In fully developed single-phase turbulent flow in straight pipes, it is known that mean motions can occur in the plane of the pipe cross-section, when the cross-section is non-circular, or when the wall roughness is non-uniform around the circumference of a circular pipe. This phenomenon is known as secondary flow of the second kind and is associated with the anisotropy in the Reynolds stress tensor in the pipe cross-section. In this work, we show, using careful laser Doppler anemometry experiments, that secondary flow of the second kind can also be promoted by a non-uniform non-axisymmetric particle-forcing, in a fully developed turbulent flow in a smooth circular pipe. In order to isolate the particle-forcing from other phenomena, and to prevent the occurrence of mean particle-forcing in the pipe cross-section, which could promote a different type of secondary flow (secondary flow of the first kind), we consider a simplified well-defined situation: a non-uniform distribution of particles, kept at fixed positions in the ‘bottom’ part of the pipe, mimicking, in a way, the particle or droplet distribution in horizontal pipe flows. Our results show that the particles modify the turbulence through ‘direct’ effects (associated with the wake of the particles) and ‘indirect’ effects (associated with the global balance of momentum and the turbulence dynamics). The resulting anisotropy in the Reynolds stress tensor is shown to promote four secondary flow cells in the pipe cross-section. We show that the secondary flow is determined by the projection of the Reynolds stress tensor onto the pipe cross-section. In particular, we show that the direction of the secondary flow is dictated by the gradients of the normal Reynolds stresses in the pipe cross-section, and . Finally, a scaling law is proposed, showing that the particle-driven secondary flow scales with the root of the mean particle-forcing in the axial direction, allowing us to estimate the magnitude of the secondary flow.

Experimental studies of the flow topology, leading-edge vortex dynamics and unsteady force produced by pitching and plunging flat-plate aerofoils in forward flight at Reynolds numbers in the range 5000–20 000 are described. We consider the effects of varying frequency and plunge amplitude for the same effective angle-of-attack time history. The effective angle-of-attack history is a sinusoidal oscillation in the range to with mean of and amplitude of . The reduced frequency is varied in the range 0.314–1.0 and the Strouhal number range is 0.10–0.48. Results show that for constant effective angle of attack, the flow evolution is independent of Strouhal number, and as the reduced frequency is increased the leading-edge vortex (LEV) separates later in phase during the downstroke. The LEV trajectory, circulation and area are reported. It is shown that the effective angle of attack and reduced frequency determine the flow evolution, and the Strouhal number is the main parameter determining the aerodynamic force acting on the aerofoil. At low Strouhal numbers, the lift coefficient is proportional to the effective angle of attack, indicating the validity of the quasi-steady approximation. Large values of force coefficients () are measured at high Strouhal number. The measurement results are compared with linear potential flow theory and found to be in reasonable agreement. During the downstroke, when the LEV is present, better agreement is found when the wake effect is ignored for both the lift and drag coefficients.

The evaporation of sessile drops in quiescent air is usually governed by vapour diffusion. For contact angles below , the evaporative flux from the droplet tends to diverge in the vicinity of the contact line. Therefore, the description of the flow inside an evaporating drop has remained a challenge. Here, we focus on the asymptotic behaviour near the pinned contact line, by analytically solving the Stokes equations in a wedge geometry of arbitrary contact angle. The flow field is described by similarity solutions, with exponents that match the singular boundary condition due to evaporation. We demonstrate that there are three contributions to the flow in a wedge: the evaporative flux, the downward motion of the liquid–air interface and the eigenmode solution which fulfils the homogeneous boundary conditions. Below a critical contact angle of , the evaporative flux solution will dominate, while above this angle the eigenmode solution dominates. We demonstrate that for small contact angles, the velocity field is very accurately described by the lubrication approximation. For larger contact angles, the flow separates into regions where the flow is reversing towards the drop centre.

