We investigate the spatial evolution of vorticity dynamics and production mechanisms of turbulent kinetic energy around a finite NACA 0018 wing with a square wingtip profile at ${\text{Re}}_c={10}^4$ and a ${10}^{\circ }$ angle of attack with the aid of direct numerical simulation. The analysis focuses on the highly inhomogeneous region around the tip and the near wake; this region is highly convoluted, strongly three-dimensional, and far from being self-similar. The flow separates close to the leading edge creating a large, open recirculation zone around the central part of the wing. In the proximity of the tip, the flow remains attached but another smaller recirculation zone forms closer to the trailing edge; this zone strongly affects the development of the main wing tip vortex. The early formation mechanisms of three vortices close to the leading edge are elucidated and discussed. More specifically, we analyze the role of vortex stretching/compression and tilting, and how it affects the strength of each vortex as it approaches the trailing edge. We find that the three-dimensional flow separation at the sharp tip close to the trailing edge plays an important role in the subsequent vortical flow development on the suction side. The production of turbulent kinetic energy and Reynolds stresses is also investigated and discussed in conjunction with the identified vortex patterns. The detailed analysis of the mechanisms that sustain vorticity and turbulent kinetic energy improves our understanding of these highly three-dimensional, nonequilibrium flows, and it can lead to better actuation methods to manipulate these flows.

Granular flow models are typically examined within steady isochoric systems where velocity divergence equals zero and properties are uniform along streamlines. Within these flows dilatancy and packing variations can be, and are, neglected. However, there exists a broad range of flows that are nonisochoric, where these variations cannot be ignored. In this paper we examine different nonisochoric systems using discrete element simulations. We first demonstrate that nonisochoric granular flows do not exhibit a simple relationship between stress and packing and that the alignment criterion relating stress to strain rate apply only to well-agitated regions of the flow. Subsequently, the discrete simulation results are used to test the velocity divergence and stress in several compressible granular flow models. We demonstrate that the models are able to capture key features of the nonisochoric flows, though none fully describe the observed behavior. We show that in some cases the predictions of the models can be improved by redefining the equilibrium condition. Finally, we discuss the challenges faced with extending these compressible models into dense regions, where granular flows require nonlocal descriptions of the rheology.

We show that a toroidal bundle of quantized vortex rings in superfluid helium generates a large-scale wake in the normal fluid which reduces the overall friction experienced by the bundle, thus greatly enhancing its lifetime, as observed in experiments. This collective effect is similar to the drag reduction observed in systems of active, hydrodynamically cooperative agents such as bacteria in aqueous suspensions, fungal spores in the atmosphere, and cyclists in pelotons.

An experimental investigation of separated flows over unswept, cantilevered wings with a NACA 0015 cross section is presented. For all experiments, the chord-based Reynolds number was $3.3\times {10}^5$. The results include qualitative surface topology from oil flow visualizations at angles of attack between ${15}^{\circ }$ and ${22}^{\circ }$ and semiaspect ratios 1, 2, and 4, as well as quantitative three-dimensional flowfield measurements using stereo particle image velocimetry (SPIV) at an angle of attack of ${22}^{\circ }$ and semiaspect ratio 4. For all aspect ratios two counterrotating surface foci appeared on the wings when reversed flow was present. At the lower aspect ratios, the surface foci did not occur until higher angles of attack due to a reduction in separation extent by downwash from the tip vortex which dominates a higher percentage of the span. The volumetric mean flowfield measured with SPIV over the semiaspect ratio of 4 model and in its wake revealed the counterrotating surface foci were connected by an arch vortex. Several vortex identification methods were employed to visualize the location of the arch vortex over the suction surface. The helicity and Reynolds stress fields were shown to be highly influenced by the shape of the arch vortex. The Reynolds shear stresses containing spanwise velocity fluctuations were influenced by the tip vortex and the root horseshoe vortex, and as such had greater magnitude than the spanwise Reynolds stresses measured in a previous study of an induced stall cell on a wall-to-wall wing. In addition, time-resolved flowfield measurements showed that power spectra at the stall cell center had a dominant shedding frequency of $\text{St}=0.17$. At the center of the stall cell focus, the power spectra peaked at $\text{St}=0.19$ and $\text{St}=0.21$. Analysis of the instantaneous flowfield at the midspan characterized the shedding of vortices into the near wake as an intermittent phenomenon where the magnitude of velocity fluctuations associated with the shedding would increase and decrease over time at periods on the order of ten shedding cycles.

