This paper details experiments in the region where an impulsively started moving wall slides under a stationary wall. The experiments were conducted over a Reynolds number range of ReΓ=5×102–5×105. The length scale for the Reynolds number is defined as the distance the wall has moved from rest and increases during an experiment. Experiments show that for ReΓ>103 a vortex forms close to the junction where the moving wall meets the stationary one. The data shows that while the vortical structure is small, in relation to the fixed-apparatus length scale, the size of the vortex normalized with respect to the wall speed and viscosity scales in a universal fashion with respect to ReΓ. The scaling rate is proportional to t5/6 when the Reynolds number is large. The kinematic behaviour of the vortex is related to the impulse that the moving wall applies to the fluid and results in a prediction that the transient structure should grow as t5/6 and the velocity field should scale as t−1/6. The spatial-growth prediction is in good agreement with the experimental results and the velocity scaling is moderately successful in collapsing the experimental data.

For ReΓ>2×104 three-dimensional instabilities appear on the perimeter of the vortical structure and the flow transitions from an unsteady two-dimensional flow to a strongly three-dimensional vortical structure at ReΓ≃ 4 × 104. The instability mechanism is centrifugal. The formation and growth of these instability structures and their ingestion into the primary vortex core causes the three-dimensional breakdown of the primary vortex. Two movies are available with the online version of the paper.

Direct numerical simulation (DNS) and large-eddy simulation (LES) are carried out to investigate the frequency effect of zero-net-mass-flux forcing (synthetic jet) on a generic separated flow. The selected test case is a rounded ramp at a Reynolds number based on the step height of 28 275. The incoming boundary layer is fully turbulent with Rθ=1410. The whole flow in the synthetic jet cavity is computed to ensure an accurate description of the actuator effect on the flow field. In a first step, DNS is used to validate LES of this particular flow. In a second step, the effect of a synthetic jet at two reduced frequencies of 0.5 and 4 (based on the separation length of the uncontrolled case and the free-stream velocity) is investigated using LES. It is demonstrated that, with a proper choice of the oscillating frequency, separation can be drastically reduced for a velocity ratio between the jet and the flow lower than one. The low frequency is close to the natural vortex shedding frequency. Two different modes of the synthetic jet have been identified. A vorticity-dominated mode is observed in the low-frequency forcing case for which the separation length is reduced by 54%, while an acoustic-dominated mode is identified in the high-frequency forcing case for which the separation length is increased by 43%. The decrease of the separation length in the low-frequency forcing case is correlated with an increase of the turbulent kinetic energy level and consequently with an increase of the entrainment in the separated zone. A linear inviscid stability analysis shows that the increase of the separation length in the high-frequency forcing case is due to a modification of the mean velocity profile suggested by Stanek and coworkers. The result is a lower amplification of the perturbations and consequently, a lower entrainment into the mixing layer. To our knowledge, it is the first time that Stanek's hypothesis has been assessed, thanks to numerical simulations of fully turbulent flow.

Direct numerical simulation is used to study a round turbulent jet in a laminar crossflow. The ratio of bulk jet velocity to free-stream crossflow velocity is 5.7 and the Reynolds number based on the bulk jet velocity and the jet exit diameter is 5000. The mean velocity and turbulent intensities from the simulations are compared to data from the experiments by Su & Mungal (2004) and good agreement is observed. Additional quantities, not available from experiments, are presented. Turbulent kinetic energy budgets are computed for this flow. Examination of the budgets shows that the near field is far from a state of turbulent equilibrium – especially along the jet edges. Also – in the near field – peak kinetic energy production is observed close to the leading edge, while peak dissipation is observed toward the trailing edge of the jet. The results are used to comment upon the difficulty involved in predicting this flow using RANS computations. There exist regions in this flow where the pressure transport term, neglected by some models and poorly modelled by others, is significant. And past the jet exit, the flow is not close to established canonical flows on which most models appear to be based.

The flow behaviour associated with the cooling of an initially quiescent isothermal Newtonian fluid with Prandtl number Pr less than unity in a rectangular container by unsteady natural convection with an imposed lower temperature on vertical sidewalls is investigated by scaling analysis and direct numerical simulation. The flow is dominated by two distinct stages of development. i.e the boundary-layer development stage adjacent to the sidewall and the subsequent cooling-down stage. The first stage can be further divided into a start-up stage, transitional stage, and steady-state stage. The parameters characterizing the flow behaviour are the boundary-layer thickness, the maximum vertical velocity within the boundary layer, the time for the boundary layer to reach the steady state, the Nusselt number across the sidewall at the boundary-layer development stage, the time for the fluid in the container to be fully cooled down, and the average fluid temperature over the whole volume of the container.