In this paper the pressure field during the early development of turbulent vortex rings at two Reynolds numbers is determined using temporally resolved two-dimensional and stereoscopic particle image velocimetry (PIV). The pressure gradient terms are obtained by solving the incompressible Euler equation so that the drag coefficients of the vortex rings can be evaluated. Maxworthy (J. Fluid Mech., vol. 64, 1974, pp. 227–239) and Glezer & Coles (J. Fluid Mech., vol. 211, 1990, pp. 243–283) each developed models to describe the long-term physics of turbulent vortex rings: the former developed a semi-empirical model which permits loss of impulse via the shedding of vorticity into the wake whereas the latter developed a similarity model based on invariance of the hydrodynamic impulse. Maxworthy’s model implies that a significant correction to the similarity solution is required to account for the drag on the vortex ring bubble. We show that during the early development of the turbulent vortex rings the drag is very small and the similarity scaling can basically be retained.

We present new observations of a controlled transition to turbulence in a fundamental but little-studied regime: circular Couette flow with only the outer cylinder rotating. Our apparatus consists of an outer cylinder of fixed radius and three inner cylinders having different radii that are used interchangeably to study the effect of flow curvature. With the smallest inner cylinder the end-cap configuration (vertical boundary conditions) may also be varied. The turbulent transition is found to be sensitive to both gap width and end-cap configuration, with wider gaps transitioning at higher rotation rates. All configurations are observed to transition with hysteresis and intermittency. A laser Doppler velocimetry (LDV)-based study of the azimuthal velocity profile as a function of gap width and rotation rate reveals that turbulence, once initiated, is confined to regions of significant shear. For wider gap widths, the radial location of these shear layers is determined by the chosen end-cap configuration. This, in turn, affects the transition Reynolds number, which we posit to be radially dependent. The narrow-gap case in particular features spiral turbulence, whose properties are found to be similar to observations of the phenomenon in related shear flows. The velocity profile in this case is correlated with overlapping boundary layers, suggesting a coupling mechanism for the origin of laminar-turbulent banding phenomena.

We derive new analytical results for the hydrodynamic force exerted on a sinusoidally oscillating porous shell and a sphere of uniform density in the Stokes limit. The coupling between the spherical particle and the solvent is done using the Debye–Bueche–Brinkman (DBB) model, i.e. by a frictional force proportional to the local velocity difference between the permeable particle and the solvent. We compare our analytical results and existing dynamic theories to lattice–Boltzmann simulations of the full Navier–Stokes equations for the oscillating porous particle. We find our analytical results to agree with simulations over a broad range of porosities and frequencies.

We study numerically a succession of transitions in pipe Poiseuille flow that lead from simple travelling waves to waves with chaotic time-dependence. The waves at the origin of the bifurcation cascade are twofold azimuthally periodic, shift–reflect symmetric, and have a non-dimensional axial wavelength of diameters. As the Reynolds number is increased, successive transitions result in a wide range of time-dependent solutions that include spiralling, modulated travelling, modulated spiralling, doubly modulated spiralling and mildly chaotic waves. Numerical evidence suggests that the latter spring from heteroclinic tangles of the stable and unstable invariant manifolds of two shift–reflect symmetric, modulated travelling waves. The chaotic set thus produced is confined to a limited range of Reynolds numbers, bounded by the occurrence of manifold tangencies. The subspace of discrete symmetry to which the states studied here belong makes many of the bifurcation and path-following investigations presented readily accessible. However, we expect that most of the phenomenology carries over to the full state space, thus suggesting a mechanism for the formation and break-up of invariant states that can give rise to chaotic dynamics.

The sensitivity of the turbulent flame speed to the geometry of the flame is investigated using direct numerical simulations of turbulent premixed flames in three canonical configurations: freely propagating statistically planar flames, planar flames stabilized in stagnating flows, and rod-stabilized V-flames. We consider both the consumption speed, which measures the integrated rate of burning, and the propagation speed, which measures the speed of an isosurface within the flame brush. An algebraic model for the propagation speed of the leading edge of the flame brush, which is blind to flame geometry, is also applied to the data for the purposes of establishing its range of validity and the causes of its failure. The turbulent consumption speed is found to be strongly geometry dependent, primarily due to the continuous growth of the flame brush thickness. Changes in the structure and consumption speed of instantaneous flame fronts are found to be only weakly sensitive to flame geometry. The turbulent propagation speed is analysed in terms of its reactive, diffusive and turbulent flux components. All three terms are shown to be significant, both through the flame brush and along the leading edge. The leading-edge propagation speed is found to be sensitive to flame geometry only in the V-flames under certain conditions. It is suggested that this apparent geometry dependence, which the model cannot capture, results from the relation between the turbulence and mean flow time scales in these particular cases, and is not intrinsic to the flame geometry itself.

