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We examine the mechanisms responsible for the onset of the three-dimensional mode B instability in the wake behind a circular cylinder. We show that it is possible to explicitly account for the stabilising effect of spanwise viscous diffusion and then demonstrate that the remaining mechanisms involved in this short-wavelength instability are preserved in the limit of zero wavelength. Using the resulting simplified equations, we show that perturbations in different fluid particles interact only through the in-plane viscous diffusion which turns out to have a destabilising effect. We also show that in the presence of viscous diffusion, the closed trajectories which had been conjectured to play a crucial role in the onset of the mode B instability are not actually a prerequisite for the growth of mode B type perturbations. We combine these observations to identify the three essential ingredients for the development of the mode B instability: (i) the amplification of perturbations in the braid regions due to the stretching mechanism; and the spreading of perturbations through (ii) viscous diffusion, and (iii) cross-flow advection which transports fluid between the two braid regions on either side of the cylinder. Finally, we develop a simple criterion that allows the prediction of the regions where three-dimensional short-wavelength perturbations are amplified by the stretching mechanism. The approach used in our study is general and has the potential to give insights into the onset of three-dimensionality via short-wavelength instabilities in other flows. [ABSTRACT FROM AUTHOR]

With the severity and frequency of significant weather events increasing, methods for alleviating unsteady wind loading for high-rise buildings are gaining interest. This study numerically investigates the three-dimensional flow structures around a canonical high-rise building immersed in an atmospheric boundary layer at different oncoming wind angles, using wall-resolved large eddy simulations. A synthetic jet located on the top surface is used as open-loop active actuation with the aim of suppressing the building's side-force fluctuations when exposed to oncoming wind variations. Three different frequencies of jet forcing are considered, all half an order of magnitude larger than the vortex shedding frequency. The behaviour of the synthetic jet and its effect on the building's unsteady side force, time-averaged flow fields and unsteady flow structures are investigated numerically. The synthetic jet actuation is found to reduce the side-force fluctuation of the building, enhance the downwash flow and successfully attenuate the antisymmetric vortex shedding. This was achieved to different extents across the range of oncoming wind angles considered and may motivate future attempts to explore experimental active control strategies for attenuation of unsteady wind loading. [ABSTRACT FROM AUTHOR]

We study the onset of the three-dimensional mode A instability in the near wake behind a circular cylinder. We show that long-wavelength perturbations organise in a time-shifting pattern such that the in-plane velocity in each streamwise slice corresponds to the base flow solution at shifted times. This observation introduces an additional unifying characteristic for certain mode A type instabilities. We then analyse the mechanisms which control the growth or decay of these perturbations and highlight the crucial role played by the tilting mechanism which operates via non-local interactions in a manner similar to Biot–Savart induction. We characterise its domain of influence using a Green's function-based approach which allows us to rationalise the non-trivial dependence of the growth rate on the spanwise wavenumber. We connect this behaviour to the subtle balance between the local growth of the perturbations as they are swept along by the flow and the feedback on the perturbations that are generated during the next period of the time-periodic base flow. Finally, we discuss generalisations of our findings to other types of flows. [ABSTRACT FROM AUTHOR]

The unsteady wind loading on high-rise buildings has the potential to influence strongly their structural performance in terms of serviceability, habitability and occupant comfort. This paper investigates numerically the flow structures around a canonical high-rise building immersed in an atmospheric boundary layer, using wall-resolved large eddy simulations. The switching between two vortex shedding modes is explored, and the influence of the atmospheric boundary layer on suppressing symmetric vortex shedding is identified. It is shown that the antisymmetric vortex shedding mode is prevalent in the near wake behind the building, with strong coherence between the periodic fluctuations of the building side force and the antisymmetric vortex shedding mode demonstrated. Two feedback control strategies, exploiting this idea, are designed to alleviate the aerodynamic side-force fluctuations, using pressure sensing on just a single building wall. The sensor response to synthetic jet actuation along the two 'leading edges' of the building is characterised using system identification. Both the designed linear controller and the least mean square adaptive controller attenuate successfully the side-force fluctuations when implemented in simulations. The linear controller exhibits a better performance, and its effect on the flow field is to delay the formation of dominant vortices and increase the extent of the recirculation region. Feedback control that requires a smaller sensing area is then explored, with a comparable control effect achieved in the attenuation of the unsteady loading. This study could motivate future attempts to understand and control the unsteady loading of a high-rise building exposed to oncoming wind variations. [ABSTRACT FROM AUTHOR]

Otherwise, the almost complimentary LHS optimum for actuators 2-5 and the one-dimensional optimum of § 5.3 should yield 10 % reduction with Graph $b 1 \approx 1$, Graph $b 2\approx 1$, Graph $b 3\approx 0.13$, Graph $b 4 \approx 1$ and Graph $b 5\approx 1$. The velocity components in the Graph $x$, Graph $y$ and Graph $z$ directions are denoted by Graph $u$, Graph $v$ and Graph $w$, respectively. The actuation velocities Graph $U 1, \ldots, U 5$ are independent parameters; Graph $U 1$ refers to the upper edge of the rear window, Graph $U 3$ to the middle edge and Graph $U 5$ to the lower edge of the vertical base; Graph $U 2$ and Graph $U 4$ correspond to the velocities at the right and left sides of the upper and lower windows, respectively. The optimal actuation reads Graph $b 1=0.7264$, Graph $b 2=0.5508$, Graph $b 3=0.1533$, Graph $b 4=0.6746$, Graph $b 5=0.7716$. In this case, the actuation energy of cases Graph $1D$, Graph $5D$ and Graph $10D$ would correspond to Graph $3.2\,\%$, Graph $3.0\,\%$ and Graph $7.9\,\%$ of the parasitic drag power, respectively. [Extracted from the article]

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 work, Joukowski's rotor wake model is considered for a two-blade rotor of radius $R_b$ rotating at the angular velocity $\varOmega _R$ in a normal incident velocity $V_{\infty }$. This model is based on a description of the wake by a limited number of vortices of core size $a$ : a tip vortex of constant circulation $\varGamma$ for each blade and a root vortex of circulation $-2\varGamma$ on the rotation axis. Using a free-vortex method, we obtain solutions matching uniform interlaced helices in the far field that are steady in the frame rotating with the rotor for a large range of tip-speed ratios $\lambda = R_b \Omega _R/V_{\infty }$ and vortex strengths $\eta = \varGamma /(R_b^{2} \Omega _R)$. Solutions are provided for a two-bladed rotor for both helicopters and wind turbines. Particular attention is brought to the study of the solutions describing steep-descent helicopter flight regimes and large tip-ratio wind turbine regimes, for which the vortex structure is strongly deformed in the near wake and crosses the rotor plane. Both the geometry of the structure and its induced velocity field are analysed in detail. The thrust and the power coefficient of the solutions are also provided and compared to the momentum theory. The stability of the solutions is studied by monitoring the linear spatio-temporal development of a localized perturbation placed at different locations. Good agreements with the theoretical predictions for uniform helices and for point vortex arrays are demonstrated for the stability properties in the far wake. However, a more complex evolution is observed for the more deformed solutions when the perturbation is placed close to the rotor. [ABSTRACT FROM AUTHOR]

We propose an image-based flow decomposition developed from the two-dimensional (2-D) tensor empirical wavelet transform (EWT) (Gilles, IEEE Trans. Signal Process., vol. 61, 2013, pp. 3999–4010). The idea is to decompose the instantaneous flow data, or their visualisation, adaptively according to the averaged Fourier supports for the identification of spatially localised structures. The resulting EWT modes stand for the decomposed flows, and each accounts for part of the spectrum, illustrating fluid physics with different scales superimposed in the original flow. With the proposed method, decomposition of an instantaneous three-dimensional (3-D) flow becomes feasible without resorting to its time series. Examples first focus on the interaction between a jet plume and 2-D wake, where only experimental visualisations are available. The proposed method is capable of separating the jet/wake flows and their instabilities. Then the decomposition is applied to an early-stage boundary layer transition, where direct numerical simulations provided a full dataset. The tested inputs are the 3-D flow data and their visualisation using streamwise velocity and $\lambda _{2}$ vortex identification criterion. With both types of inputs, EWT modes robustly extract the streamwise-elongated streaks, multiple secondary instabilities and helical vortex filaments. Results from 2-D stability analysis justify the EWT modes that represent the streak instabilities. In contrast to proper orthogonal decomposition or dynamic modal decomposition that extract spatial modes according to energy or frequency, EWT provides a new strategy for decomposing an instantaneous flow from its spatial scales. [ABSTRACT FROM AUTHOR]

