Since its foundation over 50 years ago by George Batchelor, the Journal of Fluid Mechanics has published theoretical, computational and experimental investigations on all aspects of the mechanics of fluids. Over this time, the research community of talented scientists, engineers and mathematicians contributing to the astonishing development of our understanding of fluid flow has grown enormously. This growth has naturally been reflected in the growth of the Journal. In 1956 there were 39 papers published in a single volume of 672 pages, while in 2008 there were 450 papers, extending over nearly 11000 pages and 24 volumes. The array of topics considered has similarly broadened hugely, as a quick scan of the titles of the papers can verify. Building on traditional fields such as aerodynamics, geophysical flows and wave phenomena, research into fluid dynamics has spread into new and exciting areas such as biological flow, granular media, and flows on extremely small physical and time scales.

Turbulent flows near walls have been the focus of intense study since their first description by Ludwig Prandtl over 100 years ago. They are critical in determining the drag and lift of an aircraft wing for example. Key challenges are to understand the physical mechanisms causing the transition from smooth, laminar flow to turbulent flow and how the turbulence is then maintained. Recent direct numerical simulations have contributed significantly towards this understanding.

A nominally-zero-pressure-gradient incompressible boundary layer over a smooth flat plate was simulated for a continuous momentum thickness Reynolds number range of 80 ≤ Reθ ≤ 940. Transition which is completed at approximately Reθ = 750 was triggered by intermittent localized disturbances arising from patches of isotropic turbulence introduced periodically from the free stream at Reθ = 80. Streamwise pressure gradient is quantified with several measures and is demonstrated to be weak. Blasius boundary layer is maintained in the early transitional region of 80 < Reθ < 180 within which the maximum deviation of skin friction from the theoretical solution is less than 1%. Mean and second-order turbulence statistics are compared with classic experimental data, and they constitute a rare DNS dataset for the spatially developing zero-pressure-gradient turbulent flat-plate boundary layer. Our calculations indicate that in the present spatially developing low-Reynolds-number turbulent flat-plate boundary layer, total shear stress mildly overshoots the wall shear stress in the near-wall region of 2–20 wall units with vanishing normal gradient at the wall. Overshoots as high as 10% across a wider percentage of the boundary layer thickness exist in the late transitional region. The former is a residual effect of the latter. The instantaneous flow fields are vividly populated by hairpin vortices. This is the first time that direct evidence (in the form of a solution of the Navier–Stokes equations, obeying the statistical measurements, as opposed to synthetic superposition of the structures) shows such dominance of these structures. Hairpin packets arising from upstream fragmented Λ structures are found to be instrumental in the breakdown of the present boundary layer bypass transition.

The wakes behind square cylinders with variation in incidence angle are computed over a range of Reynolds numbers to elucidate the three-dimensional stability and dynamics up to a Reynolds number of Re = 300, based on the projected height of the inclined square cylinder. Three-dimensional instability modes are predicted and computed using a linear stability analysis technique and three-dimensional simulations, respectively. Depending on the incidence angle, the flow is found to transition to three-dimensional flow through either a mode A instability, or a subharmonic mode C instability. The mode A instability is predicted as the first-occurring instability at incidence angles smaller than 12° and greater than 26°, with the mode C instability predicted between these incidence angles. At a zero-degree angle of incidence, the wake instabilities closely match modes A, B and a quasi-periodic mode predicted in earlier studies behind square and circular cylinders. With increasing angle of incidence, the three-dimensional wake transition Reynolds number first increases from Re = 164 as the mode A instability weakens, before decreasing again beyond an incidence angle of 12° as the wake becomes increasingly unstable to the mode C instability, and then again to the mode A instability as the incidence angle approaches 45°. A spanwise autocorrelation analysis from computations over a cylinder span 20 times the square cross-section side length reveals that beyond the onset of three-dimensional instabilities, the vortex street breaks down with patterns consistent with spatio-temporal chaos. This effect was more pronounced at higher incidence angles.

We study numerically the viscous phase of horizontal gravity currents of immiscible fluids in the lock-exchange configuration. A numerical technique capable of dealing with stiff density gradients is used, allowing us to mimic high-Schmidt-number situations similar to those encountered in most laboratory experiments. Plane two-dimensional computations with no-slip boundary conditions are run so as to compare numerical predictions with the ‘short reservoir’ solution of Huppert (J. Fluid Mech., vol. 121, 1982, pp. 43–58), which predicts the front position lf to evolve as t1/5, and the ‘long reservoir’ solution of Gratton & Minotti (J. Fluid Mech., vol. 210, 1990, pp. 155–182) which predicts a diffusive evolution of the distance travelled by the front xf ~ t1/2. In line with dimensional arguments, computations indicate that the self-similar power law governing the front position is selected by the flow Reynolds number and the initial volume of the released heavy fluid. We derive and validate a criterion predicting which type of viscous regime immediately succeeds the slumping phase. The computations also reveal that, under certain conditions, two different viscous regimes may appear successively during the life of a given current. Effects of sidewalls are examined through three-dimensional computations and are found to affect the transition time between the slumping phase and the viscous regime. In the various situations we consider, we make use of a force balance to estimate the transition time at which the viscous regime sets in and show that the corresponding prediction compares well with the computational results.