Using data from direct numerical simulations, linear models of the compressible flow past a rectangular cavity are found. The emphasis is on forming simple models which capture the input–output behaviour of the system, and which are useful for feedback controller design. Two different approaches for finding a linear model are investigated. The first involves using input–output data of the linearized cavity flow to form a balanced, reduced-order model directly. The second approach is conceptual, and involves modelling each element of the flow physics separately using simple analytical expressions, the parameters of which are chosen based on simulation data at salient points in the cavity’s computational domain. Both models are validated: first in the time domain by comparing their impulse responses to that of the full system in direct numerical simulations; and second in the frequency domain by comparing their frequency responses. Finally, the validity of both linear models is shown most clearly by using them for feedback controller design, and then applying each controller in direct numerical simulations. Both controllers completely eliminate oscillations, and demonstrate the advantages of model-based feedback controllers, even when the models upon which they are based are very simple.

The capability of state-of-the-art techniques integrating experimental and computational fluid dynamics has been expanding recently. In our previous study, we have developed a hybrid unsteady-flow simulation technique combining particle tracking velocimetry (PTV) and direct numerical simulation (DNS) and demonstrated its capability at low Reynolds numbers. Similar approaches have also been proposed by a few groups; however, applying algorithms of this type generally becomes more challenging with increasing Reynolds number because the time interval of the frame rate for particle image velocimetry (PIV) becomes much greater than the required computational time step, and the PIV/PTV resolution tends to be lower than that necessary for computational fluid dynamics. To extend the applicability to noisy time-resolved PIV/PTV data, the proposed algorithm optimizes the data input temporally and spatially by introducing a reduced-order Kalman filter. This study establishes a framework of the Kalman-filtered hybrid simulation and proves the concept by tackling a planar-jet flow at as an example. We evaluate the filtering functions as well as convergence of the proposed algorithm by comparing with the existing PTV–DNS hybrid simulation, and show some techniques available to hybrid velocity fields by analysing vortical motion in the shear layers of the jet.

The framework of the linearized theory of water waves in the time domain is used to examine the horizontal motion of an unrestrained floating structure. One of the principal assumptions of the theory is that an infinitesimal disturbance of the rest state will lead to an infinitesimal motion of the fluid and structure. It has been known for some time that for some initial conditions the theory predicts an unbounded horizontal motion of the structure that violates this assumption, but the possibility does not appear to have been examined in detail. Here some circumstances that lead to predictions of large motions are identified and, in addition, it is shown that not all non-trivial initial conditions lead to violations of the assumptions. In particular, it is shown that the horizontal motion of a floating structure remains bounded when it is initiated by the start up of a separate wave maker. The general discussion is supported by specific calculations for a vertical circular cylinder.

It was demonstrated recently that gas–liquid interfaces, which are usually almost perfect reflectors of acoustic waves, become anomalously transparent, and the power flux in the wave transmitted into the gas increases dramatically, when a compact sound source in the liquid approaches the interface within a fraction of the wavelength (Godin, Phys. Rev. Lett., vol. 97, 2006b, 164301). Powerful underwater explosions and certain natural sources, such as underwater landslides, generate very low-frequency waves in water and air, for which fluid buoyancy and compressibility simultaneously serve as restoring forces. In this paper, analysis of sound transmission through gas–liquid interfaces is extended to acoustic-gravity waves (AGWs) and applied to the air–water interface. It is found that, as for sound, the interface becomes anomalously transparent for sufficiently shallow compact sources of AGWs. Depending on the source type, the increase of a wave power flux into gas due to diffraction effects can reach several orders of magnitude. The physical mechanisms responsible for the anomalous transparency are discussed. Excitation of an interface wave by a point source in the liquid is shown to be an important channel of AGW transmission into the gas, which has no counterpart in the case of sound.

