Nonlinear self-excited thermoacoustic oscillations appear in systems involving confined combustion in the form of coupled acoustic pressure oscillations and unsteady heat release rate. In this paper, we investigate the nonlinear transition undergone by thermoacoustic oscillations to flame blowout via intermittency, in response to variation in the location of the combustion source with respect to the acoustic field of the confinement. A ducted laminar premixed conical flame, stabilized on a circular jet exit with a fully developed exit velocity profile, was investigated. Transition to limit cycle oscillations from a non-oscillatory state was observed to occur via a subcritical Hopf bifurcation. Limit cycle oscillations underwent a further bifurcation to quasi-periodic oscillations characterized by the repeated formation of elongated necks in the flame that pinch off as pockets of unburned fuel–air mixture. The quasi-periodic state loses stability, resulting in an intermittent state identified as type II through recurrence analysis of phase space trajectories reconstructed from the acoustic pressure time trace. In this state, the flame undergoes repeated lift-off and reattachment. Instantaneous flame images suggest that the intermittent flame behaviour is influenced by jet flow dynamics.

We consider a sequence of boundary-value problems for the acoustic wave equation, with the pressure specified on the boundary as a function of space and time, and simulating features of the pressure field measured just outside a turbulent shear layer supporting large-scale coherent structures. The boundary pressure field has the form of a travelling subsonic plane wave, modulated by a large-scale envelope function. Three models for the envelope distribution are studied in detail, and the particular features which they exhibit are shown to be representative of large classes of amplitude functions.

We start by looking at the hydrodynamic near field of the boundary pressure fluctuations, over spatial regions throughout which the motion can be taken as incompressible. Very close to the boundary, the pressure fluctuations decay exponentially with transverse distance, while at sufficiently large distances from the whole wave packet on the boundary, the pressure fluctuations have a dipole algebraic decay. We investigate the transition from exponential to algebraic decay, and find that it is effected through quite a complicated multilayer structure which depends crucially on the detailed form of the envelope.

Acoustic fields are then determined both from exact solutions to the wave equation, and from matching arguments. In some cases, where the boundary source is compact, the distant acoustic fields have a simple compressible dipole type of behaviour. In other cases, however, when the boundary source is non-compact, the acoustic field has a superdirective character, the angular variation being described by exponentials of cosines of the angle with the streamwise direction. It is shown how the superdirective acoustic sources are completely compatible with the features of the inner incompressible field, and a criterion for the occurrence of the superdirective acoustic fields will be given. Superdirective fields of this kind have been observed in measurements by Laufer & Yen (1983) on a low-speed round jet of Mach number 0.1, and the general relation of our results to those experiments is explained.

The Stokes flow problem is concerned with fluid motion about an obstacle when the motion is such that inertial effects can be neglected. This problem is considered here for the case in which the obstacle (or configuration of obstacles) has an axis of symmetry, and the flow at distant points is uniform and parallel to this axis. The differential equation for the stream function ψ then assumes the form L2−1ψ = 0, where L−1 is the operator which occurs in axiallysymmetric flows of the incompressible ideal fluid. This is a particular case of the fundamental operator of A. Weinstein's generalized axially symmetric potential theory. Using the results of this theory and theorems regarding representations of the solutions of repeated operator equations, the authors (1) give a general expression for the drag of an axially symmetric configuration in Stokes flow, and (2) indicate a procedure for the determination of the stream function. The stream function is found for the particular case of the lens-shaped body.

Explicit calculation of the drag is difficult for the general lens, without recourse to numerical procedures, but is relatively easy in the case of the hemispherical cup. As examples illustrative of their procedures, the authors briefly consider three Stokes flow problems whose solutions have been given previously.