A numerical and experimental modelling study was carried out in a curved tube to analyse the behaviour of unsteady flows in a bend. Based on a test bench, with no mechanical disturbances, the flow behaviour was observed using fluorescein injection. Velocity measurements were performed using hot-film anemometry. In addition, a finite volume method was used to perform three-dimensional unsteady numerical simulations. Womersley parameter values between 8 and 21 and Dean number values between 110 and 420 were used to assess the parameters affecting the flow behaviour. Secondary motions were observed, experimentally and numerically, showing the complexity of the flow patterns. The initiation and subsequent development are explained quantitatively. Based on our analysis of the starting effect, the secondary patterns were found to be highly dependent on both the initial conditions and the flow waveforms.

Instability and transition to turbulence in a temporally evolving free shear layer of an electrically conducting fluid affected by an imposed parallel magnetic field is investigated numerically. The case of low magnetic Reynolds number is considered. It has long been known that the neutral disturbances of the linear problem are three-dimensional at sufficiently strong magnetic fields. We analyse the details of this instability solving the generalized Orr–Sommerfeld equation to determine the wavenumbers, growth rates and spatial shapes of the eigenmodes. The three-dimensional perturbations are identified as oblique waves and their properties are described. In particular, we find that at high hydrodynamic Reynolds number, the effect of the strength of the magnetic field on the fastest growing perturbations is limited to an increase of their oblique angle. The dimensions and spatial shape of the waves remain unchanged. The transition to turbulence triggered by the growing oblique waves is investigated in direct numerical simulations. It is shown that initial perturbations in the form of superposition of two symmetric waves are particularly effective in inducing three-dimensionality and turbulence in the flow.

The spatial signatures of retrograde spanwise vortices in wall turbulence are assessed from particle-image velocimetry measurements in the streamwise–wall-normal plane of a zero-pressure-gradient turbulent boundary layer at Reτ≡u*δ/ν=2350. The present results suggest that a proportion of retrograde spanwise vortices have a well-defined spatial relationship with neighbouring prograde vortices. Two-point cross-correlations and conditionally averaged velocity fields given a retrograde vortex reveal that such structures are typically oriented either upstream of and below or downstream of and above a prograde core. While these pairings are consistent with the typical-eddy patterns reported by Falco and co-workers, we offer an alternative interpretation for a proportion of these retrograde/prograde pairs. In particular, the arrangement of a retrograde spanwise vortex upstream of and below a prograde core is also consistent with the spatial signature revealed if an omega-shaped hairpin structure were sliced through its shoulder region by a fixed streamwise–wall-normal measurement plane.

This paper considers the incompressible two-dimensional laminar flow around a square cylinder symmetrically positioned in a channel. In this type of flow, even if vortices of opposite sign are alternately shed from the body into the wake as in the unconfined case, an inversion of their position with respect to the flow symmetry line takes place further downstream. A numerical analysis is carried out to investigate the physical origin of this phenomenon and to characterize the position in the wake at which the vortices cross the symmetry line. It is shown that, for low to moderate blockage ratios, the fundamental cause of the inversion of the vortices is the amount of vorticity present in the incoming flow, and a dynamic interpretation in terms of vorticity interference in the wake is given. Further insight is gained through a linear stability analysis of the vortex shedding instability.

Fluidic assembly provides solutions for assembling particles with sizes from nanometres to centimetres. Fluidic techniques based on patterned shapes of monolayers and capillary forces are widely used to assemble microfabrication devices. Usually, for self-assembly, the precondition is that the components must be mobile in a fluidic environment. In the present work, a shape-directed fluidic self-assembly of rod-like microstructures, such as an optical fibre on a wettable pad is demonstrated experimentally with submicrometre positioning precision. A model of the process is proposed, which accounts for the following two stages of the orientation of a fibre submerged in a sessile drop: (i) the drop melting and spreading over a wettable pad; (ii) fibre reorientation related to the surface-tension-driven shrinkage of the drop surface area. At the end of stage (ii), the fibre is oriented along the pad. The experimental results for the optical-fibre assembly by a solder joint have been compared to the modelling results, and a reasonable agreement has been found. The major outcome of the experiments and modelling is that surface tension forces on the fibre piercing a drop align the fibre rather than the flow owing to the spreading of the drop over the horizontal pad, i.e. stage (ii) mostly contributes to the alignment.