The theory of Kolmogorov, enunciated for very large Reynolds numbers, has progressively been shown to be inoperative for characterizing flows of practical relevance. Yet, in a recent study by Alves Portela et al. (J. Fluid Mech., vol. 896, 2020, A16), the turbulence statistics in the very near wake of a square prism at modest Reynolds numbers, reveal a significant portion of scales complying with a cascade of Kolmogorov type. By resorting to a generalized version of the Kármán–Howarth–Kolmogorov equation, this intriguing observation is shown to be an illusion, hiding a measurable influence of coherent structures and statistical inhomogeneity. This striking conclusion highlights that a complete statistical theory of turbulence cannot dispense with the influence of large scales, possibly coherent, motions. [ABSTRACT FROM AUTHOR]

The separating and reattaching flows and the wake of a finite rectangular plate are studied by means of direct numerical simulation data. The large amount of information provided by the numerical approach is exploited here to address the multi-scale features of the flow and to assess the self-sustaining mechanisms that form the basis of the main unsteadinesses of the flows. We first analyse the statistically dominant flow structures by means of three-dimensional spatial correlation functions. The developed flow is found to be statistically dominated by quasi-streamwise vortices and streamwise velocity streaks as a result of flow motions induced by hairpin-like structures. On the other hand, the reverse flow within the separated region is found to be characterized by spanwise vortices. We then study the spectral properties of the flow. Given the strongly inhomogeneous nature of the flow, the spectral analysis has been conducted along two selected streamtraces of the mean velocity field. This approach allows us to study the spectral evolution of the flow along its paths. Two well-separated characteristic scales are identified in the near-wall reverse flow and in the leading-edge shear layer. The first is recognized to represent trains of small-scale structures triggering the leading-edge shear layer, whereas the second is found to be related to a very large-scale phenomenon that embraces the entire flow field. A picture of the self-sustaining mechanisms of the flow is then derived. It is shown that very-large-scale fluctuations of the pressure field alternate between promoting and suppressing the reverse flow within the separation region. Driven by these large-scale dynamics, packages of small-scale motions trigger the leading-edge shear layers, which in turn created them, alternating in the top and bottom sides of the rectangular plate with a relatively long period of inversion, thus closing the self-sustaining cycle. [ABSTRACT FROM AUTHOR]

In this work, the coupled dynamics of the gap flow and the vortex-induced vibration (VIV) of a side-by-side (SBS) arrangement of two circular cylinders is numerically investigated at Reynolds numbers 100 6 Re 6 500. The influence of VIV is incorporated by allowing one of the cylinders to vibrate freely in the transverse direction, which is termed as a vibrating side-by-side (VSBS) arrangement. A comparative three-dimensional study is performed between the stationary side-by-side (SSBS) and the VSBS arrangements to examine the characteristics of the complex coupling between the VIV and the gap flow. The results are also contrasted against the isolated configurations without any proximity and gap-flow interference. Of particular interest is to establish a relationship between the VIV, the gap flow and the near-wake instability behind bluff bodies. We find that the kinematics of the VIV regulates the streamwise vorticity concentration, which accompanies a recovery of the two-dimensional hydrodynamic response at the peak lock-in. Moreover, the near-wake instability may develop around an indeterminant two-dimensional streamline saddle point along the interfaces of a pair of imbalanced counter-signed vorticity clusters. The interaction between the imbalanced vorticity clusters and the gap-flow momentum are closely interlinked with the prominence of streamwise vortical structures. In both SSBS and VSBS arrangements, the flip-flopping frequency is significantly low for the three-dimensional flow, except at the VIV lock-in for the VSBS arrangement. While an early onset of VIV lock-in is observed for the vibrating configuration, a quasi-stable deflected gap-flow regime with stably deflected gap flow is found at the peak lock-in. The increase of the gap-flow proximity interference promotes the energy transfer and stabilizes the VIV lock-in. Finally, we employ the dynamic mode decomposition procedure to characterize the space--time evolution of the vortex wake system behind the cylinders. [ABSTRACT FROM AUTHOR]

A direct numerical simulation (DNS) of a plane wall jet is performed at a Reynolds number of Rej = 7500. The streamwise length of the domain is long enough to achieve self-similarity for the mean flow and the Reynolds shear stress. This is the highest Reynolds number wall jet DNS for a large domain achieved to date. The high resolution simulation reveals the unsteady flow field in great detail and shows the transition process in the outer shear layer and inner boundary layer. Mean flow parameters of maximum velocity decay, wall shear stress, friction coefficient and jet spreading rate are consistent with several other studies reported in the literature. Mean flow, Reynolds normal and shear stress profiles are presented with various scalings, revealing the self-similar behaviour of the wall jet. The Reynolds normal stresses do not show complete similarity for the given Reynolds number and domain length. Previously published inner layer budgets based on LES are inaccurate and those that have been measured are only available in the outer layer. The current DNS provides fully balanced, explicitly calculated budgets for the turbulence kinetic energy, Reynolds normal stresses and Reynolds shear stress in both the inner and outer layers. The budgets are scaled with inner and outer variables. The inner-scaled budgets in the near wall region show great similarity with turbulent boundary layers. The only remarkable difference is for the turbulent diffusion in the wall-normal Reynolds stress and Reynolds shear stress budgets. The outer layer interacts with the inner layer through turbulent diffusion and the excess energy from the wall-normal direction is transferred to the spanwise direction. [ABSTRACT FROM AUTHOR]

Direct numerical simulations were conducted to uncover physical aspects of a transverse sonic jet injected into a supersonic cross-flow at a Mach number of 2.7. Simulations were carried out for two different jet-to-cross-flow momentum flux ratios (J) of 2.3 and 5.5. It is identified that collision shock waves behind the jet induce a herringbone separation bubble in the near-wall jet wake and a reattachment valley is formed and embayed by the herringbone recirculation zone. The recirculating flow in the jet leeward separation bubble forms a primary trailing counter-rotating vortex pair (TCVP) close to the wall surface. Analysis on streamlines passing the separation region shows that the wing of the herringbone separation bubble serves as a micro-ramp vortex generator and streamlines acquire angular momentum downstream to form a secondary surface TCVP in the reattachment valley. Herringbone separation wings disappear in the far field due to the cross-interaction of lateral supersonic flow and the expansion flow in the reattachment valley, which also leads to the vanishing of the secondary TCVP. A three-dimensional schematic of surface trailing wakes is presented and explains the formation mechanisms of the surface TCVPs. [ABSTRACT FROM AUTHOR]

We study experimentally the effects of spanwise confinement on turbulent miscible fountains issuing from a round source of radius r0. A dense saline solution is ejected vertically upwards into a fresh-water environment between two parallel plates, separated by a gap of width W, which provide restraint in the spanwise direction. The resulting fountain, if sufficiently forced, rapidly attaches to the side plates as it rises and is therefore ‘confined’. We report on experiments for five confinement ratios W=r0, spanning from strongly confined (W=r0 →2) to weakly confined (W=r0 ≈ 24), and for source Froude numbers Fr0 ranging between 0:5 ≤ Fr0 ≤ 96. Four distinct flow regimes are observed across which the relative importance of confinement, as manifested by the formation and growth of quasi-two-dimensional structures, varies. The onset of each regime is established as a function of both W=r0 and Fr0. From our analysis of the time-averaged rise heights, we introduce a ‘confined’ Froude number Frc ≡ Fr0(W=r0)-5/4, which encompasses the effects of confinement and acts as the governing parameter for confined fountains. First-order statistics extracted from the flow visualisation, such as the time-averaged rise height and lateral excursions, lend further insight into the flow and support the proposed classification into regimes. For highly confined fountains, the flow becomes quasi-two-dimensional and, akin to quasi-two-dimensional jets and plumes, flaps (or meanders). The characteristic frequency of this flapping motion, identified through an ‘eddy counting’ approach, is non-dimensionalised to a Strouhal number of St = 0:12–0:16, consistent with frequencies found in quasi-two-dimensional jets and plumes. [ABSTRACT FROM AUTHOR]