This paper discusses the general idea that in systems where a flexible solid is coupled with a flowing fluid three different types of instability are possible. These were originally designated by Brooke Benjamin (1960) as ‘class A’, ‘class B’ and ‘Kelvin-Helmholtz’ instability, and their collective significance has been clarified recently by Landahl (1962). Class A and class B disturbances are essentially oscillations involving conservative energy-exchanges between the fluid and solid, but their stability is determined by the net effect of irreversible processes, which include dissipation and energy-transfer to the solid by non-conservative hydrodynamic forces. Dissipation in the solid tends to stabilize class B distrbances but to destabilize class A ones. Class C instability (i.e. the ‘Kelvin-Helmholtz’ type) occurs when conservative hydrodynamic forces cause a unidirectional transfer of energy to the solid.

In § 2 this idea is examined fundamentally by way of the Lagrangian method of generalized co-ordinates, and in § 3 the example of inviscid-fluid flow past a flexible plane boundary is considered. The treatment of this example amplifies the work of Landahl, in particular by including the effect of non-conservative forces of the kind investigated by Miles in his series of papers on water-wave generation by wind.

We perform direct numerical simulations of a rigid sphere translating parallel to a flat wall in an otherwise quiescent ambient fluid. A spectral element method is employed to perform the simulations with high accuracy. For $Re\,{<}\,100$, we observe the lift coefficient to decrease with both Reynolds number and distance from the wall. In this regime the present results are in good agreement with the low-Reynolds-number theory of Vasseur & Cox (1977), with the recent experiments of Takemura & Magnaudet (2003) and with the simulations of Kim et al. (1993). The most surprising result from the present simulations is that the wall-induced lift coefficient increases dramatically with increasing $Re$ above about 100. Detailed analysis of the flow field around the sphere suggests that this increase is due to an imperfect bifurcation resulting in the formation of a double-threaded wake vortical structure. In addition to a non-rotating sphere, we also simulate a freely rotating sphere in order to assess the importance of free rotation on the translational motion of the sphere. We observe the effect of sphere rotation on lift and drag forces to be small. We also explore the effect of the wall on the onset of unsteadiness.

This paper describes an experiment in which a cylindrical vortex, formed in a long tube, was used to study the ‘vortex breakdown’ that has been previously reported in investigations of the flow over slender delta wings. By varying the amount of swirl that was imparted to the fluid before it entered the tube, it was found that the breakdown was the intermediate stage between the two basic types of rotating flows, that is, those that do and those that do not exhibit axial velocity reversal. In addition, it was shown that an unusual flow pattern was established after the breakdown and that certain features of this pointed to it being a ‘critical’ phenomenon. The tests were concluded by measuring the swirl angle distribution a short distance ahead of the breakdown and comparing these results with the prediction of Squire's theory (1960).

The linear-eddy approach for modelling molecular mixing in turbulent flow involves stochastic simulation on a one-dimensional domain with sufficient resolution to include all physically relevant lengthscales. In each realization, molecular diffusion is implemented deterministically, punctuated by a sequence of instantaneous, statistically independent ‘rearrangement events’ (measure-preserving maps) representing turbulent stirring. These events emulate the effect of compressive strain on the scalar field. An inertial-range similarity law is incorporated.

The model reproduces key features of scalar power spectra, including dependences of spectra! amplitudes and transition wavenumbers on Reynolds and Schmidt numbers. Computed scaling exponents governing scalar power spectra, higher-order fluctuation statistics such as structure functions, and the spatial distribution of scalar level crossings are close to measured exponents. It is inferred that the characterization of stirring as a sequence of independent events (the model analogue of eddies) leads to a useful representation of mixing-field microstructure.