Large coherent structures over vegetation canopies are responsible for a substantial part of the turbulent transfer of momentum, heat and mass between the canopy and the atmosphere. As forested landscapes are often fragmented, edge regions may be of importance in turbulent transfer. The development of coherent structures from the leading edge of a forest is investigated here for the first time. For this purpose, the turbulent flow over a clearing–forest pattern is simulated using the Advanced Regional Prediction System (ARPS). In previous studies the code has been modified so as to simulate turbulent flows at very fine scale (0.1h, where h is the mean canopy height) within and above heterogeneous vegetation canopies, using a large-eddy simulation (LES) approach. Validations have also been performed over homogeneous forest canopies and over a simple forest–clearing–forest pattern, against field and wind-tunnel measurements. Here, a schematic picture of the development of coherent eddies downstream from the leading edge of a forest is extracted from the mean vorticity components, the Q-criterion field, the cross-correlation of the wind velocity components and the length and separation length scales of coherent structures, determined by using a wavelet transform. This schematic picture shows strong similarities with the development of coherent structures observed in a mixing layer, with four different regions: (i) close to the edge, Kelvin–Helmholtz instabilities develop when a strong wind gust hits the canopy; (ii) these instabilities roll over to form transverse vortices from around 3h downstream from the edge, characterized by a length scale close to the depth of the internal boundary layer that develops from the canopy edge; (iii) secondary instabilities destabilize these rollers and increase the vertical and streamwise vorticity components from around 6h, and two counter-rotating streamwise vortices appear; (iv) at about 9h the initial rollers have become complex three-dimensional coherent structures, with spatially constant mean length and separation length scales. These four stages of development occur closer to the edge with increasing canopy density. While this average picture of the development of coherent structures is similar to that observed in a mixing layer, the analysis of instantaneous fields shows that coherent structures behind the leading edge appear as resulting from the ‘branching’ of tubes localized in regions of low pressure, where their cores are characterized by high values of enstrophy and Q-criterion.

The laminar separation bubble on an SD7003 aerofoil at a Reynolds number Re = 66000 was investigated to determine the dominant frequencies of the transition process and the flapping of the bubble. The measurements were performed with a high-resolution time-resolved particle image velocimetry (TR-PIV) system. Contrary to typical measurements performed through conventional PIV, the different modes can be identified by applying TR-PIV. The interaction between the shed vortices is analysed, and their significance for the production of turbulence is presented. In the shear layer above the bubble the generation and amplification of vortices due to Kelvin–Helmholtz instabilities is observed. It is found that these instabilities have a weak coherence in the spanwise direction. In a later stage of transition these vortices lead to a three-dimensional breakdown to turbulence.

This paper examines the evolution of an axisymmetric two-dimensional vortex in a steadily rotating strain field and the dynamical interactions that can enhance vortex spreading through resonant behaviour. Starting with a point vortex localized at the origin, the applied strain field generates a cat's eye topology in the co-rotating streamfunction, localized around a radius rext. Now the vortex is allowed to spread viscously: initially rext lies outside the vortex, but as it spreads, vorticity is advected into the cat's eyes, leading to a local flattening of the mean profile of the vortex and so to enhanced mixing and spreading of the vortex. Together with this is a feedback: the response of the vortex to the external strain depends on the modified profile. The feedback is particularly strong when rext coincides with the radius rcat at which the vortex can support cat's eyes of infinitesimal width. There is a particular time at which this occurs, as these radii change with the viscous spread of the vortex: rext moves inwards and rcat outwards. This resonance behaviour leads to increased mixing of vorticity, along with a rapid stretching of vorticity contours and a sharp increase in the amplitude of the non-axisymmetric components. The dynamical feedback and enhanced diffusion are studied for viscously spreading vortices by means of numerical simulations of their time evolution, parameterized only by the Reynolds number R and the dimensionless strength A of the external strain field.