The effect of high-amplitude harmonic surging on airfoil laminar separation bubbles, at small angles of attack, was investigated experimentally in a dedicated surging-flow wind tunnel. A generalized pressure coefficient was developed that accounts for local static pressure variations due to surging. This critical generalization facilitated direct comparisons between surging and quasisteady pressure coefficients, and thus unsteady effects could be distinguished from Reynolds number effects. A momentum-integral boundary layer analysis was implemented to determine movement of the bubble separation point, and movement of the transition point was extracted from experimental surface pressure coefficients. The most significant finding was that bubble bursting occurs, counterintuitively, during early imposition of the favorable temporal pressure gradient, because the favorable pressure gradient rapidly drives the bubble aft, rendering it unable to reattach. This surge-induced dynamic stall mechanism resulted in large lift and form-drag coefficient oscillations. Furthermore, failure to implement the generalized pressure coefficient definition resulted in temporal form-drag coefficient errors of up to 400 counts.

To understand the nonequilibrium relaxation dynamics of a liquid droplet on a switchable substrate, the interplay of different length and timescales needs to be understood. We present a method to map the microscopic information from a molecular-dynamics simulation to a mesoscopic scale, reflected by a thin-film model. After a discussion of the mapping procedure, we first analyze the relaxation of a liquid droplet upon switching the wettability of the substrate. Furthermore, we show that a nearly identical mapping procedure can be used to describe two coalescing droplets. With our procedure we take a first step to extend the mapping from the equilibrium case to nonequilibrium wetting dynamics, thus allowing for quantitative multiscale analysis.

We investigate viscous fingering (VF) during the miscible displacement in a cylindrical packed column using linear stability analysis and numerical solutions. Linear stability theory is carried out in a self-similar domain, and the linearized equations are solved with and without the quasi-steady-state approximation. We obtain the onset of instability and the associated critical parameters as functions of the log-viscosity ratio and Péclet number for the onset of instability using linear stability analysis. Further, we perform nonlinear simulations based on the finite-element method, both in two- and three-dimensional domains. It is shown that the critical Péclet numbers obtained from the linear and nonlinear analyses are in good agreement. One of the main objectives of this study is to explore the effects of lateral boundary conditions on VF. Through two-dimensional (2D) and three-dimensional (3D) simulations, we have clearly shown that the onset and the growth of VF are strongly dependent on the lateral boundary conditions. Finally, through our present 3D numerical simulations, we successfully produce the experimental results available in the literature by suitably choosing the parameters that replicate the experimental conditions under consideration.

The collision efficiency of cloud droplets settling under gravity in quiescent air is investigated by means of numerical simulations. In the developed model, the droplets are represented as either rigid spheres or nondeformable liquid particles of finite viscosity. For the latter, both the internal circulation of the fluid and the mobility of interfaces are accounted for. The aerodynamic interaction, resulting from relative motion of the particles in a viscous medium, is evaluated by making use of a Stokes flow solution. The effect of noncontinuum lubrication for the flow in the gap between surfaces of the droplets is also analyzed. This provides a more physical description of aerodynamic interactions valid for a wide range of the Knudsen number and gap sizes. In contrast to an earlier study by Rother et al. [Int. J. Multiphase Flow 146, 103876 (2022)], noncontinuum lubrication and internal circulation effects have been analyzed separately. Additionally, rotational motion is considered for rigid particles. An objective comparison of the obtained results with the reference data has been performed as well. Compared to the standard continuum description of aerodynamic interaction for nonrotating rigid spherical particles, noncontinuum lubrication and internal circulation effects both lead to a larger collision efficiency, whereas rotation reduces collision efficiency. In general, noncontinuum lubrication has a larger impact on the collision efficiency compared to the internal circulation of drops, which loses its influence as their inertia (size) increases. In numerical simulations, therefore, treating medium-sized cloud droplets as rigid particles is an accurate assumption, but considering noncontinuum effects in their aerodynamic interaction is expected to alter the results. In the limit of a large viscosity ratio, the values of collision efficiency for the liquid drops and freely rotating rigid particles are in a quantitative agreement. Numerical aspects are also discussed, with a focus on assessing computational complexity and algorithm parallelization. The simplified problem studied here is an important step towards improving the representation of aerodynamic interaction in systems with a large number of droplets interacting in a turbulent flow.