The high-Reynolds-number behaviour of the canonical incompressible turbulent channel flow is investigated through large-scale direct numerical simulation (DNS). A Reynolds number is achieved ($Re_{\tau } = h/\delta _v \approx 4000$, where $h$ is the channel half-height, and $\delta _v$ is the viscous length scale) at which theory predicts the onset of phenomena typical of the asymptotic Reynolds number regime, namely a sensible layer with logarithmic variation of the mean velocity profile, and Kolmogorov scaling of the velocity spectra. Although higher Reynolds numbers can be achieved in experiments, the main advantage of the present DNS study is access to the full three-dimensional flow field. Consistent with refined overlap arguments (Afzal & Yajnik, J. Fluid Mech. vol. 61, 1973, pp. 23–31; Jiménez & Moser, Phil. Trans. R. Soc. Lond. A, vol. 365, 2007, pp. 715–732), our results suggest that the mean velocity profile never achieves a truly logarithmic profile, and the logarithmic diagnostic function instead exhibits a linear variation in the outer layer whose slope decreases with the Reynolds number. The extrapolated value of the von Kármán constant is $k \approx 0.41$. A near logarithmic layer is observed in the spanwise velocity variance, as predicted by Townsend’s attached eddy hypothesis, whereas the streamwise variance seems to exhibit a shoulder, perhaps being still affected by low-Reynolds-number effects. Comparison with previous DNS data at lower Reynolds number suggests enhancement of the imprinting effect of outer-layer eddies onto the near-wall region. This mechanisms is associated with excess turbulence kinetic energy production in the outer layer, and it reflects in flow visualizations and in the streamwise velocity spectra, which exhibit sharp peaks in the outer layer. Associated with the outer energy production site, we find evidence of a Kolmogorov-like inertial range, limited to the spanwise spectral density of $u$, whereas power laws with different exponents are found for the other spectra. Finally, arguments are given to explain the ‘odd’ scaling of the streamwise velocity variances, based on the analysis of the kinetic energy production term.

The results of a laboratory experiment designed to study turbulent entrainment at sheared density interfaces are described. A stratified shear layer, across which a velocity difference ΔU and buoyancy difference Δb is imposed, separates a lighter upper turbulent layer of depth D from a quiescent, deep lower layer which is either homogeneous (two-layer case) or linearly stratified with a buoyancy frequency N (linearly stratified case). In the parameter ranges investigated the flow is mainly determined by two parameters: the bulk Richardson number RiB = ΔbD/ΔU2 and the frequency ratio fN = ND=ΔU.

When RiB > 1.5, there is a growing significance of buoyancy effects upon the entrainment process; it is observed that interfacial instabilities locally mix heavy and light fluid layers, and thus facilitate the less energetic mixed-layer turbulent eddies in scouring the interface and lifting partially mixed fluid. The nature of the instability is dependent on RiB, or a related parameter, the local gradient Richardson number Rig = N2L/ (∂u/∂z)2, where NL is the local buoyancy frequency, u is the local streamwise velocity and z is the vertical coordinate. The transition from the Kelvin–Helmholtz (K-H) instability dominated regime to a second shear instability, namely growing Hölmböe waves, occurs through a transitional regime 3.2 < RiB < 5.8. The K-H activity completely subsided beyond RiB ∼ 5 or Rig ∼ 1. The transition period 3.2 < RiB < 5 was characterized by the presence of both K-H billows and wave-like features, interacting with each other while breaking and causing intense mixing. The flux Richardson number Rif or the mixing efficiency peaked during this transition period, with a maximum of Rif ∼ 0.4 at RiB ∼ 5 or Rig ∼ 1. The interface at 5 < RiB < 5.8 was dominated by ‘asymmetric’ interfacial waves, which gradually transitioned to (symmetric) Hölmböe waves at RiB > 5:8.

Laser-induced fluorescence measurements of both the interfacial buoyancy flux and the entrainment rate showed a large disparity (as large as 50%) between the two-layer and the linearly stratified cases in the range 1.5 < RiB < 5. In particular, the buoyancy flux (and the entrainment rate) was higher when internal waves were not permitted to propagate into the deep layer, in which case more energy was available for interfacial mixing. When the lower layer was linearly stratified, the internal waves appeared to be excited by an ‘interfacial swelling’ phenomenon, characterized by the recurrence of groups or packets of K-H billows, their degeneration into turbulence and subsequent mixing, interfacial thickening and scouring of the thickened interface by turbulent eddies.