Yawing wind turbines has emerged as an appealing method for wake deflection. However, the associated flow properties, including the magnitude of the transverse velocity associated with yawed turbines, are not fully understood. In this paper, we view a yawed turbine as a lifting surface with an elliptic distribution of transverse lift. Prandtl's lifting line theory provides predictions for the transverse velocity and magnitude of the shed counter-rotating vortex pair known to form downstream of the yawed turbine. The streamwise velocity deficit behind the turbine can then be obtained using classical momentum theory. This new model for the near-disk inviscid region of the flow is compared to numerical simulations and found to yield more accurate predictions of the initial transverse velocity and wake skewness angle than existing models. We use these predictions as initial conditions in a wake model of the downstream evolution of the turbulent wake flow and compare predicted wake deflection with measurements from wind tunnel experiments. [ABSTRACT FROM AUTHOR]

Vertical axis wind turbine blades are subject to rapid, cyclical variations in angle of attack and relative airspeed which can induce dynamic stall. This phenomenon poses an obstacle to the greater implementation of vertical axis wind turbines because dynamic stall can reduce turbine efficiency and induce structural vibrations and noise. This study seeks to provide a more comprehensive description of dynamic stall in vertical axis wind turbines, with an emphasis on understanding its parametric dependence and scaling behaviour. This problem is of practical relevance to vertical axis wind turbine design but the inherent coupling of the pitching and velocity scales in the blade kinematics makes this problem of more broad fundamental interest as well. Experiments are performed using particle image velocimetry in the vicinity of the blades of a straight-bladed gyromill-type vertical axis wind turbine at blade Reynolds numbers of between 50 000 and 140 000, tip speed ratios between λ=1 to λ = 5, and dimensionless pitch rates of ≤:10 6 Kc 6 ≤:20. The effect of these factors on the evolution, strength and timing of vortex shedding from the turbine blades is determined. It is found that tip speed ratio alone is insufficient to describe the circulation production and vortex shedding behaviour from vertical axis wind turbine blades, and a scaling incorporating the dimensionless pitch rate is proposed. [ABSTRACT FROM AUTHOR]

During a droplet impact onto a substrate, splashing is known to be caused by the presence of surrounding gas or by surface roughness. Impact occurring in a vacuum onto a smooth rigid wall results in droplet spreading, rather than development of a corona or prompt splash. Here we present an analytical and numerical study of a third potential splashing mechanism, namely elastic deformation of the substrate. An axisymmetric Wagner-style model of droplet impact is formulated and solved using the method of normal modes, together with asymptotic analysis and numerical methods. We highlight the effect that a flexible substrate brings to the contact line velocity and jet behaviour, demonstrating that oscillation of the substrate can cause blow-up of the splash jet which is absent for a rigid substrate and indicate the onset of splashing. [ABSTRACT FROM AUTHOR]

A characteristic feature of axisymmetric jets, and turbulent shear flows in general, is the entrainment of mass across the turbulent/non-turbulent interface (TNTI). The multi-scale nature of the TNTI surface area was recently observed to exhibit power-law scaling with a fractal dimension, Df, between Df = 2.3-2.4, inferred from two-dimensional data, in both high Reynolds number boundary layers and the far field of axisymmetric jets. In this paper, we show that the fractal scaling previously observed in the far field of an axisymmetric jet is established at the end of the potential core. Simultaneous measurements of the velocity and scalar fields were obtained and coarse grain filtering was applied over two decades of scale separation, showing that Df evolves to ≈2.35 at x/d = 4.6, which is similar to Df found in the far field between x/d = 40-60. This is evidence that scale separation becomes sufficiently developed to achieve scale invariance of the TNTI surface area in the near field of the jet well before self-similarity is established. We also observe that the onset of this geometric scale invariance coincides with the onset of radial homogeneity shown by two-point velocity correlations. Finally, we present a simple theoretical basis for these results using an exact fractal construction based on the Koch curve and applying a coarsegrain filtering analysis. [ABSTRACT FROM AUTHOR]

This paper examines flow-separation lines on axisymmetric bodies with tapered tails, where the separating flow takes into account the effect of local body radius r(x), incidence angle ψ and the body-length Reynolds number ReL. The flow is interpreted as a transient problem which relates the longitudinal distance x to time t* = x tan(ψ)/r(x), similar to the approach of Jeans & Holloway (J. Aircraft, vol. 47 (6), 2010, pp. 2177-2183) on scaling separation lines. The windward and leeward sides correspond to the body azimuth angles ⊝ = 0 and 180°, respectively. From China-clay flow visualisation on axisymmetric bodies and from a literature review of slender-body flows, the present study shows three findings. (i) The time scale t* provides a collapse of the separation-line data, ⊝, for incidence angles between 6 and 35°, where the data fall on a power law ⊝ ~ (t*)k. (ii) The data suggest that the separation rate k is independent of the Reynolds number over the range 2.1 x 106 ⩽ReL ⩽23 x 106; for a primary separation k1 ≃ -0.190, and for a secondary separation k2 ≃ 0.045. (iii) The power-law curve fits trace the primary and secondary lines to a characteristic start time t*s ≃ 1.5. [ABSTRACT FROM AUTHOR]

The effect of weak compressibility on the speed of steadily translating staggered vortex streets of hollow vortices in isentropic subsonic flow is studied. A small-Machnumber perturbation expansion about the incompressible solutions for staggered streets of hollow vortices found recently by Crowdy & Green (Phys. Fluids, 2011, vol. 23, 126602) is carried out; the latter solutions provide a desingularization of the classical point vortex streets of von Kármán. The first-order compressible flow correction is calculated. We employ a novel scheme based on a complex variable formulation of the compressible flow equations (the Imai-Lamla method) combined with conformal mapping theory to track the vortex shape in this free boundary problem. The analysis to find the perturbed streamfunction and compressible vortex shapes is greatly facilitated by exploiting a calculus based on use of the Schottky-Klein prime function of a conformally equivalent parametric annulus. It is found that, for a vortex street of specified aspect ratio comprising vortices of specified circulation, the vortex core size is a key determinant of whether compressibility increases or decreases the steady propagation speed (relative to the incompressible street with the same parameters) and that both eventualities are possible. We focus attention on streets with aspect ratios around 0.28, which is close to the neutrally stable case for incompressible flow, and find that a critical vortex core size exists at which compressibility does not affect the speed of the street at first order in the (squared) Mach number. Streets comprising vortices with core size below the critical value speed up due to compressibility; larger vortices slow down. [ABSTRACT FROM AUTHOR]