The Earth's atmosphere is an aerosol; it contains suspended particles. When air flows over an obstacle such as an aircraft wing or tree branch, these particles may not follow the same paths as the air flowing around the obstacle. Instead, the particles in the air may deviate from the path of the air and so collide with the surface of the obstacle. It is known that particle inertia can drive this deposition and that there is a critical value of this inertia, below which no point particles deposit. Particle inertia is measured by the Stokes number St. We show that near the critical value of the Stokes number ${\mathrm{St}}_c$, the amount of deposition has the unusual scaling law of $\exp [-1/{(\mathrm{St}-{\mathrm{St}}_c)}^{1/2}]$. The scaling is controlled by the stagnation point of the flow. This scaling is determined by the time it takes the particle to reach the surface of the cylinder, varying as $1/{(\mathrm{St}-{\mathrm{St}}_c)}^{1/2}$, together with the distance away from the stagnation point (perpendicular to the flow direction), increasing exponentially with time. The scaling law applies to inviscid flow, a model for flow at high Reynolds numbers. The unusual scaling means that the number of particles deposited increases only very slowly above the critical Stokes number. This has consequences for applications ranging from rime formation and fog harvesting to pollination.

Developing deterministic neighborhood-informed point-particle closure models using machine learning has garnered interest recently from the dispersed multiphase flow community. The robustness of neural models for this complex multibody problem is hindered by the availability of particle-resolved data. The present work addresses this unavoidable limitation of data paucity by implementing two strategies: (1) by using a rotation and reflection equivariant neural network and (2) by pursuing a physics-based hierarchical machine learning approach. The resulting machine-learned models are observed to achieve a maximum accuracy of 85% and 96% in the prediction of neighbor-induced force and torque fluctuations, respectively, for a wide range of Reynolds number and volume fraction conditions considered. Furthermore, we pursue force and torque network architectures that provide universal prediction spanning a wide range of Reynolds number ($0.25\le \text{Re}\le 250$) and particle volume fraction ($0\le \varphi \le 0.4$). The hierarchical nature of the approach enables improved prediction of quantities such as streamwise torque, by going beyond binary interactions to include trinary interactions.

In this paper, we carry out large eddy simulation of incident flow around polygonal cylinders of side number $N=5-8$ at Reynolds number $\mathrm{Re}={10}^4$. In total, six incidence angles ($\alpha$) are studied on each polygon between the face and the corner orientations, thus covering the entire $\alpha$ spectrum. It is found that the separated shear layers behind the cylinders are highly dynamic, manifesting a flapping motion with frequency matching the Strouhal frequency and strength varying significantly at different incidence angles. The energy of the flapping motion is found to be a significant factor influencing the dynamic flow separation behavior, the distribution of the separation points, and features of the time mean shear layer, such as characteristic length and width. Equations for the separation points are analytically derived and are found to be consistent with available experimental results. The time mean penetration distance of the separated shear layers on the top and bottom of the cylinders is found to be a robust scaling factor for the aerodynamic forces and the near-wake length scales. Based on this, a wake deflection angle is proposed, which is demonstrated to be a universal scaling factor for lift, drag, and Strouhal number, working for all available polygonal and circular cylinder data. Finally, the critical separation angle is empirically derived for the condition at which the Strouhal number is a maximum and drag is minimized.

Free surface waves with two or more spectral peaks propagating at an oblique angle to each other are commonly termed “crossing sea states”. Such crossing patterns have been suggested as possible causes for rogue waves and maritime accidents. Modulation instabilities of plane waves using coupled Schrödinger or Zakharov equations have been adopted as theoretical models in the literature. Here, extensions to layered and stratified fluids are conducted. For a two-layer fluid with long-wave–short-wave resonance, crossing patterns with two short waves will enhance instability compared with the single-wave case. Analytical treatment beyond the linear instability regime is elucidated by a cascading mechanism. Growth of the higher-order harmonics eventually leads to finite-amplitude pulsating modes or breathers. Breathers subsequently exhibit a Fermi-Pasta-Ulam-Tsingou type recurrence. The time for the first formation of breathers predicted by the cascading mechanism attains excellent agreements with the full numerical simulations. A similar study is performed for a continuously stratified fluid with constant buoyancy frequency. Triad resonance with two components as a pair of oblique waves also produces enhanced instability and a preferred inclination of maximum growth rate. These crossing patterns will likely play critical roles in many wave-propagation configurations in fluid mechanics.

Intermittent swimming, also termed “burst-and-coast swimming,” has been reported as a strategy for fish to enhance their energetical efficiency. Intermittent swimming involves additional control parameters, which complexifies its understanding by means of quantitative and parametrical analysis, in comparison with continuous swimming. In this study, we used a hybrid computational fluid dynamic (CFD) model to assess the swimming performance in intermittent swimming parametrically and quantitatively. A Navier-Stokes solver is applied to construct a database in the multidimensional space of the control parameters to connect the undulation kinematics to swimming performance. Based on the database, an indirect numerical approach named “gait assembly” is used to generate arbitrary burst-and-coast gaits to explore the parameter space. Our simulations directly measured the hydrodynamics and energetics under the unsteady added-mass effect during burst-and-coast swimming. The results suggest that the instantaneous power of burst is basically determined by undulatory kinematics. The results show that the energetical performance of burst-and-coast swimming can be better than that of continuous swimming, but also that an unoptimized burst-and-coast gait may become very energetically expensive. These results shed light on the mechanisms at play in intermittent swimming, enabling us to better understand fish behavior and to propose design guidelines for fishlike robots.