Estimation of the turbulent kinetic energy (TKE) budget in the interfacial zone for the two-layer case based on the parameter α, where α = (−B + ε)/P, indicated an approximate balance (α ∼ 1) between the shear production P, buoyancy flux B and the dissipation rate ε, except in the range RiB < 5 where K-H driven mixing was active.

Laboratory experiments have been conducted to study the shoaling of internal solitary waves of depression in a two-layer system on a uniform slope. The shoaling of a single solitary wave results in wave breaking and the production of multiple turbulent surges, or boluses, which propagate up the slope. Significant vertical mixing occurs everywhere inshore of the breaking location. The kinematics of the breaking and bolus runup are described and a breaking criterion is found. The energetics of the breaking are investigated. Over the range of parameters examined, 15 (±5) % of the energy lost from first-mode wave motion inshore of the break point goes into vertical mixing.

Laser-induced fluorescence was used to measure the lateral dispersion of passive solute in random arrays of rigid, emergent cylinders of solid volume fraction φ=0.010–0.35. Such densities correspond to those observed in aquatic plant canopies and complement those in packed beds of spheres, where φ≥0.5. This paper focuses on pore Reynolds numbers greater than Res=250, for which our laboratory experiments demonstrate that the spatially averaged turbulence intensity and Kyy/(Upd), the lateral dispersion coefficient normalized by the mean velocity in the fluid volume, Up, and the cylinder diameter, d, are independent of Res. First, Kyy/(Upd) increases rapidly with φ from φ =0 to φ=0.031. Then, Kyy/(Upd) decreases from φ=0.031 to φ=0.20. Finally, Kyy/(Upd) increases again, more gradually, from φ=0.20 to φ=0.35. These observations are accurately described by the linear superposition of the proposed model of turbulent diffusion and existing models of dispersion due to the spatially heterogeneous velocity field that arises from the presence of the cylinders. The contribution from turbulent diffusion scales with the mean turbulence intensity, the characteristic length scale of turbulent mixing and the effective porosity. From a balance between the production of turbulent kinetic energy by the cylinder wakes and its viscous dissipation, the mean turbulence intensity for a given cylinder diameter and cylinder density is predicted to be a function of the form drag coefficient and the integral length scale lt. We propose and experimentally verify that lt=min{d, 〈sn〉A}, where 〈sn〉A is the average surface-to-surface distance between a cylinder in the array and its nearest neighbour. We farther propose that only turbulent eddies with mixing length scale greater than d contribute significantly to net lateral dispersion, and that neighbouring cylinder centres must be farther than r* from each other for the pore space between them to contain such eddies. If the integral length scale and the length scale for mixing are equal, then r*=2d. Our laboratory data agree well with predictions based on this definition of r*.

We analyse the dilute, steady, fully developed flow of relatively massive particles in a turbulent gas in the context of a vertical pipe. The idea is that the exchange of momentum in collisions between the grains and between the grains and the wall plays a significant role in the balance of forces in the particle phase. Consequently, the particle phase is considered to be a dilute system of colliding grains, in which the velocity fluctuations are produced by collisions rather than by the gas turbulence. The balance equations for rapid granular flow are modified to incorporate the drag force from the gas, and boundary conditions, based on collisional exchanges of momentum and energy at the wall, are employed. The turbulence of the gas is treated using a one-equation closure. A numerical solution of the resulting governing equations provides velocity and turbulent energy profiles in agreement with the measurements of Tsuji et al. (1984).