Geophysical flows occur over a large range of scales, with Reynolds numbers and Richardson numbers varying over several orders of magnitude. For this study, jets of different densities were ejected vertically into a large ambient region, considering conditions relevant to some geophysical phenomena. Using particle image velocimetry, the velocity fields were measured for three different gases exhausting into air - specifically helium, air and argon. Measurements focused on both the jet core and the entrained ambient. Experiments considered relatively low Reynolds numbers from approximately 1500 to 10 000 with Richardson numbers near 0.001 in magnitude. These included a variety of flow responses, notably a nearly laminar jet, turbulent jets and a transitioning jet in between. Several features were studied, including the jet development, the local entrainment ratio, the turbulent Reynolds stresses and the eddy strength. Compared to a fully turbulent jet, the transitioning jet showed up to 50% higher local entrainment and more significant turbulent fluctuations. For this condition, the eddies were non-axisymmetric and larger than the exit radius. For turbulent jets, the eddies were initially smaller and axisymmetric while growing with the shear layer. At lower turbulent Reynolds number, the turbulent stresses were more than 50% higher than at higher turbulent Reynolds number. In either case, the low-density jet developed faster than a comparable non-buoyant jet. Quadrant analysis and proper orthogonal decomposition were also utilized for insight into the entrainment of the jet, as well as to assess the energy distribution with respect to the number of eigenmodes. Reynolds shear stresses were dominant in Q1 and Q3 and exhibited negligible contributions from the remaining two quadrants. Both analysis techniques showed that the development of stresses downstream was dependent on the Reynolds number while the spanwise location of the stresses depended on the Richardson number. [ABSTRACT FROM AUTHOR]

Dielectric-barrier-discharge plasma actuators are arranged to produce counter-rotating streamwise vortices to control flow separation on a cylindrical bump on a flat plate that is approached by a turbulent boundary layer. The control was tested for different free-stream velocities and actuation driving voltages. The recirculation area downstream of the bump was reduced by the actuation for velocities up to 15 m s-1 at the highest voltage achievable of the present set-up. However, the flow shows a bi-modality, the nominal two-dimensional wake flow is shown to consist of large-scale streamwise vortices, which are energised by the actuation until a phenomenon of lock-on of these vortices occurs at sufficiently high driving voltages. The wavelength of the actuation is half that of the large-scale vortices. The lock-on shifts sometimes, i.e. the large streamwise vortices centre switch spanwise location, explaining the bi-modality in the flow. The details of the bi-modality are further investigated by conditional averaging and proper orthogonal decomposition. [ABSTRACT FROM AUTHOR]

The present experiments explored the dynamical character of the gaseous jet injected flush into cross-flow for variable jet-to-cross-flow momentum flux ratios J (5, 12 and 41) and density ratios S (0.35 and 1.0). Contoured nozzle and straight pipe injectors were studied here, with the jet Reynolds number fixed at 1900 as other flow parameters were varied. Simultaneous acetone planar laser-induced fluorescence (PLIF) imaging and stereo particle image velocimetry (PIV) were used to study the relationships between scalar and velocity/vorticity fields, with a special focus on comparing PLIF-based extraction of scalar dissipation rates and local strain rates with PIV-based local strain rates in the upstream and downstream shear layers of the jet. There was remarkable similarity between the scalar and vorticity fields for the jet in cross-flow, spanning conditions for absolutely unstable upstream jet shear layers at low J or S values to conditions for convectively unstable shear layers for larger J, equidensity conditions (Megerian et al., J. Fluid Mech., vol. 593, 2007, pp. 93–129; Getsinger et al., Exp. Fluids, vol. 53, 2012, pp. 783–801). Proper orthogonal decomposition applied to both scalar and velocity fields revealed strengthening instabilities in both the upstream shear layer and in the jet’s wake as J was reduced. The simultaneous measurements allowed PLIF-extracted scalar dissipation rates and strain rates to be determined via a flamelet-like model and compared with PIV-extracted strain rates, each in the diffusion layer-normal direction. There was generally very good qualitative and quantitative agreement for these metrics in both the jet upstream and downstream shear layers for most flow conditions, with excellent correspondence to locations of shear layer vorticity roll up, although downstream shear layer strain rates in some cases showed lesser correspondence between PLIF- and PIV-based data. Such differences are shown to potentially result from diffusion and resolution effects as well as the influence of three-dimensional and transient effects which can be more significant in the lee side of the jet. Nevertheless, the present results reveal interesting dynamics and demonstrate the importance of strain fields in enhanced diffusion and transport phenomena. [ABSTRACT FROM AUTHOR]

A numerical study of the flow-induced vibration of two elastically mounted cylinders in tandem and staggered arrangements at Reynolds number Re D 200 is presented. The cylinder centres are set at a streamwise distance of 1.5 cylinder diameters, placing the rear cylinder in the near-wake region of the front cylinder for the tandem arrangement. The cross-stream or lateral offset is varied between 0 and 5 cylinder diameters. The two cylinders are identical, with the same elastic mounting, and constrained to oscillate only in the cross-flow direction. The variation of flow behaviours is examined for static cylinders and for elastic mountings of a range of spring stiffnesses, or reduced velocity. At least seven major modes of flow response are identified, delineated by whether the oscillation is effectively symmetric, and the strength of the influence of the flow through the gap between the two cylinders. Submodes of these are also identified based on whether or not the flow remains periodic. More subtle temporal behaviours, such as period doubling, quasi-periodicity and chaos, are also identified and mapped. Across all of these regimes, the amplitudes of vibration and the magnitude of the fluid forces are quantified. The modes identified span the parameter space between two important limiting cases: two static bodies at varying lateral offset; and two elastically mounted bodies in a tandem configuration at varying spring stiffnesses. Some similarity in the response of extremely stiff or static bodies and extremely slack bodies is shown. This is explained by the fact that the slack bodies are free to move to an equilibrium position and stop, effectively becoming a static system. However, the most complex behaviour appears between these limits, when the bodies are in reasonably close proximity, and the natural structural frequency is close to the vortex shedding frequency of a single cylinder. This appears to be driven by the interplay between a series of time scales, including the vortex formation time, the advection time across the gap between the cylinders and the oscillation period of both bodies. This points out an important difference between this multi-body system and the classic single-cylinder vortex-induced vibration: two bodies in close proximity will not oscillate in a synchronised, periodic manner when their natural structural frequencies are close to the nominal vortex shedding frequency of a single cylinder. [ABSTRACT FROM AUTHOR]

The linear stability of two incompressible coaxial jets, separated by a thick duct wall, is investigated by means of both a modal and a non-modal approach within a global framework. The attention is focused on the range of unitary velocity ratios for which an alternate vortex shedding from the duct wall is known to dominate the flow. In spite of the inherent convective nature of jet flow instabilities, such behaviour is shown to originate from an unstable global mode of the dynamics linearised around the axisymmetric base flow. The corresponding wavemaker is located in the recirculating-flow region formed behind the duct wall. At the same time, the transient-growth analysis reveals that huge amplifications (up to 20 orders of magnitude) of small flow perturbations at the nozzle exit can occur in the subcritical regime, especially for high ratios between the outer and the inner velocities. [ABSTRACT FROM AUTHOR]

Gas injection into a liquid cross-flow is examined for the case where the gas is injected beneath a horizontal flat surface. For moderate Froude numbers, the gas pocket that is formed will rise toward the flow boundary under the action of buoyancy, a condition that is conducive to the formation of gas layers for friction-drag reduction on the surface. At the location of gas injection, a plume whose geometry is related to the mass and momentum flux of the injected gas and liquid cross-flow is formed, and the influence of buoyancy is minimal. However, as the gas pocket convects downstream, buoyancy brings the gas back upward to the flow boundary, and leads to the bifurcation of the pocket into two distinct branches, forming a stable 'V'-shape. Under some conditions, the flow between the two gas branches is almost entirely liquid, while for others there exists a bubbly flow or a continuous sheet of gas between the branches. The sweep angle and cross-sectional geometry of the gas branches are related to free-stream speed and boundary-layer thickness of the liquid cross-flow, the mass-injection rate of the gas, the diameter of the injection orifice and the gas outlet mean velocity and gas-jet angle. Data for a range of experimental conditions are used to scale the flow and results are compared to numerical computations of the flow, and these data are used to illustrate the underlying flow processes responsible leading to the formation the stable and straight gas branches. A simple model based on the balance of forces around a stable gas branch is presented and used to scale the observed data, and we use the results of this analysis and the computations to discuss how the process of gas injection may interact with the formation of the stable gas pockets farther downstream. [ABSTRACT FROM AUTHOR]