The dynamics of particles in turbulence when the particle size is larger than the dissipative scale of the carrier flow are studied. Recent experiments have highlighted signatures of particles' finiteness on their statistical properties, namely a decrease of their acceleration variance, an increase of correlation times (at increasing the particles size) and an independence of the probability density function of the acceleration once normalized to their variance. These effects are not captured by point-particle models. By means of a detailed comparison between numerical simulations and experimental data, we show that a more accurate description is obtained once Faxén corrections are included.

Direct numerical simulations (DNS) are performed to investigate the behaviour of a weakly stratified shear layer in the presence of a strongly stratified region beneath it. Both, coherent Kelvin–Helmholtz (KH) rollers and small-scale turbulence, are observed during the evolution of the shear layer. The deep stratification measured by the Richardson number Jd is varied to study its effect on the dynamics. In all cases, a pycnocline is found to develop at the edges of the shear layer. The region of maximum shear shifts downward with increasing time. Internal waves are excited, initially by KH rollers, and later by small-scale turbulence. The wave field generated by the KH rollers is narrowband and of stronger amplitude than the broadband wave field generated by turbulence. Linear theory based on Doppler-shifted frequency of the KH mode is able to predict the angle of the internal wave phase lines during the direct generation of internal waves by KH rollers. Waves generated by turbulence are relatively weaker with a broader range of excitation angles which, in the deep region, tend towards a narrower band. The linear theory that works for the internal waves excited by KH rollers does not work for the turbulence generated waves. The momentum transported by the internal waves into the interior can be large, about 10% of the initial momentum in the shear layer, when Jd ≃ 0.25. Integration of the turbulent kinetic energy budget in time and over the shear layer thickness shows that the energy flux can be up to 17% of the turbulent production, 33% of the turbulent dissipation rate and 75% of the buoyancy flux. These numbers quantify the dynamical importance of internal waves. In contrast to linear theory where the effect of deep stratification on the shear layer instabilities has been found to be weak, the present nonlinear simulations show that the evolution of the shear layer is significantly altered because of the significant momentum and energy carried away by the internal waves.

The response of the mean and turbulent flow structure of a supersonic high-Reynolds-number turbulent boundary layer flow subjected to local and global mechanical distortions was experimentally examined. Local disturbances were introduced via small-scale wall patterns, and global distortions were induced through streamline curvature-driven pressure gradients. Local surface topologies included k-type diamond and d-type square elements; a smooth wall was examined for comparison purposes. Three global distortions were studied with each of the three surface topologies. Measurements included planar contours of the mean and fluctuating velocity via particle image velocimetry, Pitot pressure profiles, pressure sensitive paint and Schlieren photography. The velocity data were acquired with sufficient resolution to characterize the mean and turbulent flow structure and to examine interactions between the local surface roughness distortions and the imposed pressure gradients on the turbulence production. A strong response to both the local and global distortions was observed with the diamond elements, where the effect of the elements extended into the outer regions of the boundary layer. It was shown that the primary cause for the observed response was the result of local shock and expansion waves modifying the turbulence structure and production. By contrast, the square elements showed a less pronounced response to local flow distortions as the waves were significantly weaker. However, the frictional losses were higher for the blunter square roughness elements. Detailed quantitative characterizations of the turbulence flow structure and the associated production mechanisms are described herein. These experiments demonstrate fundamental differences between supersonic and subsonic rough-wall flows, and the new understanding of the underlying mechanisms provides a scientific basis to systematically modify the mean and turbulence flow structure all the way across supersonic boundary layers.

We use slender-body theory to simulate a rigid fibre within simple shear flow and parabolic flow at zero Reynolds number and high Péclet numbers (weak Brownian motion). Hydrodynamic interactions of bulk fibres with the bounding walls are included using previously developed methods (Harlen, Sundararajakumar & Koch, J. Fluid Mech., vol. 388, 1999, pp. 355–388; Butler & Shaqfeh, J. Fluid Mech., vol. 468, 2002, pp. 205–237). We also extend a previous analytic theory (Park, Bricker & Butler, Phys. Rev. E, vol. 76, 2007, 04081) predicting the centre-of-mass distribution of rigid fibre suspensions undergoing rectilinear flow near a wall to compare the steady and transient distributions. The distributions obtained by the simulation and theory are in good agreement at sufficiently high shear rates, validating approximations made in the theory which predicts a net migration of the rigid fibres away from the walls due to a hydrodynamic lift force. The effect of the inhomogeneous distribution on the effective stress is also investigated.