This study investigates the free transverse flow-induced vibration (FIV) of an elastically mounted low-mass-ratio square cylinder in a free stream, at three different incidence angles: ${{\alpha }}=0^\circ $, $20^\circ $ and $45^\circ $. This geometric setup presents a body with an angle of attack, sharp corners and some afterbody, and therefore is a generic body that can be used to investigate a wide range of FIV phenomena. A recent study by Nemes et al. (J. Fluid Mech., vol. 710, 2012, pp. 102–130) provided a broad overview of the flow regimes present as a function of both the angle of attack ${{\alpha }}$ and reduced flow velocity ${U^{*}}$. Here, the focus is on the three aforementioned representative angles of attack: ${{\alpha }}=0^\circ $, where the FIV is dominated by transverse galloping; ${{\alpha }}=45^\circ $, where the FIV is dominated by vortex-induced vibration (VIV); and an intermediate value of ${{\alpha }}=20^\circ $, where the underlying FIV phenomenon has previously been difficult to determine. For the ${{\alpha }}=0^\circ $ case, the amplitude of oscillation increases linearly with the flow speed except for a series of regimes that occur when the vortex shedding frequency is in the vicinity of an odd-integer multiple of the galloping oscillation frequency, and the vortex shedding synchronizes to this multiple of the oscillation frequency. It is shown that only odd-integer multiple synchronizations should occur. These synchronizations explain the ‘kinks’ in the galloping amplitude response for light bodies first observed by Bearman et al. (J. Fluids Struct., vol. 1, 1987, pp. 19–34). For the ${{\alpha }}=45^\circ $ case, the VIV response consists of a number of subtle, but distinctly different regimes, with five regimes of high-amplitude oscillations, compared to two found in the classic VIV studies of a circular cylinder. For the intermediate ${{\alpha }}=20^\circ $ case, a typical VIV ‘upper branch’ occurs followed by a ‘higher branch’ of very large-amplitude response. The higher branch is caused by a subharmonic synchronization between the vortex shedding and the body oscillation frequency, where two cycles of vortex shedding occur over one cycle of oscillation. It appears that this subharmonic synchronization is a direct result of the asymmetric body. Overall, the FIV of the square cylinder is shown to be very rich, with a number of distinct regimes, controlled by both ${{\alpha }}$ and ${U^{*}}$. Importantly, ${{\alpha }}$ controls the underlying FIV phenomenon, as well as controlling the types of possible synchronization between the oscillation and vortex shedding.

The gravitational exchange of two fluids with different densities between reservoirs connected by a channel of constant depth and slowly varying breadth is analysed as a problem of internal hydraulics. It is shown that maximal two-way exchange with a net barotropic flow requires the presence of two controls, one at the narrrowest section and a second or ‘virtual’ control lying to one side of the narrowest section. The two controls are connected by a subcritical region, but are separated from subcritical conditions in the reservoirs by supercritical flow and stationary internal bores. Solutions are found for maximal exchange without a net barotropic component, in which case the problem is similar to that first examined by Stommel & Farmer (1953). The Stommel & Farmer analysis is shown to be a rather special limiting example of submaximal exchange, not generally applicable to natural flows. The addition of a net barotropic flow yields a range of different flow types, including maximal exchange, one-layer baroclinic flow, one-layer barotropic flow, submaximal flow governed by a reservoir condition and two-layer unidirectional flow. The maximal-exchange solution is integrated for periodic barotropic flow.

A new definition of concentration fluctuations in turbulent flows is proposed. The definition implicitly incorporates smearing effects of molecular diffusion and instrumental averaging. A stochastic model of two-particle dispersion, consistent with this definition, is formulated. The stochastic model is an extension of Taylor's (1921) model and is consistent with Richardson's $\frac{4}{3}$ law. Its predictions of concentration fluctuations are contrasted with predictions based on a more usual one-particle model.