A reduced-order analysis based on optimized dynamic mode decomposition (DMD) is performed on the turbulent wake of a generic axisymmetric space launcher configuration computed via a zonal large-eddy simulation at the free stream Mach number Ma∞=0.8 and the Reynolds number based on the main body diameter ReD = 6 × 105 to investigate the buffet phenomenon. The transonic wake is characterized by an unsteady recirculation region occurring around the nozzle due to the separation of the turbulent boundary layer at the main body shoulder and subsequent dynamic interaction of the unstable free-shear layer with the nozzle surface. This results in strongly periodic and antisymmetric wall pressure fluctuations, for which three distinct frequency ranges are identified using conventional spectral analysis, i.e. SrD ≈ 0.1, SrD ≈ 0.2 and SrD ≈ 0.35. For the spatially integrated side (buffet) loads on the nozzle, the second range is found to be energetically most dominant. To clarify the origin of the detected wake dynamics, the underlying spatio-temporal coherent modes are extracted using DMD. Subsequent analysis of the reduced-order modelled flow field based on the identified DMD modes reveals that at SrD ≈ 0.1 a longitudinal cross-pumping motion of the separation bubble takes place, caused by a harmonic antisymmetric oscillation of the main recirculation vortex in the streamwise direction. At SrD ≈ 0.2, a cross-flapping motion of the shear layer is determined, triggered by antisymmetric vortex shedding which is in phase with the cross-pumping motion such that it occurs at twice the frequency value. The last range of SrD ≈ 0.35 is attributed to a swinging motion of the shear layer caused by a higher harmonic of the vortex shedding mode. Conclusively, the controversial aspect of the true three-dimensional shape of the antisymmetric mode at SrD ≈ 0.2 that dominates the buffet phenomenon is scrutinized. Inclined elongated closed-loop vortices are identified that are shed in alternating sequence from azimuthally opposite positions in a longitudinal plane of symmetry that changes its momentary orientation irregularly, maintaining an axisymmetric time-averaged field and spatially isotropic buffet loads. [ABSTRACT FROM AUTHOR]

A theory is presented where the weakly nonlinear analysis of laminar globally unstable flows in the presence of external forcing is extended to the turbulent regime. The analysis is demonstrated and validated using experimental results of an axisymmetric bluff-body wake at high Reynolds numbers, ReD∼1.88×105, where forcing is applied using a zero-net-mass-flux actuator located at the base of the blunt body. In this study we focus on the response of antisymmetric coherent structures with azimuthal wavenumbers m=±1 at a frequency StD=0.2, responsible for global vortex shedding. We found experimentally that axisymmetric forcing (m=0) couples nonlinearly with the global shedding mode when the flow is forced at twice the shedding frequency, resulting in parametric subharmonic resonance through a triadic interaction between forcing and shedding. We derive simple weakly nonlinear models from the phase-averaged Navier–Stokes equations and show that they capture accurately the observed behaviour for this type of forcing. The unknown model coefficients are obtained experimentally by producing harmonic transients. This approach should be applicable in a variety of turbulent flows to describe the response of global modes to forcing. [ABSTRACT FROM AUTHOR]

We present experimental data to demonstrate that the far wake of a vertical-axis wind turbine (VAWT) exhibits features that are quantitatively similar to that of a circular cylinder with the same aspect ratio. For a fixed Reynolds number (Re ≈ 0.8 × 105) and variable tip-speed ratio, two-dimensional particle image velocimetry (PIV) is used to measure the velocity field in the wake of four different laboratory-scale models: a 2-bladed, 3-bladed and 5-bladed VAWT, as well as a circular cylinder. With these measurements, we use spectral analysis and proper orthogonal decomposition (POD) to evaluate statistics of the velocity field and investigate the large-scale coherent motions of the wake. In all cases, we observe three distinct regions in the VAWT wake: (i) the near wake, where periodic blade vortex shedding dominates; (ii) a transition region, where growth of a shear-layer instability occurs; (iii) the far wake, where bluff-body wake oscillations dominate. We define a dynamic solidity parameter, σD, that relates the characteristic scales of the flow to the streamwise transition location in the wake. In general, we find that increasing σD leads to an earlier transition, a greater initial velocity deficit and a faster rate of recovery in the wake. We propose a coordinate transformation using σD in which the minimum velocity recovery profiles of the VAWT wake closely match that of the cylinder wake. The results have implications for manipulating VAWT wake recovery within a wind farm. [ABSTRACT FROM AUTHOR]

Wake vortex evolution of a square cylinder with a slot synthetic jet issuing from the cylinder’s rear surface has been experimentally investigated using the time-resolved particle image velocimetry technique. The Reynolds number based on the side length of the square cylinder is Re=836. The excitation frequency normalized by the natural shedding frequency fe/f0 varies from 0 to 6 at the dimensionless stroke length L0/w=72.6. The distributions of the time-averaged Reynolds stresses present significant differences as the excitation frequency increases. With control, the mean streamwise velocity deficit of the wake recovers more quickly in comparison with the natural case, and the vertical velocity fluctuation intensity becomes weaker. Moreover, a drag reduction can be achieved for the control cases, especially, for fe/f0=4 and fe/f0=6, a thrust instead of drag reduction can be obtained. The profiles of the mean streamwise velocity tend to have jet-like distributions. The wake vortex dynamics and its evolution with the excitation frequency are revealed. (i) For the low excitation frequency cases (fe/f0=0.5, 1, 2), no significant changes in the dominant frequency and the spanwise vortex structures are observed in comparison with the natural case. (ii) For the moderate excitation frequency case (fe/f0=3), the wake vortex shedding frequency is locked on half of the control frequency. In this case, the shear layer is divided into two parts by the synthetic jet vortex, and the wake vortices with smaller scales still shed asymmetrically and appear closer to the square cylinder. (iii) For the high excitation frequency case (fe/f0=6), the flow is governed by the synthetic jet. As a result of strong perturbations of the synthetic jet, the wake vortex shedding becomes symmetric with the shedding frequency consistent with the control frequency. And the separation is suppressed effectively. The different control effects of the slot synthetic jet on a square cylinder and a circular cylinder are also compared in detail. Generally speaking, the circular cylinder is easier to be controlled due to its non-fixed separation points. [ABSTRACT FROM AUTHOR]

We present a combined numerical (particle vortex method) and experimental (soap film tunnel) study of a symmetric foil undergoing prescribed oscillations in a two-dimensional free stream. We explore pure pitching and pure heaving, and contrast these two generic types of kinematics. We compare measurements and simulations when the foil is forced with pitching oscillations, and we find a close correspondence between flow visualisations using thickness variations in the soap film and the numerically determined vortex structures. Numerically, we determine wake maps spanned by oscillation frequency and amplitude, and we find qualitatively similar maps for pitching and heaving. We determine the drag–thrust transition for both pitching and heaving numerically, and we discuss it in relation to changes in wake structure. For heaving with low oscillation frequency and high amplitude, we find that the drag–thrust transition occurs in a parameter region with wakes in which two vortex pairs are formed per oscillation period, in contrast to the common transition scenario in regions with inverted von Kármán wakes. [ABSTRACT FROM AUTHOR]

The caudal fin of swimming animals can be modelled as a thrust-producing flapping foil. When considered alone, such a foil produces on average a jet wake with a positive net momentum. It has been argued that the instability characteristics of these averaged wakes are linked to the propulsion efficiency of swimming animals. Here, we reconsider this question by taking into account both the thrust and the drag exerted on a self-propelled swimming body. To do so, we study the stability of a family of momentumless wakes, constructed as the Oseen approximation of a force doublet moving at constant velocity. By performing a local stability analysis, we first show that these wakes undergo a transition from absolute to convective instability. Then, using the time stepper approach by integrating the linearised Navier-Stokes system, we investigate the global stability and reveal the influence of a non-parallel base flow as well as the role of the locally absolutely unstable upstream region in the wake. Finally, to complete the global scenario, we address the nonlinear evolution of the wake disturbance. These results are then discussed in the context of aquatic locomotion. According to the present stability results, and assuming the Oseen approximation whose validity has been assessed only for moderate Reynolds number, the momentumless wake of aquatic animals is generally stable, whereas the corresponding thrust part is unstable. It is therefore essential to consider all forces exerted on a self-propelled animal when discussing its wake stability and its propulsion efficiency. [ABSTRACT FROM AUTHOR]