Transport equations for heavy inertial particles in turbulent boundary layers may be derived from an underlying phase-space probability density function (PDF) equation. These equations, however, are unclosed, and the standard closure approach is to use a quasinormal approximation (QNA) in which the fourth moments are approximated as behaving as if the velocities were Normally distributed. Except for particles with weak inertia, the QNA leads to large quantitative errors, and is not consistent with the known asymptotic predictions of [D. P. Sikovsky, Flow, Turbul. Combust. 92, 41 (2014)] for the moments of the PDF in the viscous sublayer. We derive a closure approximation based on an asymptotic solution to the transport equations in regions where the effect of particle inertia is significant. The closure is consistent with the asymptotic predictions of Sikovsky, but applies even outside the viscous sublayer. Comparisons with direct numerical simulations (DNSs) show that the closure gives similar results to the QNA (with the QNA results in slightly better agreement with the DNS) when the viscous Stokes number is $\text{St}<10$, but for $\text{St}>10$ our model is in far better agreement with the DNS than the QNA. While the predictions from our model leave room for improvement, the results suggest that our closure strategy is a very effective alternative to the traditional QNA approach, and the closure could be refined in future work.

Direct numerical simulation of purely elastic turbulence (ET) in the Taylor-Couette flow of dilute polymer solutions is used to identify the dominant flow structures, namely, unsteady diwhirls that almost span the entire gap and axially and azimuthally elastic waves that occupy the inner rotating cylinder region to midgap. In accord with experiment, the azimuthal wave speed increases monotonically with enhanced $Wi$ and it travels nearly 50 times faster than the axial waves. The interaction of elastic waves with unsteady diwhirls leads to stochastic or chaotic cycles of polymer stretch and relaxation and commensurate fluctuations in elastic stresses over a broad range of spatiotemporal frequency that produce turbulent kinetic energy and sustain turbulent dynamics. To this end, the self-sustaining cycle of ET is elucidated. Overall, this study paves the way for mechanistic understanding of this inertia less turbulence in curvilinear flows.

We investigate how the presence of a vertically sheared current affects wave statistics, including the probability of rogue waves, and apply it to a real-world case using measured spectral and shear current data from the mouth of the Columbia River. A theory for weakly nonlinear waves valid to second order in wave steepness is derived and used to analyze statistical properties of surface waves; the theory extends the classic theory by Longuet-Higgins [J. Fluid Mech. 12, 321 (1962)] to allow for an arbitrary depth-dependent background flow, $U\left(z\right)$, with $U$ the horizontal velocity along the main direction of wave propagation and $z$ the vertical axis. Numerical statistics are collected from a large number of realizations of random, irregular sea-states following a JONSWAP spectrum, on linear and exponential model currents of varying strengths. A number of statistical quantities are presented and compared to a range of theoretical expressions from the literature; in particular the distribution of wave surface elevation, surface maxima, and crest height; the exceedance probability including the probability of rogue waves; the maximum crest height among $N_s$ waves, and the skewness of the surface elevation distribution. We find that compared to no-shear conditions, opposing vertical shear $[U^{\prime }\left(z\right)>0]$ leads to increased wave height and increased skewness of the nonlinear-wave elevation distribution, while a following shear $[U^{\prime }\left(z\right)<0]$ has opposite effects. With the wave spectrum and velocity profile measured in the Columbia River estuary by Zippel and Thomson [J. Geophys. Res.: Oceans 122, 3311 (2017)] our second-order theory predicts that the probability of rogue waves is significantly reduced and enhanced during ebb and flood, respectively, adding support to the notion that shear currents need to be accounted for in wave modeling and prediction.

