This work belongs to the ongoing debate surrounding the mechanism responsible for low-angle sound emission from subsonic jets. The flow, simulated by large eddy simulation (Bogey & Bailly, Comput. Fluids, vol. 35 (10), 2006a, pp. 1344–1358), is a Mach 0.9 jet with Reynolds number, based on the exit diameter, of . A methodology is implemented to educe, explore and model the flow motions associated with low-angle sound radiation. The eduction procedure, which is based on frequency–wavenumber filtering of the sound field and subsequent conditional analysis of the turbulent jet, provides access to space- and time-dependent (hydrodynamic) pressure and velocity fields. Analysis of these shows the low-angle sound emission to be underpinned by dynamics comprising space and time modulation of axially coherent wavepackets: temporally localized energization of wavepackets is observed to be correlated with the generation of high-amplitude acoustic bursts. Quantitative validation is provided by means of a simplified line-source Ansatz (Cavalieri et al. J. Sound Vib., vol. 330, 2011b, pp. 4474–4492). The dynamic nature of the educed field is then assessed using linear stability theory (LST). The educed pressure and velocity fields are found to compare well with LST: the radial structures of these match the corresponding LST eigenfunctions; the axial evolutions of their fluctuation energy are consistent with the LST amplification rates; and the relative amplitudes of the pressure and velocity fluctuations, which are educed independently of one another, are consistent with LST.

Asymptotic expansion techniques are used, in the limit of large Reynolds number, to study the structure of fully turbulent shear layers. The relevant Reynolds number characterizes the ratio of the local turbulent stress to the local laminar stress, so that a relatively thick outer defect layer, in which, to lowest order, there is a balance between turbulent stress and convection of momentum, may be distinguished from a relatively thin wall layer, in which, to lowest order, there is a balance between turbulent and laminar stresses. The two cases examined are channel (or pipe) flow and two-dimensional boundary-layer flow with an applied pressure gradient, upstream of any separation. Attention, for these two cases, is confined to the flow of incompressible constant property fluids. Closure is effected through the introduction of an eddy-viscosity model formulated with sufficient generality for most existing models to be special cases. Results are carried to higher orders of approximation to indicate what properties for the friction velocity, integral thicknesses, and velocity profiles, and what conditions for similarity are implied by current eddy-viscosity closures.

A number of experiments have been performed on the properties of propane diffusion flames at relatively low fuel flow rates and using a variety of burner types. Optical methods were used to observe the flame and plume above it. We have studied the transition from a steady flame, with a plume exhibiting a helical instability at low flow rates, to an axisymmetric instability of the whole flame/plume, that grows from the base of the flame and oscillates at a well-defined and robust frequency, at higher flow rates. These results and the observation of the effects of various external modifications, e.g. the generation of an annular counter flow, a pressure perturbation, etc. are consistent with the view that the transition to the axisymmetric state, at which the flame flickers, is one to a globally excited oscillation forced by a region of absolutely unstable flow at or near the base of the burners used in this study.

Using high-speed photography coupled with optical interference, we experimentally study the air entrapment during a liquid drop impacting a solid substrate. We observe the formation of a compressed air film before the liquid touches the substrate, with internal pressure considerably higher than the atmospheric value. The degree of compression highly depends on the impact velocity, as explained by balancing the liquid deceleration with the large pressure of the compressed air. After contact, the air film expands vertically at the edge, reducing its pressure within a few tens of microseconds and producing a thick rim on the perimeter. This thick-rimmed air film subsequently contracts into an air bubble, governed by the complex interaction between surface tension, inertia and viscous drag. Such a process is universally observed for impacts above a few centimetres high.

The atmospheric ventilation of a surface-piercing hydrofoil is examined in a series of towing-tank experiments, performed on a vertically cantilevered hydrofoil with an immersed free tip. The results of the experiments expand upon previous studies by contributing towards a comprehensive understanding of the topology, formation and elimination of ventilated flows at low-to-moderate Froude and Reynolds numbers. Fully wetted, fully ventilated and partially ventilated flow regimes are identified, and their stability regions are presented in parametric space. The stability of partially and fully ventilated regimes is related to the angle of the re-entrant jet, leading to a set of criteria for identifying flow regimes in a laboratory environment. The stability region of fully wetted flow overlaps those of partially and fully ventilated flows, forming bi-stable regions where hysteresis occurs. Ventilation transition mechanisms are classified as formation and elimination mechanisms, which separate the three steady flow regimes from one another. Ventilation formation requires air ingress into separated flow at sub-atmospheric pressure from a continuously available air source. Ventilation washout is caused by upstream flow of the re-entrant jet. The boundary denoting washout of fully ventilated flow is expressed as a semi-theoretical scaling relation, which captures past and present experimental data well across a wide range of Froude and Reynolds numbers.