This work is dedicated to systematically studying and predicting the wake characteristics of a yawed wind turbine immersed in a turbulent boundary layer. To achieve this goal, wind tunnel experiments were performed to characterize the wake of a horizontal-axis wind turbine model. A high-resolution stereoscopic particle image velocimetry system was used to measure the three velocity components in the turbine wake under different yaw angles and tip-speed ratios. Moreover, power and thrust measurements were carried out to analyse the performance of the wind turbine. These detailed wind tunnel measurements were then used to perform a budget study of the continuity and Reynolds-averaged Navier-Stokes equations for the wake of a yawed turbine. This theoretical analysis revealed some notable features of the wakes of yawed turbines, such as the asymmetric distribution of the wake skew angle with respect to the wake centre. Under highly yawed conditions, the formation of a counter-rotating vortex pair in the wake cross-section as well as the vertical displacement of the wake centre were shown and analysed. Finally, this study enabled us to develop general governing equations upon which a simple and computationally inexpensive analytical model was built. The proposed model aims at predicting the wake deflection and the far-wake velocity distribution for yawed turbines. Comparisons of model predictions with the wind tunnel measurements show that this simple model can acceptably predict the velocity distribution in the far wake of a yawed turbine. Apart from the ability of the model to predict wake flows in yawed conditions, it can provide valuable physical insight on the behaviour of turbine wakes in this complex situation. [ABSTRACT FROM AUTHOR]

Direct numerical simulations (DNS) are performed to study the behaviour of flow past a sphere in the regime of high stratification (low Froude number Fr). In contrast to previous results at lower Reynolds numbers, which suggest monotone suppression of turbulence with increasing stratification in flow past a sphere, it is found that, below a critical Fr, increasing the stratification induces unsteady vortical motion and turbulent fluctuations in the near wake. The near wake is quantified by computing the energy spectra, the turbulence energy equation, the partition of energy into horizontal and vertical components, and the buoyancy Reynolds number. These diagnostics show that the stabilizing effect of buoyancy changes flow over the sphere to flow around the sphere. This qualitative change in the flow leads to a new regime of unsteady vortex shedding in the horizontal planes and intensified horizontal shear which result in turbulence regeneration. [ABSTRACT FROM AUTHOR]

We examine the dynamics of a semi-infinite vortex sheet attached not to a semi-infinite plate but instead to a rigid right-angled wedge, with the sheet aligned along one of its edges. Our approach to this problem, which was suggested by David Crighton, accords well with the fundamental ethos of Crighton’s work, which was characterized by ‘the application of rigorous mathematical approximations to fluid mechanical idealizations of practically relevant problems’ (Ffowcs Williams, Annu. Rev. Fluid Mech., vol. 34, 2002, pp. 37–49). The resulting linearised unsteady potential flow is forced by an oscillatory dipole in the uniform stream passing along the top of the wedge, while there is stagnant fluid in the remaining quadrant. Spatial instability is considered according to well-established methods: causality is enforced by allowing the frequency to become temporarily complex. The essentially quadrant-type geometry replaces the usual Wiener–Hopf technique by the Mellin transform. The core difficulty is that a first-order difference equation of period 4 requires a solution of period unity. As a result, the complex fourth roots $(\pm 1\pm \text{i})$ of $-4$ appear in the complementary function. The Helmholtz instability wave is excited and requires careful handling to obtain explicit results for the amplitude of the instability wave. [ABSTRACT FROM AUTHOR]

We consider the scaling of the mass flux and entrainment velocity across the turbulent/non-turbulent interface (TNTI) in the far field of an axisymmetric jet at high Reynolds number. Time-resolved, simultaneous multi-scale particle image velocimetry (PIV) and planar laser-induced fluorescence (PLIF) are used to identify and track the TNTI, and directly measure the local entrainment velocity along it. Application of box-counting and spatial-filtering methods, with filter sizes $\unicode[STIX]{x1D6E5}$ spanning over two decades in length, show that the mean length of the TNTI exhibits a power-law behaviour with a fractal dimension $D\approx 0.31{-}0.33$. More importantly, we invoke a multi-scale methodology to confirm that the mean mass flux, which is equal to the product of the entrainment velocity and the surface area, remains constant across the range of filter sizes. The results, within experimental uncertainty, also show that the entrainment velocity along the TNTI exhibits a power-law behaviour with $\unicode[STIX]{x1D6E5}$, such that the entrainment velocity increases with increasing $\unicode[STIX]{x1D6E5}$. In fact, the mean entrainment velocity scales at a rate that balances the scaling of the TNTI length such that the mass flux remains independent of the coarse-grain filter size, as first suggested by Meneveau & Sreenivasan (Phys. Rev. A, vol. 41, no. 4, 1990, pp. 2246–2248). Hence, at the smallest scales the entrainment velocity is small but is balanced by the presence of a very large surface area, whilst at the largest scales the entrainment velocity is large but is balanced by a smaller (smoother) surface area. [ABSTRACT FROM PUBLISHER]

We perform a comprehensive characterization of the propulsive performance of a thrust generating pitching foil over a wide range of Reynolds (10 ⩽ Re ⩽ 2000) and Strouhal (St) numbers using a high-resolution viscous vortex particle method. For a given Re, we show that the mean thrust coefficient ... increases monotonically with St, exhibiting a sharp rise as the location of the inception of the wake asymmetry shifts towards the trailing edge. As a result, the propulsive efficiency too rises steeply before attaining a maximum and eventually declining at an asymptotic rate that is consistent with the inertial scalings of St² for ... and St³ for the mean power coefficient, with the latter scaling holding, quite remarkably, over the entire range of Re. We find the existence of a sharp increase in the peak propulsive efficiency ηmax (at a given Re) in the Re range of 50 to approximately 1000, with ηmax increasing rapidly from about 1.7% to the saturated asymptotic value of approximately 16 %. The St at which ηmax is attained decreases progressively with Re towards an asymptotic limit of 0:45 and always exceeds the one for transition from a reverse von Kármán to a deflected wake. Moreover, the drag-to-thrust transition occurs at a Strouhal number Sttr that exceeds the one for von Kármán to reverse von Kármán transition. The Sttr and the corresponding power coefficient ... are found to be remarkably consistent with the simple scaling relationships Sttr ~ Re-0.37 and ... ~ Re-1.12 that are derived from a balance of the thrust generated from the pitching motion and the drag force arising out of viscous resistance to the foil motion. The fact that the peak propulsive efficiency degrades appreciably only below Re ≈ 10³ establishes a sharp lower threshold for energetically efficient thrust generation from a pitching foil. Our findings should be generalizable to other thrust-producing flapping foil configurations and should aid in establishing the link between wake patterns and energetic cost of thrust production in similar systems. [ABSTRACT FROM AUTHOR]

Blindfolded harbour seals are able to use their uniquely shaped whiskers to track vortex wakes left by moving animals and identify objects that passed by 30 s earlier, an impressive feat, as the flow features have velocities as low as 1 mm s-1. The seals sense while swimming, hence their whiskers are sensitive enough to detect small-scale changes in the flow, while rejecting self-generated flow noise. Here we identify and illustrate a novel flow mechanism, causing a large-amplitude 'slaloming' whisker response, which allows artificial whiskers with the identical unique undulatory geometry as those of the harbour seal to detect the features of minute flow fluctuations when placed within wakes. Whereas in open water the whisker responds with very low-amplitude vibration, once within a wake, it oscillates with large amplitude and, importantly, its response frequency coincides with the Strouhal frequency of the upstream cylinder, making the detection of an upstream wake and an estimation of the size and shape of the wake-generating body possible. This mechanism has some similarities with the flow mechanisms observed in actively controlled propulsive foils within upstream wakes and trout swimming behind bluff cylinders in a stream, but there are also differences caused by the unique whisker morphology, which enables it to respond passively and within a much wider parametric range. [ABSTRACT FROM AUTHOR]