The present model is used to predict fluctuations in three case studies. For example (case (i) of § 6), downstream of a linear concentration gradient we find $\overline{c^{\prime 2}}=\frac{1}{2}m^2(\overline{Z^2}-\overline{\Delta^2})$. Here m is the linear gradient, $\overline{Z^2}$ is related to centre-of-mass dispersion and $\overline{\Delta^2}$ is related to relative dispersion (see equation (3.1)). The term $\frac{1}{2}m^2\overline{Z^2} $ represents net production of fluctuations by random centre-of-mass dispersion, whereas $\frac{1}{2}m^2\overline{\Delta^2} $ represents net destruction of fluctuations by relative dispersion. Only the first term is included in the usual one-particle model (Corrsin 1952).

We present experimental results for the acoustic field of jets with Mach numbers between 0.35 and 0.6. An azimuthal ring array of six microphones, whose polar angle, , was progressively varied, allows the decomposition of the acoustic pressure into azimuthal Fourier modes. In agreement with past observations, the sound field for low polar angles (measured with respect to the jet axis) is found to be dominated by the axisymmetric mode, particularly at the peak Strouhal number. The axisymmetric mode of the acoustic field can be clearly associated with an axially non-compact source, in the form of a wavepacket: the sound pressure level for peak frequencies is found be superdirective for all Mach numbers considered, with exponential decay as a function of , where is the Mach number based on the phase velocity of the convected wave. While the mode spectrum scales with Strouhal number, suggesting that its energy content is associated with turbulence scales, the axisymmetric mode scales with Helmholtz number – the ratio between source length scale and acoustic wavelength. The axisymmetric radiation has a stronger velocity dependence than the higher-order azimuthal modes, again in agreement with predictions of wavepacket models. We estimate the axial extent of the source of the axisymmetric component of the sound field to be of the order of six to eight jet diameters. This estimate is obtained in two different ways, using, respectively, the directivity shape and the velocity exponent of the sound radiation. The analysis furthermore shows that compressibility plays a significant role in the wavepacket dynamics, even at this low Mach number. Velocity fluctuations on the jet centreline are reduced as the Mach number is increased, an effect that must be accounted for in order to obtain a correct estimation of the velocity dependence of sound radiation. Finally, the higher-order azimuthal modes of the sound field are considered, and a model for the low-angle sound radiation by helical wavepackets is developed. The measured sound for azimuthal modes 1 and 2 at low Strouhal numbers is seen to correspond closely to the predicted directivity shapes.

The deformation and conditions for breakup of a single slender drop placed symmetrically in a uniaxial extensional flow are examined theoretically. For the case of an inviscid drop in zero-Reynolds-number flow, Buckmaster (1972) showed, using slender-body analysis, that the shape of the drop is given by r≡εR(z)=ε(1−|z|ν)/2ν, where εεγ/Gμl and γ is the interfacial tension, G the strength of the extensional flow, μ the viscosity of the suspending fluid and l the drop half-length; also v = ½P − 1, where P is the unknown constant pressure inside the drop rendered dimensionless with respect to Gμ. By requiring that R be analytic at z = 0, Buckmaster then concluded that v had to be an even integer and thereby obtained a countably infinite set of slender profiles for any (large) value of the flow strength G. In the present work, the expression for R(z) shown above is obtained readily using the method of inner and outer expansions, the method failing when |z|[les ]O(ε) and ν is not an even integer. Thus, in general, a new solution is needed to describe the shape within the ‘singular’ region |z|[les ]O(ε). The requirement that the two solutions match in their domain of overlap then leads to the conclusion that v can be either equal to 2 or greater than or equal to 3. However, a stability analysis reveals that only the solution with v = 2 is stable, and hence a unique shape exists.