The method of matched asymptotic expansions is applied to several long-wave problems including the scattering of acoustic waves by a grating of cylinders and the scattering of water waves incident on horizontal cylinders. It is shown that a naïve application of the method can lead to incorrect results. A modified expansion procedure is developed and applied to a number of problems.

A numerical study of swimming particle motion and nutrient transport is conducted for a semidilute to dense suspension in a thin film. The steady squirmer model is used to represent the motion of living cells in suspension with the nutrient uptake by swimming particles modelled using a first-order kinetic equation representing the absorption process that occurs locally at the particle surface. An analysis of the dynamics of the neutral squirmers inside the film shows that the vertical motion is reduced significantly. The mean nutrient uptake for both isolated and populations of swimmers decreases for increasing swimming speeds when nutrient advection becomes relevant as less time is left for the nutrient to diffuse to the surface. This finding is in contrast to the case where the uptake is modelled by imposing a constant nutrient concentration at the cell surface and the mass flux results to be an increasing monotonic function of the swimming speed. In comparison to non-motile particles, the cell motion has a negligible influence on nutrient uptake at lower particle absorption rates since the process is rate limited. At higher absorption rates, the swimming motion results in a large increase in the nutrient uptake that is attributed to the movement of particles and increased mixing in the fluid. As the volume fraction of swimming particles increases, the squirmers consume slightly less nutrients and require more power for the same swimming motion. Despite this increase in energy consumption, the results clearly demonstrate that the gain in nutrient uptake make swimming a winning strategy for micro-organism survival also in relatively dense suspensions.

The stability of a thin flexible plate confined inside an inviscid two-dimensional channel is examined using a nonlinear eigenvalue analysis method. A new Green’s function for the vortex wake of the flexible plate inside the channel, as well as its rapidly convergent series approximation, is proposed. Comparison with a fully coupled Navier–Stokes fluid–structure interaction model indicates that the current inviscid model successfully predicts the flutter boundary for a confined flexible plate. The analysis also shows that confinement has a destabilizing effect on heavy plates. Furthermore, as the confinement is increased, the oscillating frequency of the plate increases and new peaks appear in its stability curve. Asymmetric placement of the plate within the channel, especially when the plate is very close to one wall, also modifies the stability curve of the system by shifting the mode transition points toward smaller fluid-to-plate inertia ratios. Our study suggests that the degree of confinement and asymmetric placement of the plate in the channel could be used to alter the flutter instability of the plate, and to adjust the frequency of flutter.

The flow in a stationary open cylinder driven by the constant rotation of the bottom endwall is unstable to three-dimensional perturbations for sufficiently large rotation rates. The bifurcated state takes the form of a rotating wave. Two distinct physical mechanisms responsible for the symmetry breaking are identified, which depend on whether the fluid depth is sufficiently greater or less than the cylinder radius. For deep systems, the rotating wave results from the instability of the near-wall jet that forms as the boundary layer on the rotating bottom endwall is turned into the interior. In this case the three-dimensional perturbations vanish at the air/water interface. On the other hand, for shallow systems, the fluid at radii less than about half the cylinder radius is in solid-body rotation whereas the fluid at larger radii has a strong meridional circulation. The interface between these two regions of flow is unstable to azimuthal disturbances and the resulting rotating wave persists all the way to the air/water interface. The flow dynamics are explored using three-dimensional Navier–Stokes computations and experimental results obtained via digital particle image velocimetry. The use of a flat stress-free model for the air/water interface reproduces the experimental results in the deep system but fails to capture the primary instability in the shallow system, even though the experimental imperfections, i.e. departures from a perfectly flat and clean air/water interface, are about the same for the deep and the shallow systems. The flat stress-free model boundary conditions impose a parity condition on the numerical solutions, and the consideration of an extended problem which reveals this hidden symmetry provides insight into the symmetry-breaking instabilities.