Non-dispersive and weakly dispersive single-layer flows over axisymmetric obstacles, of non-dimensional height M measured relative to the layer depth, are investigated. The case of transcritical flow, for which the Froude number F of the oncoming flow is close to unity, and that of supercritical flow, for which F > 1, are considered. For transcritical flow, a similarity theory is developed for small obstacle height and, for non-dispersive flow, the problem is shown to be isomorphic to that of the transonic flow of a compressible gas over a thin aerofoil. The non-dimensional drag exerted by the obstacle on the flow takes the form D(Γ) M5/3, where Γ = (F-1)M−2/3 is a transcritical similarity parameter and D is a function which depends on the shape of the ‘equivalent aerofoil’ specific to the obstacle. The theory is verified numerically by comparing results from a shock-capturing shallow-water model with corresponding solutions of the transonic small-disturbance equation, and is found to be generally accurate for M≲0.4 and |Γ| ≲ 1. In weakly dispersive flow the equivalent aerofoil becomes the boundary condition for the Kadomtsev–Petviashvili equation and (multiple) solitary waves replace hydraulic jumps in the resulting flow patterns.

For Γ ≳ 1.5 the transcritical similarity theory is found to be inaccurate and, for small M, flow patterns are well described by a supercritical theory, in which the flow is determined by the linear solution near the obstacle. In this regime the drag is shown to be , where cd is a constant dependent on the obstacle shape. Away from the obstacle, in non-dispersive flow the far-field behaviour is known to be described by the N-wave theory of Whitham and in dispersive flow by the Korteweg–de Vries equation. In the latter case the number of emergent solitary waves in the wake is shown to be a function of , where δ is the ratio of the undisturbed layer depth to the radial scale of the obstacle.

Turbulent buoyant plumes in cold fresh water are analysed, assuming a quadratic dependence of density on temperature. The model is based on the assumption that entrainment velocity is proportional to vertical velocity in the plume. Numerical and asymptotic solutions are obtained for both rising and descending plumes from virtual sources with all possible combinations of buoyancy, volume and momentum fluxes. Physical sources can be identified as points on trajectories of plumes from virtual sources.

The zero-buoyancy condition, at which the plume and the ambient have equal densities but their temperatures are on opposite sides of the temperature of maximum density, is of particular importance. If an upwardly buoyant plume rising through a body of water reaches the surface before passing through its zero-buoyancy level, it will form a surface gravity current; otherwise, the plume water will return to the source as a fountain. The height at which zero buoyancy is attained generally decreases as the source momentum flux increases: greater plume velocity produces greater entrainment and hence more rapid temperature change. Descending plumes, if ejected downwards against upward buoyancy, may be classified as strongly or weakly forced according to whether they reach the zero-buoyancy condition before being brought to rest. If they do, they continue to descend with favourable buoyancy; otherwise, they may form an inverted fountain. Once a descending plume has attained downward buoyancy, it can continue to descend indefinitely, ultimately behaving like a plume in a fluid with a linear equation of state. In contrast, a rising plume will eventually come to rest, however large its initial upward buoyancy and momentum fluxes are.

Two asymptotic analyses of the generation of lee waves by horizontal flow at velocity U of a stratified fluid of buoyancy frequency N past a sphere of radius a are presented, for either weak or strong stratification, corresponding to either large or small internal Froude number F=U/(Na), respectively. For F⋙1, the fluid separates into two regions radially: an inner region of scale a with three-dimensional irrotational flow unaffected by the stratification, and an outer region of scale U/N with small-amplitude lee waves generated by the O(1) vertical motion in the inner region. For F⋘1, the fluid separates into five layers vertically: from the lower dividing streamsurface situated at a distance U/N above the bottom of the sphere to the upper dividing streamsurface situated at a distance U/N below the top, there is a middle layer with two-dimensional horizontal irrotational flow; from the upper dividing streamsurface to the top of the sphere, and from the lower dividing streamsurface to the bottom, there are top and bottom transition layers, respectively, with three-dimensional flow; above the top and below the bottom, there are upper and lower layers, respectively, with small-amplitude lee waves generated by the O(F) vertical motion in the transition layers.