Blister-actuated laser-induced forward transfer (BA-LIFT) is a versatile printing technique in which fine jets of ink are ejected from a thin donor film onto an acceptor substrate, enabling high-resolution patterns to be formed. Fluid ejections are initiated by the rapid expansion of micrometre-sized blisters that form on a polymer film underneath the ink layer. Recent work has demonstrated that these ejections exhibit novel flow phenomena due to the unique dimensions and geometry of the BA-LIFT configuration. In this work, we study the dynamics of BA-LIFT printing using a computational model in which fluid is forced by a boundary that deforms according to experimental time-resolved measurements of an expanding blister profile. This allows the model’s predictions to be unambiguously correlated with experimental blister-actuated ejections without any fitting parameters. First, we validate the model’s predictive capabilities against experimental results, including the ability to accurately reproduce the size, shape and temporal evolution of the jet as well as the total volume of ink released. The validated model is then used to interrogate the flow dynamics in order to better understand the mechanisms for fluid ejection. Finally, parametric studies are conducted to investigate the influence of ink density, surface tension, viscosity and film thickness as well as the size of the blister used. These results provide key insights into avenues for optimization and better control of the BA-LIFT process for improved resolution and repeatability of the printed features.

We consider the propagation of a shallow-water undular bore over a gentle monotonic bottom slope connecting two regions of constant depth, in the framework of the variable-coefficient Korteweg–de Vries equation. We show that, when the undular bore advances in the direction of decreasing depth, its interaction with the slowly varying topography results, apart from an adiabatic deformation of the bore itself, in the generation of a sequence of isolated solitons – an expanding large-amplitude modulated solitary wavetrain propagating ahead of the bore. Using nonlinear modulation theory we construct an asymptotic solution describing the formation and evolution of this solitary wavetrain. Our analytical solution is supported by direct numerical simulations. The presented analysis can be extended to other systems describing the propagation of undular bores (dispersive shock waves) in weakly non-uniform environments.

A linear stability analysis of the laminar flow in the boundary layer at the bottom of a solitary wave is made to determine the conditions leading to transition and the appearance of turbulence. The Reynolds number of the phenomenon is assumed to be large and a ‘momentary’ criterion of instability is used. The results show that the laminar regime becomes unstable during the decelerating phase, when the height of the solitary wave exceeds a threshold value which depends on the ratio between the boundary layer thickness and the local water depth. A comparison of the theoretical results with the experimental measurements of Sumer et al. (J. Fluid Mech., vol. 646, 2010, pp. 207–231) supports the analysis.

The near field of a Reynolds number and low-Mach-number cylindrical jet has been investigated by means of a high-speed stereo PIV setup that provides the spatio-temporal velocity field in a transverse plane, two diameters downstream of the jet exit. Proper orthogonal decomposition (POD) and spatio-temporal correlations are used to identify some of the main dynamical features of this flow. We show that the flow is dominated by streamwise vortices whose production and spatial organization can be related to and perturbations, and to the mean shear of the mixing layer. A dynamical scenario is proposed which describes this interaction, in accordance with our observations.

The paper presents a model for particle–particle and particle–wall collisions during interface-resolving numerical simulations of particle-laden flows. The accurate modelling of collisions in this framework is challenging due to methodological problems generated by interface approach and contact as well as due to the greatly different time scales involved. To cope with this situation, multiscale modelling approaches are introduced avoiding excessive local grid refinement during surface approach and time step reduction during the surface contact. A new adaptive model for the normal forces in the phase of ‘dry contact’ is proposed, stretching the collision process in time to match the time step of the fluid solver. This yields a physically sound and robust collision model with modified stiffness and damping determined by an optimization scheme. Furthermore, the model is supplemented with a new approach for modelling the tangential force during oblique collisions which is based on two material parameters: a critical impact angle separating rolling from sliding and the friction coefficient for the sliding motion. The resulting new model is termed the adaptive collision model (ACM). All proposed sub-models only contain physical parameters, and virtually no numerical parameters requiring adjustment or tuning. The new model is implemented in the framework of an immersed boundary method but is applicable with any spatial and temporal discretization. Detailed validation against experimental data was performed so that a general and versatile model for arbitrary collisions of spherical particles in viscous fluids is now available.

