortices is altered such that the generated impulse better aligns with the propulsive direction, thus increasing the efficiency. [ABSTRACT FROM AUTHOR]

In this paper, we develop a theory to establish that the thermo-osmotic (TOS) effects, induced by the application of an axial temperature gradient, lead to a massive enhancement in liquid transport in nanochannels grafted with charged polyelectrolyte (PE) brushes. We quantify the TOS transport by quantifying the induced electric field and the induced TOS flow field. The different components of the electric field, namely the ionic component, the thermal component and the osmotic component, as well as the contributions of different ions to these components, are quantified. Furthermore, we express the TOS velocity as a combination of chemiosmotic (COS), thermal and electro-osmotic (EOS) components. The COS and the thermal components augment each other and the overall strength and direction of the TOS flow are dictated by the direction and the relative strength of the EOS component. Most importantly, we compare the cases of brush-grafted nanochannels with those of the brush-free nanochannels of identical surface charge densities: the TOS transport is massively augmented in the brush-grafted nanochannels attributed to the combination of the localization of the electric double layer (EDL) (and hence any body force that depends on the EDL charge density) away from the nanochannel wall (i.e. the location of the maximum drag force) and the presence of a possible molecular slip (experienced by the liquid) along the brush surface. [ABSTRACT FROM AUTHOR]

Trees are known to reduce the wind momentum efficiently. Yet, firm quantitative estimates of their contribution to the land surface drag have remained elusive, partly because trees have complex shapes that consist of elastic multi-scale elements. This structural complexity makes trees inherently difficult to scale for wind tunnel studies. Here, we test a new method for quantifying the drag force on a solitary mature tree in its natural environment. The method is based on the application of mass and momentum conservation over a control volume that encloses the tree. For this control volume, the drag force is estimated through the momentum deficit in the wake. For the characterisation of the heterogeneous and high-gradient wind field in the wake, spatially distributed measurements of the wind vector were acquired using three synchronously scanning wind lidar instruments in a vertical plane encompassing the wake. The resulting drag force estimate is compared to a reference measurement from a tree-mounted sensor at the base of the stem. We find that the drag force in both methods shows a dependence on the wind speed raised to an exponent of 1.8 and that the drag force, based on the momentum deficit method, is consistently underestimated by 1%–10%. Potential reasons for this bias are discussed in light of the accuracy of both methods. The relatively close agreement between the two methods indicates that scanning Doppler lidar measurements can be used to determine the drag force on complex objects in their natural environment, such as trees. [ABSTRACT FROM AUTHOR]