We discuss energetic restrictions on the entrainment coefficient α for axisymmetric jets and plumes. The resulting entrainment relation includes contributions from the mean flow, turbulence and pressure, fundamentally linking α to the production of turbulence kinetic energy, the plume Richardson number Ri and the profile coefficients associated with the shape of the buoyancy and velocity profiles. This entrainment relation generalises the work by Kaminski et al. (J. Fluid Mech., vol. 526, 2005, pp. 361-376) and Fox (J. Geophys. Res., vol. 75, 1970, pp. 6818-6835). The energetic viewpoint provides a unified framework with which to analyse the classical entrainment models implied by the plume theories of Morton et al. (Proc. R. Soc. Lond. A, vol. 234, 1955, pp. 1-23) and Priestley & Ball (Q. J. R. Meteorol. Soc., vol. 81, 1954, pp. 144-157). Data for pure jets and plumes in unstratified environments indicate that to first order the physics is captured by the Priestley and Ball entrainment model, implying that (1) the profile coefficient associated with the production of turbulence kinetic energy has approximately the same value for pure plumes and jets, (2) the value of α for a pure plume is roughly a factor of 5/3 larger than for a jet and (3) the enhanced entrainment coefficient in plumes is primarily associated with the behaviour of the mean flow and not with buoyancy-enhanced turbulence. Theoretical suggestions are made on how entrainment can be systematically studied by creating constant-Ri flows in a numerical simulation or laboratory experiment. [ABSTRACT FROM AUTHOR]

When a vertical rigid plate is uniformly accelerated horizontally from rest into an initially stationary layer of inviscid incompressible fluid, the free surface will undergo a deformation in the locality of the contact point. This deformation of the free surface will, in the early stages, cause a jet to rise up the plate. An understanding of the local structure of the free surface in the early stages of motion is vital in many situations, and has been developed in detail by King & Needham (J. Fluid Mech., vol. 268, 1994, pp. 89–101). In this work we consider the effects of introducing weak surface tension, characterized by the inverse Weber number $\mathscr{W}$, into the problem considered by King & Needham. Our approach is based upon matched asymptotic expansions as $\mathscr{W}\rightarrow 0$. It is found that four asymptotic regions are needed to describe the problem. The three largest regions have analytical solutions, whilst a numerical method based on finite differences is used to solve the time-dependent harmonic boundary value problem in the last region. Our results identify the local structure of the jet near the vicinity of the contact point, and we highlight a number of key features, including the height of this jet as well as its thickness and strength. We also present some preliminary experimental results that capture the spatial structure near the contact point, and we then show promising comparisons with the theoretical results obtained within this paper. [ABSTRACT FROM AUTHOR]

Detailed velocity measurements in the wake of a body of revolution are reported for pitch angles up to $12^{\circ }$, over an unprecedented range of Reynolds numbers ($2.4\times 10^{6}\leqslant \mathit{Re}_{L}\leqslant 30\times 10^{6}$). The body of revolution, an idealized submarine shape (DARPA SUBOFF), is mounted using a support that mimics a semi-infinite sail. The wake measurements at all pitch angles and Reynolds numbers reveal the presence of a pair of streamwise vortices of unequal strengths which tend to rotate around each other as they evolve downstream. Various attempts to perturb the upstream conditions on the body had no significant impact on the relative strength of the vortices. In addition, two different models, tested in two different wind tunnels, show similar asymmetries, and we propose that wake asymmetry appears to be a robust feature of this flow, a result previously only seen for sharp-nosed bodies at high angles of attack. It is also shown that the wake behaviour for $x/D>5$, in terms of the streamwise mean velocity and turbulence intensity distributions, appears to become invariant with Reynolds number for $\mathit{Re}_{L}>4.8\times 10^{6}$. [ABSTRACT FROM PUBLISHER]

Direct numerical simulations are performed to study the evolution of a towed stratified wake subject to external turbulence in the background. A field of isotropic turbulence is combined with an initial turbulent wake field and the combined wake is simulated in a temporally evolving framework similar to that of Rind & Castro (J. Fluid Mech. vol. 710, 2012a, p. 482). Simulations are performed for external turbulence whose initial level varies between zero and a moderate intensity of up to 7 % relative to the free stream and whose initial integral length scale is of the same order as that of the wake turbulence. A series of simulations are carried out at a Reynolds number of 10000 and Froude number of 3. Background turbulence, especially at a level of 3 % or above, is found to have substantial quantitative effects in the stratified simulations. Turbulence inside the wake increases due to the entrainment of external turbulence, and the energy transfer through turbulent production from mean to fluctuating velocity also increases, leading to reduced mean velocity. The profiles of normalized mean and turbulence quantities in the stratified wake exhibit little change in the vertical direction but the horizontal spread increases in comparison to the case with undisturbed background. The spatial organization of the internal wave field is disrupted even at the 1 % level of external turbulence. However, key characteristics of stratified wakes such as the formation of coherent pancake vortices and the long lifetime of the mean wake are robust to the presence of fluctuations in the background. A corresponding series of simulations for the unstratified situation is carried out at the same Reynolds number of 10000 and with similar levels of external turbulence. The change of mean and turbulence statistics is found to be weaker in the unstratified cases compared with the corresponding stratified cases and also weaker relative to that found by Rind & Castro (J. Fluid Mech., vol. 710, 2012a, p. 482) at a similar level of external turbulence relative to the free stream and similar integral length scale. Theoretical arguments and additional simulations are provided to show that the level of external turbulence relative to wake turbulence (dissimilar between the present investigation and Rind & Castro (J. Fluid Mech., vol. 710, 2012a, p. 482)) is a key governing parameter in both stratified and unstratified backgrounds. [ABSTRACT FROM AUTHOR]

The present study is an experimental investigation of the relationship between the large- and small-scale motions in the far field of an air jet at high Reynolds number. In the first part of our investigation, the analysis is based on time series of hot-wire anemometry (HWA), which are converted into space series after applying the Taylor hypothesis. By using a spectral filter, two signals are constructed, one representative of the large-scale motions (2λT -- L, where λT is the Taylor length scale, and L is the integral length scale) and the other representative of the small-scale motions (1.5-5η, where η is the Kolmogorov length scale). The small-scale signal is found to be modulated both in amplitude and in frequency by the energy-containing scales in an analogous way, both at the centreline and around the centreline. In particular, for positive fluctuations of the large-scale signal, the small-scale signal is locally stronger in amplitude (amplitude modulation), and it locally exhibits a higher number of local maxima and minima (frequency modulation). The extent of this modulation is quantified based on the strength of the large-scale fluctuations. The response of the small-scale motions to amplitude modulation can be considered instantaneous, being on the order of one Kolmogorov time scale. In the second part of our investigation we use long-range μPIV to study the behaviour of the small-scale motions in relation to their position in either high-speed or low-speed regions of the flow. The spatially resolved velocity vector fields allow us to quantify amplitude modulation directly in physical space. From this direct estimation in physical space, amplitude modulation is only 25 % of the value measured from HWA. The remaining 75 % comes from the fixed spectral band filter used to obtain the large- and small-scale signals, which does not consider the local convection velocity. A very similar overestimation of amplitude modulation when quantified in the time-frame is also obtained analytically. Furthermore, the size of the structures of intense vorticity does not change significantly in relation to the large-scale velocity fluctuation, meaning that there is no significant spatial frequency modulation. The remaining amplitude modulation in space can be explained as a statistical coupling between the strength of the structures of vorticity and their preferential location inside large-scale high-velocity regions. Finally, the implications that the present findings have on amplitude and frequency modulation in turbulent boundary layers (TBLs) are discussed. [ABSTRACT FROM AUTHOR]