The waves are calculated where they have small amplitudes. The forcing is represented by a source of mass: for F⋙1, the surface distribution of singularities equivalent to the sphere in three-dimensional irrotational flow; for F⋘1, the horizontal distribution of singularities equivalent, in the upper (resp. lower) layer, to the flat cut-off obstacle made up of the top (resp. bottom) portion of the sphere protruding above (resp. below) the upper (resp. lower) dividing streamsurface. The analysis is validated by comparison of the theoretical wave drag with existing experimental determinations. For F⋙1, the drag coefficient decreases as (ln F+7/4-γ)/(4F4), with γ the Euler constant; for F⋘1, it increases as . The waves have the crescent shape of the three-dimensional lee waves from a dipole, modulated by interferences associated with the finite size of the forcing. For strong stratification, the hydrostatic approximation is seen to produce correct leading-order drag, but incorrect waves.

In this work, natural convection in a differentially heated binary mixture is studied analytically and numerically. The fluid is subjected to the Soret effect and is contained in a shallow rectangular porous cavity. All four faces are exposed to uniform heat fluxes, opposite faces being heated and cooled, respectively. Analytical solutions for the stream function, temperature and concentration fields are obtained using a parallel flow assumption in the core region of the cavity and an integral form of the energy and constituent equations. Numerical confirmation of the analytical predictions is also obtained. Results are presented first in the presence of a vertical temperature gradient (a = 0) for which the solution takes the form of a standard Bénard bifurcation. For this situation, steady bifurcations are either pitchfork or subcritical, depending on the separation parameter ϕ and Lewis number Le. The imperfection brought by a horizontal temperature gradient (a≠0) to the bifurcation is then investigated. Both the nonlinear analytical model and the numerical solution indicate that, depending on a, ϕ and Le, the onset of motion occurs through subcritical bifurcations. The existence of transcritical bifurcations is also demonstrated. The special case where the buoyancy forces induced by the thermal and solutal forces are opposing and of equal intensity (ϕ =-1) is also discussed. For this particular situation, the supercritical Rayleigh number for the onset of convection is predicted on the basis of a linear stability analysis. Multiple steady states near the threshold of convection are found.

We study the dewetting of a porous plate withdrawn from a liquid bath. The contact angle is fixed to zero and the flow is assumed to be almost parallel to the plate (lubrication approximation). The ordinary differential equation involving the position of the water surface is analysed in phase space by means of numerical integration. We show the existence of a stationary moving contact line with zero contact angle below a critical value of the capillary number η U/γ. Above this value, no stationary contact line can exist. An analytical model, based on asymptotic matching is developed, which reproduces the dependence of the critical capillary number on the angle of the plate with respect to the horizontal (3/2 power law), provided the capillary length is much larger than the square root of the porous-medium permeability. In addition, it is shown that the classical lubrication equation leads not only to the well-known Landau–Levich–Derjaguin films, but also to a family of films for which thickness is not imposed by the problem parameters.

An advanced moving-wall control strategy to manage the unsteady separated flow over a circular cylinder is developed. A two-dimensional numerical simulation of the flow over the cylinder at Re=500 based on diameter indicates that, when the downstream half of the cylinder surface is made flexible to form an appropriate travelling transverse wave, a ‘fluid roller bearing’ (FRB) is produced consisting of a row of vortices trapped by each wave trough, which can keep the global flow attached against a strong adverse pressure gradient, eliminating the vortex shedding and reducing the average drag by 85%. Physically, the FRB serves as a sheath to effectively inhibit the momentum–energy exchange between the thin fluid layer adjacent to the wall and the main stream, so that the wall layer is scaled only to the local wavelength and frequency and is independent of the global scales. Therefore, the global adverse pressure gradient on the lee side of the cylinder no longer influences the near-wall flow, and the common root cause of flow separation is removed. The input power for actuating the flexible wall is found to be 94% of the power saving due to drag reduction.

This paper presents an experimental study on the propagation speed of gravity currents at moderate values of a gravity Reynolds number. Two cases are considered: gravity currents propagating along a rigid boundary and intrusive gravity currents. For the first case, a semi-empirical formula for the front propagation speed derived from simple energy arguments is shown to capture well the effect of flow deceleration because of viscous dissipation. In the second case, the propagation speed is shown to agree with the one predicted for energy-conserving virtually inviscid flows (Shin, Dalziel & Linden, J. Fluid Mech. vol. 521, 2004, p. 1), which implies that the losses due to vorticity generation and mixing at the liquid–liquid interface play only a minor role in the total balance of energy.