Two-phase viscous gravity current theory has numerous applications in the natural sciences, from small-scale lava, sedimentary and glacial flows, to large-scale flows of partially molten mantle. We develop the general equations for two-phase viscous gravity currents composed of a high viscosity matrix and low viscosity fluid for both constant volume and constant flux conditions. A loss of fluid phase is taken into account at the current's upper boundary and corresponds to the degassing of a lava flow or loss of water in sedimentary flows. As the current spreads, its surface increases and fluid loss is facilitated, which modifies the mixture density and viscosity and thus the current's shape; hence spreading of the flow affects fluid loss and vice-versa. Our results show that two-phase gravity currents retain and transport the fluid out to large distances, but the fluid is almost entirely lost within a region of finite radius. This ‘loss radius’ depends on the flow's volume or flux, fluid and matrix properties as well as on the size of fluid parcels or matrix permeability. Application to lava flows shows that degassing occurs over a large area, which affects gas release and transport in the atmosphere.

The stability of the laminar flow in the narrow gap between infinitely long concentric cylinders, the inner of which rotates, is examined for the case of compliant bounding walls, modelled as thin cylindrical shells supported by rigid frames through arrays of springs and dampers. Sufficiently soft walls have a destabilizing influence on the axisymmetric Taylor vortices produced by the centrifugal force, although the effect is limited to modes with large axial wavelengths. Due to the walls flexibility, hydroelastic modes are generated. Complex modal exchanges are observed, as function of the wall properties and the Reynolds number. For axisymmetric modes an asymptotic analysis is conducted in the limit of small axial wavenumber, to show the correspondence between such exchanges and singularities in the analytical solutions. While the axisymmetric modes dominate the spectrum when the walls are rigid or very mildly compliant, a critical non-zero azimuthal wavenumber exists for which the hydroelastic modes become more unstable. Shorter azimuthal waves are favoured by increasing spring stiffness.

We report an experimental study of the large-scale circulation (LSC) in a turbulent Rayleigh–Bénard convection cell with aspect ratio unity. The temperature-extrema-extraction (TEE) method for obtaining the dynamic information of the LSC is presented. With this method, the azimuthal angular positions of the hot ascending and cold descending flows along the sidewall are identified from the measured instantaneous azimuthal temperature profile. The motion of the LSC is then decomposed into two different modes based on these two angles: the azimuthal mode and the translational or sloshing mode that is perpendicular to the vertical circulation plane of the LSC. Comparing to the previous sinusoidal-fitting (SF) method, it is found that both the TEE and the SF methods give the same information about the azimuthal motion of the LSC, but the TEE method in addition can provide information about the sloshing motion of the LSC. The sloshing motion is found to oscillate time-periodically around the cell's central vertical axis with an amplitude being nearly independent of the turbulent intensity and to have a π/2 phase difference with the torsional mode. It is further found that the azimuthal angular positions of the hot ascending and cold descending flows oscillate out of phase with each other by π, which leads to the observations of the torsional mode when these two flows are near the top and the bottom plates, respectively, and of the sloshing mode when they are both near the mid-height plane. A direct velocity measurement further confirms the existence of the bulk sloshing mode of the flow field.

The formation of sand ripples in oscillating flows is thought to be due to a steady streaming current which near the bottom is towards the crests. We present quantitative observations of this mean flow over self-formed and artificial ripples, by observing the displacement of a coloured filament after a number of oscillations in the simple situation of viscous Couette flow. Confusingly, the filament moves in the ‘wrong’ direction, because it follows the Lagrangian mean flow. We calculate the Lagrangian mean flow. A complication is that the amplitudes of the oscillations in the experiments are not small. We compare the predictions with the experimental observations of displacements of the filament, showing good agreement.

After validation with experimental data, large-eddy simulation (LES) is used to study in detail the open-channel flow through a curved flume. Based on the LES results, the present paper addresses four issues. Firstly, features of the complex bicellular pattern of the secondary flow, occurring in curved open-channel flows, and its origin are investigated. Secondly, the turbulence characteristics of the flow are studied in detail, incorporating the anisotropy of the turbulence stresses, as well as the distribution of the kinetic energy and the turbulent kinetic energy. Moreover, the implications of the pattern of the production of turbulent kinetic energy is discussed within this context. Thirdly, the distribution of the wall shear stresses at the bottom and sidewalls is computed. Fourthly, the effects of changes in the subgrid-scale model and the boundary conditions are investigated. It turns out that the counter-rotating secondary flow cell near the outer bank is a result of the complex interaction between the spatial distribution of turbulence stresses and centrifugal effects. Moreover, it is found that this outer bank cell forms a region of a local increase of turbulent kinetic energy and of its production. Furthermore, it is shown that the bed shear stresses are amplified in the bend. The distribution of the wall shear stresses is deformed throughout the bend due to curvature. Finally, it is shown that changes in the subgrid-scale model, as well as changes in the boundary conditions, have no strong effect on the results.