It is well known that wettability exerts fundamental control over multiphase flow in porous media, which has been extensively studied in uniform-wet porous media. In contrast, multiphase flow in porous media with heterogeneous wettability (i.e., mixed-wet) is less well understood, despite its common occurrence. Here, we study the displacement of silicone oil by water in a mostly oil-wet porous media patterned with discrete water-wet clusters that have precisely controlled wettability. Surprisingly, the macroscopic displacement pattern varies dramatically depending on the details of wettability alteration—the invading water preferentially fills strongly water-wet clusters but encircles weakly water-wet clusters instead, resulting in significant trapping of the defending oil. We explain this counterintuitive observation with pore-scale simulations, which reveal that the fluid-fluid interfaces at mixed-wet pores resemble an $\mathsf{S}$-shaped saddle with mean curvatures close to zero. We show that incorporation of the capillary entry pressures at mixed-wet pores into a dynamic pore-network model reproduces the experiments. Our work demonstrates the complex nature of wettability control in mixed-wet porous media, and it presents experimental and numerical platforms upon which further insights can be drawn.

We analyze the diffusion-controlled evaporation of multiple droplets placed near each other on a planar substrate. Specifically, we calculate the change in the volume of sessile droplets with various initial contact angles that are arranged in different configurations. The calculations are supplemented by experimental measurements using a technique that interprets the variable magnification of a pattern placed beneath the droplet array, which is applied to the case of initially hemispherical droplets deposited in four distinct arrangements. We find excellent agreement between the predictions based on the theory of Masoud et al. [Evaporation of multiple droplets, J. Fluid Mech. 927, R4 (2021)] and the data gathered experimentally. Perhaps unexpectedly, we also find that when comparing different arrays, the droplets with the same order of disappearance within their respective array, i.e., fastest evaporating, second-fastest evaporating, etc., follow similar drying dynamics. Our study provides not only experimental validation of the theoretical framework introduced by Masoud et al., but also offers additional insights into the evolution of the volume of individual droplets when evaporating within closely-spaced arrays.

Traditional mathematical models of Hele-Shaw flow consider the injection (or withdrawal) of an air bubble into (or from) an infinite body of viscous fluid. The most commonly studied feature of such a model is how the Saffman-Taylor instability drives viscous fingering patterns at the interface between the fluid and air. Here we consider a more realistic model, which assumes the viscous fluid is finite, covering a doubly connected two-dimensional region bounded by two such interfaces. For the case in which the flow is driven by a prescribed pressure difference across the two interfaces, we explore this model numerically, highlighting the development of viscous fingering patterns on the interface with the higher pressure. Our numerical scheme is based on the level set method, where each interface is represented as a separate level set function. We show that the scheme is able to reproduce the characteristic finger patterns observed experimentally up to the point at which one of the interfaces bursts through the other. The simulations are shown to compare well with experimental results. Further, we consider a model for the problem in which an annular body of fluid is evolving in a rotating Hele-Shaw cell. In this case, our simulations explore how either one or both interfaces can be unstable and develop fingering patterns, depending on the rotation rate and the volume of fluid present.

Turbulent boundary layer experiments above a smooth wall and two-dimensional (2D) rod-roughened walls are conducted to investigate the effects of friction Reynolds numbers ${\text{Re}}_{\tau }$ and streamwise spacing of the roughness elements on the flow properties. The first study uses the roughness pitch $p$ to height $k$ ratio $p/k=8$ and a range of friction Reynolds numbers, $1840\le {\mathrm{Re}}_{\tau }\le 7500$. The result shows that the drag coefficient $C_f$ converges to the fully rough condition (akin to the classic k-type roughness at a fully developed state) with large roughness Reynolds numbers ($k^{+}>75$) when the friction Reynolds number reaches ${\mathrm{Re}}_{\tau }\ge 3900$ and the relative roughness height is $k/{\delta }_{99}\ge 0.02$, where ${\delta }_{99}$ is the boundary layer thickness. As ${\mathrm{Re}}_{\tau }$ increases, the premultiplied energy spectra show that the normalized energy of the near-wall cycle decreases, while the large-scale structures become more dominant. The second study uses a wide range of $p/k$ ($2\le p/k\le 128$) at ${\mathrm{Re}}_{\tau }\approx 3500$. The $C_f$ and the roughness function $\mathrm{\Delta }{U}^{+}$ results indicate that the increase of streamwise spacing of the roughness elements $p/k$ induces higher $C_f$ and $\mathrm{\Delta }{U}^{+}$, and it reaches the maximum value at $p/k=8$. For $p/k>8$, the $C_f$ and $\mathrm{\Delta }{U}^{+}$ values decrease as $p/k$ increases, indicating a less severe drag increase. The premultiplied energy spectra also show that the highly energetic near-wall cycle of streaks and quasistreamwise vortices decreases as $p/k$ increases (for all cases from $p/k=2$–128), and they seem to be transported farther from the wall. The trend is slightly different for the largest-scale structures located around the log region. The result suggests that 2D square-bar roughness can reduce the energy distribution for the largest-scale structure for $p/k=2–128$.