The vertical structure of freely evolving, continuously stratified, quasi-geostrophic flow is investigated. We predict the final state organization, and in particular its vertical structure, using statistical mechanics and these predictions are tested against numerical simulations. The key role played by conservation laws in each layer, including the fine-grained enstrophy, is discussed. In general, the conservation laws, and in particular that enstrophy is conserved layer-wise, prevent complete barotropization, i.e. the tendency to reach the gravest vertical mode. The peculiar role of the effect, i.e. of the existence of planetary vorticity gradients, is discussed. In particular, it is shown that increasing increases the tendency toward barotropization through turbulent stirring. The effectiveness of barotropization may be partially parameterized using the Rhines scale . As this parameter decreases ( increases) then barotropization can progress further, because the term provides enstrophy to each layer. However, if the effect is too large then the statistical mechanical predictions fail and wave dynamics prevent complete barotropization.

Direct numerical simulations are performed to investigate the transient upstream propagation (flashback) of premixed hydrogen–air flames in the boundary layer of a fully developed turbulent channel flow. Results show that the well-known near-wall velocity fluctuations pattern found in turbulent boundary layers triggers wrinkling of the initially flat flame sheet as it starts propagating against the main flow direction, and that the structure of the characteristic streaks of the turbulent boundary layer ultimately has an important impact on the resulting flame shape and on its propagation mechanism. It is observed that the leading edges of the upstream-propagating premixed flame are always located in the near-wall region of the channel and assume the shape of several smooth, curved bulges propagating upstream side by side in the spanwise direction and convex towards the reactant side of the flame. These leading-edge flame bulges are separated by thin regions of spiky flame cusps pointing towards the product side at the trailing edges of the flame. Analysis of the instantaneous velocity fields clearly reveals the existence, on the reactant side of the flame sheet, of backflow pockets that extend well above the wall-quenching distance. There is a strong correspondence between each of the backflow pockets and a leading edge convex flame bulge. Likewise, high-speed streaks of fast flowing fluid are found to be always colocated with the spiky flame cusps pointing towards the product side of the flame. It is suggested that the origin of the formation of the backflow pockets, along with the subsequent mutual feedback mechanism, is due to the interaction of the approaching streaky turbulent flow pattern with the Darrieus–Landau hydrodynamic instability and pressure fluctuations triggered by the flame sheet. Moreover, the presence of the backflow pockets, coupled with the associated hydrodynamic instability and pressure–flow field interaction, greatly facilitate flame propagation in turbulent boundary layers and ultimately results in high flashback velocities that increase proportionately with pressure.

Particle-size segregation can have a significant feedback on the bulk motion of granular avalanches when the larger grains experience greater resistance to motion than the fine grains. When such segregation-mobility feedback effects occur the flow may form digitate lobate fingers or spontaneously self-channelize to form lateral levees that enhance run-out distance. This is particularly important in geophysical mass flows, such as pyroclastic currents, snow avalanches and debris flows, where run-out distance is of crucial importance in hazards assessment. A model for finger formation in a bidisperse granular avalanche is developed by coupling a depth-averaged description of the preferential transport of large particles towards the front with an established avalanche model. The coupling is achieved through a concentration-dependent friction coefficient, which results in a system of non-strictly hyperbolic equations. We compute numerical solutions to the flow of a bidisperse mixture of small mobile particles and larger more resistive grains down an inclined chute. The numerical results demonstrate that our model is able to describe the formation of a front rich in large particles, the instability of this front and the subsequent evolution of elongated fingers bounded by large-rich lateral levees, as observed in small-scale laboratory experiments. However, our numerical results are grid dependent, with the number of fingers increasing as the numerical resolution is increased. We investigate this pathology by examining the linear stability of a steady uniform flow, which shows that arbitrarily small wavelength perturbations grow exponentially quickly. Furthermore, we find that on a curve in parameter space the growth rate is unbounded above as the wavelength of perturbations is decreased and so the system of equations on this curve is ill-posed. This indicates that the model captures the physical mechanisms that drive the instability, but additional dissipation mechanisms, such as those considered in the realm of flow rheology, are required to set the length scale of the fingers that develop.