Three-dimensional computations are carried out for a spinning cylinder placed in a uniform flow. The non-dimensional rotation rate is varied in the range $0.0\leqslant {\it\alpha}\leqslant 5.0$. A stabilized finite element method is utilized to solve the incompressible Navier–Stokes equations in primitive variables formulation. Linear stability analysis of the steady state shows the existence of several new unstable three-dimensional modes for $200\leqslant \mathit{Re}\leqslant 350$ and $4.0\leqslant {\it\alpha}\leqslant 5.0$. The curves of neutral stability of these modes are presented in the $\mathit{Re}{-}{\it\alpha}$ parameter space. For the flow at $\mathit{Re}=200$ and rotation rate in the ranges $0.0\leqslant {\it\alpha}\leqslant 1.91$ and $4.34\leqslant {\it\alpha}\leqslant 4.7$, the vortex shedding, earlier reported in two dimensions and commonly referred to as parallel shedding, can also exist as oblique shedding. In this mode of shedding, the vortices are inclined to the axis of the cylinder. In fact, parallel shedding is a special case of oblique shedding. It is found that the span of the cylinder plays a significant role in the time evolution of the flow. Of all the unstable eigenmodes, with varied spanwise wavenumber, only the ones whose integral number of wavelengths fit the span length of the cylinder are selected to grow. For the flow at $\mathit{Re}=200$, two steady states exist for $4.8\leqslant {\it\alpha}\leqslant 5.0$. While one of them is associated with unstable eigenmodes, the other is stable to all infinitesimal perturbations. In this regime, irrespective of the initial conditions, the fully developed flow is steady and devoid of any instabilities. [ABSTRACT FROM PUBLISHER]

This paper presents the results of numerical stability analysis of the wake of an elliptical cylinder. Aspect ratios where the ellipse is longer in the streamwise direction than in the transverse direction are considered. The focus is on the dependence on the aspect ratio of the ellipse of the various bifurcations to three-dimensional flow from the two-dimensional Kármán vortex street. It is shown that the three modes present in the wake of a circular cylinder (modes A, B and QP) are present in the ellipse wake, and that in general they are all stabilized by increasing the aspect ratio of the ellipse. Two new pertinent modes are found: one long-wavelength mode with similarities to mode A, and a second that is only unstable for aspect ratios greater than approximately 1.75, which has similar spatiotemporal symmetries to mode B but has a distinct spatial structure. Results from fully three-dimensional simulations are also presented confirming the existence and growth of these two new modes in the saturated wakes. [ABSTRACT FROM AUTHOR]

This study considers the interaction of two identical solid axisymmetric bodies (of diameter $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}d$ and thickness $h$) freely falling in a fluid at rest. We determine the domains of existence of the different interaction behaviour of the two bodies (i.e. attraction, repulsion and indifference) as a function of their initial relative position. We then investigate in detail the case of bodies falling in tandem, for both rectilinear and periodic paths, and the associated attraction behaviour. For all the Reynolds numbers and aspect ratios of the bodies ($\chi = d/h$) investigated, the trailing body catches up with the leading body. We provide a quantitative description of the kinematics leading to the regrouping of the bodies and analyse its relationship with the wake of the leading body. In the case of rectilinear paths, a dynamical model that takes into account the axial evolution of the wake of the leading body is proposed to reproduce the acceleration observed for the trailing body until a vertical separation distance between the bodies of 1.5 diameters. In parallel, direct numerical simulations (DNS) of the flow about two fixed bodies in tandem in an oncoming flow are carried out, providing a good estimation of the motion of the bodies for separation distances larger than 5 diameters. For periodic paths, the kinematics leading to the regrouping of the bodies is slower than for rectilinear paths. However, in this case, the interaction also leads to significant changes in the characteristics of the oscillatory motion and is strongly dependent on the aspect ratio of the bodies. To explain the observed differences, we consider the effect of the transverse inhomogeneity of the wake of the leading body on the oscillatory motion of the trailing disk. [ABSTRACT FROM PUBLISHER]

A new model to account for the presence of the test-section wall in wind-turbine or propeller measurements is proposed. The test section, here assumed to be cylindrical, is modelled by means of axisymmetric source panels, while the wind turbine (or the propeller) is modelled with a simplified vortex model (Segalini & Alfredsson, J. Fluid Mech., vol. 725, 2013, pp. 91–116). Combining both models in an iterative scheme allows the simulation of the effect of the test-section wall on the flow field around the rotor. Based on this novel approach, an analysis of the flow modification due to blockage is conducted together with a comparison of actuator-disk theory results. Glauert’s concept of equivalent unconfined turbine is reviewed and extended to account for the angular velocity of the rotor. It is shown that Glauert’s equivalent free-stream velocity concept is beneficial and can correct most of the systematic error introduced by the presence of the test-section wall, although some discrepancies remain, especially in the power coefficient. The effect of the confinement on the wake structure is also discussed in terms of wake expansion/contraction, pitch of the tip vortices and forces at the rotor. [ABSTRACT FROM PUBLISHER]

The coherent structures of a turbulent wake generated behind a bluff three-dimensional axisymmetric body are investigated experimentally at a diameter-based Reynolds number of $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}{\sim }2\times 10^5$. Proper orthogonal decomposition of base pressure measurements indicates that the most energetic coherent structures retain the structure of the symmetry-breaking laminar instabilities and are manifested as unsteady vortex shedding with azimuthal wavenumber $m={\pm }1$. In a rotating reference frame, the shedding preserves the reflectional symmetry and is linked with a reflectionally symmetric mean pressure distribution on the base. Due to a slow rotation of the symmetry plane of the turbulent wake around the axis of the body, statistical axisymmetry is recovered in the time average. The ratio of the time scales associated with the slow rotation of the symmetry plane and the vortex shedding is of order 100. [ABSTRACT FROM PUBLISHER]

The two-dimensional inviscid incompressible steady flow past an inclined flat plate is considered. A locus of asymmetric equilibrium configurations for vortex pairs is detected. It is shown that the flat geometry has peculiar properties compared to other geometries: (i) in order to satisfy the Kutta condition at both edges, which ensures flow regularity, the total circulation and the force acting on the plate must be zero; and (ii) the Kutta condition and the free vortex equilibrium conditions are not independent of each other. The non-existence of symmetric equilibrium configurations for an orthogonal plate is extended to more general asymmetric flows. [ABSTRACT FROM PUBLISHER]

Sensitivity analysis has successfully located the most efficient regions in which to apply passive control in many globally unstable flows. As is shown here and in previous studies, the standard sensitivity analysis, which is linear (first order) with respect to the actuation amplitude, predicts that steady spanwise wavy alternating actuation/modification has no effect on the stability of planar flows, because the eigenvalue change integrates to zero in the spanwise direction. In experiments, however, spanwise wavy modification has been shown to stabilize the flow behind a cylinder quite efficiently. In this paper, we generalize sensitivity analysis by examining the eigenvalue drift (including stabilization/destabilization) up to second order in the perturbation, and show how the second-order eigenvalue changes can be computed numerically by overlapping the adjoint eigenfunction with the first-order global eigenmode correction, shown here for the first time. We confirm the prediction against a direct computation, showing that the eigenvalue drift due to a spanwise wavy base flow modification is of second order. Further analysis reveals that the second-order change in the eigenvalue arises through a resonance of the original (2-D) eigenmode with other unperturbed eigenmodes that have the same spanwise wavelength as the base flow modification. The eigenvalue drift due to each mode interaction is inversely proportional to the distance between the eigenvalues of the modes (which is similar to resonance), but also depends on mutual overlap of direct and adjoint eigenfunctions (which is similar to pseudoresonance). By this argument, and by calculating the most sensitive regions identified by our analysis, we explain why an in-phase actuation/modification is better than an out-of-phase actuation for control of wake flows by spanwise wavy suction and blowing. We also explain why wavelengths several times longer than the wake thickness are more efficient than short wavelengths. [ABSTRACT FROM PUBLISHER]