Lagrangian auto- and cross-correlation functions of the rate of strain s2, enstrophy ω2, their respective production terms −sijsjkski and ωiωjsij, and material derivatives, Ds2/Dt and Dω2/Dt are estimated using experimental results obtained through three-dimensional particle tracking velocimetry (three-dimensional-PTV) in homogeneous turbulence at Reλ=50. The autocorrelation functions are used to estimate the Lagrangian time scales of different quantities, while the cross-correlation functions are used to clarify some aspects of the interaction mechanisms between vorticity ω and the rate of strain tensor sij, that are responsible for the statistically stationary, in the Eulerian sense, levels of enstrophy and rate of strain in homogeneous turbulent flow. Results show that at the Reynolds number of the experiment these quantities exhibit different time scales, varying from the relatively long time scale of ω2 to the relatively shorter time scales of s2, ωiωjsij and −sijsjkski. Cross-correlation functions suggest that the dynamics of enstrophy and strain, in this flow, is driven by a set of different-time-scale processes that depend on the local magnitudes of s2 and ω2. In particular, there are indications that, in a statistical sense, (i) strain production anticipates enstrophy production in low-strain–low-enstrophy regions (ii) strain production and enstrophy production display high correlation in high-strain–high-enstrophy regions, (iii) vorticity dampening in high-enstrophy regions is associated with weak correlations between −sijsjkski and s2 and between −sijsjkski and Ds2/Dt, in addition to a marked anti-correlation between ωiωjsij and Ds2/Dt. Vorticity dampening in high-enstrophy regions is thus related to the decay of s2 and its production term, −sijsjkski.

We study numerically the scale-to-scale transfers of enstrophy and passive-tracer variance in two-dimensional turbulence, and show that these transfers display significant differences in the inertial range of the enstrophy cascade. While passive-tracer variance always cascades towards small scales, enstrophy is characterized by the simultaneous presence of a direct cascade in hyperbolic regions and of an inverse cascade in elliptic regions. The inverse enstrophy cascade is particularly intense in clusters of small-scales elliptic patches and vorticity filaments in the turbulent background, and it is associated with gradient-decreasing processes. The inversion of the enstrophy cascade, already noticed by Ohkitani (Phys. Fluids A, vol. 3, 1991, p. 1598), appears to be the main difference between vorticity and passive-tracer dynamics in incompressible two-dimensional turbulence.

Liu & Orfila (J. Fluid Mech. vol. 520, 2004, p. 83) derived analytical solutions for viscous boundary layer flows under transient long waves. Their analytical solutions were obtained with the assumption that the nonlinear inertia force was negligible in the momentum equations. In this paper, using Liu & Orfila's solution and the solutions for the nonlinear boundary layer equations, we examine the boundary layer flow characteristics under a solitary wave. It is found that while the horizontal component of the free-stream velocity outside the boundary layer always moves in the direction of wave propagation, the fluid particle velocity near the bottom inside the boundary layer reverses direction as the wave decelerates. Consequently, the bed shear stress also changes sign during the deceleration phase. Laboratory measurements, including the free-surface displacement, particle image velocimetry (PIV) resolved velocity fields of the viscous boundary layer, and the calculated bed shear stress were also collected to check the theoretical results. Excellent agreement is observed.

Acoustic Doppler velocity profiler (ADVP) measurements of instantaneous three-dimensional velocity profiles over the entire turbulent boundary layer height, δ, of rough-bed open-channel flows at moderate Reynolds numbers show the presence of large scale coherent shear stress structures (called LC3S herein) in the zones of uniformly retarded streamwise momentum. LC3S events over streamwise distances of several boundary layer thicknesses dominate the mean shear dynamics. Polymodal histograms of short streamwise velocity samples confirm the subdivision of uniform streamwise momentum into three zones also observed by Adrian et al. (J. Fluid Mech., vol. 422, 2000, p. 1). The mean streamwise dimension of the zones varies between 1δ and 2.5δ. In the intermediate region (0.2<z/δ<0.75), the contribution of conditionally sampled u'w' events to the mean vertical turbulent kinetic energy (TKE) flux as a function of threshold level H is found to be generated by LC3S events above a critical threshold level Hmax for which the ascendant net momentum flux between LC3S of ejection and sweep types is maximal. The vertical profile of Hmax is nearly constant over the intermediate region, with a value of 5 independent of the flow conditions. Very good agreement is found for all flow conditions including the free-stream shear flows studied in Adrian et al. (2000). If normalized by the squared bed friction velocity, the ascendant net momentum flux containing 90% of the mean TKE flux is equal to 20% of the shear stress due to bed friction. In the intermediate region this value is nearly constant for all flow conditions investigated herein. It can be deduced that free-surface turbulence in open-channel flows originates from processes driven by LC3S, associated with the zonal organization of streamwise momentum. The good agreement with mean quadrant distribution results in the literature implies that LC3S identified in this study are common features in the outer region of shear flows.