Next, drops of low viscosity μi = O(ε2μ) are examined in zero-Reynolds-number flow. Here, again, a unique solution is obtained according to which a steady shape cannot exist if (Gμa/γ) (μi/μ)⅙ > 0·148, where $a \equiv(3V4\pi)^{\frac{1}{3}}$ and V is the volume of the drop. This breakup criterion is identical to that found by Taylor (1964). A similar analysis for the case of an inviscid drop in a flow with non-zero Reynolds number shows that drop breakup will occur if $(G\mu a/\gamma) (\rho a\gamma/\mu^2)^{\frac{1}{5}} > 0.284$, where ρ is the density of the suspending fluid. Finally, when μi = O(ε2μ) and inertial effects are neglected within the drop but retained in the surrounding fluid, the critical value of $(G\mu a/\gamma) (\rho a\gamma/\mu^2)^{\frac{1}{5}}$ required for drop breakup is found as a function of the dimensionless group \[ (\rho a\gamma/\mu^2)^{\frac{1}{5}}(\mu/\mu_i)^{\frac{1}{6}}, \] which depends only on the physical properties of the system and the size of the drop. These last two results are the first which take into account inertial effects in determining the deformation and breakup conditions of a drop placed in a shear field.

Burst structures in the near wall region of turbulent flows are associated with a large portion of the turbulent momentum transport from the wall. However, quantitative measures of the timescales associated with the burst event are not well defined, largely due to ambiguities associated with the methods used to detect a burst.

In the present study, Eulerian burst-detection schemes were developed through extensions of the uv quadrant 2, VITA, and u-level techniques. Each of the basic techniques detects ejections. One or more ejections are contained in each burst and hence the key idea is to identify and to group those ejections from a single burst into a single-burst detection. When the ejection detections were grouped appropriately into burst detections, all of the extended techniques yielded the same average time between bursts as deduced from flow visualization for fully-developed channel flow in the range 8700 [les ] Reh [les ] 17 800. The present results show that inner variables (wall shear stress and kinematic viscosity) are the best candidates for the proper scaling of the average time between bursts. Conditional velocity sampling during burst and ejection detections shows that these burst events are closely correlated with slower-than-average moving fluid, moving both away from the wall and toward the wall.

Flapping wings often feature a leading-edge vortex (LEV) that is thought to enhance the lift generated by the wing. Here the lift on a wing featuring a leading-edge vortex is considered by performing experiments on a translating flat-plate aerofoil that is accelerated from rest in a water towing tank at a fixed angle of attack of 15°. The unsteady flow is investigated with dye flow visualization, particle image velocimetry (PIV) and force measurements. Leading- and trailing-edge vortex circulation and position are calculated directly from the velocity vectors obtained using PIV. In order to determine the most appropriate value of bound circulation, a two-dimensional potential flow model is employed and flow fields are calculated for a range of values of bound circulation. In this way, the value of bound circulation is selected to give the best fit between the experimental velocity field and the potential flow field. Early in the trajectory, the value of bound circulation calculated using this potential flow method is in accordance with Kelvin’s circulation theorem, but differs from the values predicted by Wagner’s growth of bound circulation and the Kutta condition. Later the Kutta condition is established but the bound circulation remains small; most of the circulation is contained instead in the LEVs. The growth of wake circulation can be approximated by Wagner’s circulation curve. Superimposing the non-circulatory lift, approximated from the potential flow model, and Wagner’s lift curve gives a first-order approximation of the measured lift. Lift is generated by inertial effects and the slow buildup of circulation, which is contained in shed vortices rather than bound circulation.

Statistical properties of the subgrid-scale stress tensor, the local energy flux and filtered velocity gradients are analysed in numerical simulations of forced three-dimensional homogeneous turbulence. High Reynolds numbers are achieved by using hyperviscous dissipation. It is found that in the inertial range the subgrid-scale stress tensor and the local energy flux allow simple parametrization based on a tensor eddy viscosity. This parametrization underlines the role that negative skewness of filtered velocity gradients plays in the local energy transfer. It is found that the local energy flux only weakly correlates with the locally averaged energy dissipation rate. This fact reflects basic difficulties of large-eddy simulations of turbulence, namely the possibility of predicting the locally averaged energy dissipation rate through inertial-range quantities such as the local energy flux is limited. Statistical properties of subgrid-scale velocity gradients are systematically studied in an attempt to reveal the mechanism of local energy transfer.