Fully developed flow in an infinite helically coiled pipe is studied, motivated by physiological applications. Most of the bends in the mammalian arterial system curve in a genuinely three-dimensional way, so that the arterial centreline has not only curvature but torsion and can be modelled by a helix. Flow in a helically symmetric pipe generalizes related problems in axisymmetry (Dean flow) and two-dimensionality, but the geometry ensures that even irrotational flow has a cross-pipe component. Fully developed helical flows driven by a steady pressure gradient are studied analytically and numerically. Varying the radius and pitch of the helical pipe, the effects of curvature and torsion on the flow are investigated.

We describe experiments in which we have observed the onset of Rayleigh-Bénard convection in normal liquid 3He–4He mixtures. Evidence of overstability was seen when heating from below but only stationary convection was observed when heating from above. Measurements of the critical Rayleigh number are presented and compared with the predictions of current theories of marginal stability in a binary mixture. These experiments exemplify liquid 3He–4He mixtures as a system for the study of convective instabilities.

An experimental investigation is carried out into the characteristics of the velocity and thermal fields in free and wall jets in which the buoyancy force opposes the flow. The flow configuration considered is that of a negatively buoyant two-dimensional jet discharged adjacent to a vertical surface, as well as that discharged away from the boundaries of the region. Such convective flows are frequently encountered in heat-rejection processes and in enclosure fires, where, at various locations, the buoyancy force is upward while the flow is downward, resulting in negative buoyancy. An experimental system is developed to study the downward penetration of such jets in which the buoyancy force opposes the externally induced flow. The penetration distance is measured and related to the inflow conditions, particularly the temperature and velocity at the discharge location. A steady state is simulated by allowing the fluid to flow out of the enclosure at the open top. The velocity and temperature distributions are also measured, in order to understand the basic nature of such flows. Several other effects, such as the entrainment into the flow, are also considered in this study.

Thermal convection in a rapidly rotating spherical shell is investigated experimentally and numerically. The experiments are performed in water (Prandtl number P=7) and in gallium (P=0.025), at Rayleigh numbers R up to 80 times the critical value in water (up to 6 times critical in gallium) and at Ekman numbers E∼10−6. The measurements of fluid velocities by ultrasonic Doppler velocimetry are quantitatively compared with quasi-geostrophic numerical simulations incorporating a varying β-effect and boundary friction (Ekman pumping). In water, unsteady multiple zonal jets, weaker in amplitude than the non-axisymmetric flow, are experimentally observed and numerically reproduced at moderate forcings (R/Rc<40). In this regime, zonal flows and vortices share the same length scale. Gallium experiments and strongly supercritical convection experiments in water correspond to another regime. In these turbulent flows, the zonal motion amplitude U dominates the non-axisymmetric motion amplitude Ũ. As a result of the reverse cascade of kinetic energy, the characteristic Rhines length scale of zonal jets emerges, and the boundary friction becomes the main brake on the growth of the zonal flow. A scaling law U ∼ Ũ4/3 is then derived and verified both numerically and experimentally.

Previous analyses of natural convection in a porous medium have drawn seemingly contradictory conclusions as to whether the motion is two- or three-dimensional. This investigation uses numerical results to show the relationship between previous contending observations, and demonstrates that there exists more than one mode of convection for any particular physical configuration and Rayleigh number. In some cases, a particular flow situation may be stable even though it does not maximize the energy transfer across the system.

The methods used are based on the efficient numerical solution of the governing equations, formulated with the definition of a vector potential. This approach is shown to be superior to formulating the equations in terms of pressure.

For a cubic region the flow pattern at a particular value of the Rayleigh number is not unique and is determined by the initial conditions. In some cases there exist four alternatives, two- and three-dimensional, steady and unsteady.

Experiments to determine the value of Taylor's longitudinal diffusivity in turbulent flows in open channels and circular pipes have produced results which are in many cases inconsistent with one another and with theoretical estimates due respectively to Elder (1959) and Taylor (1954). Neither is there general agreement on when Taylor's theory becomes applicable. In an attempt to clarify the discrepancies two well-known sets of experiments by Fischer (1966) and Taylor (1954) are re-examined by using a natural procedure which, it is argued, has certain advantages over more usual methods. It is shown that Fischer's observations in an open channel were not made at a sufficient distance downstream from the point of injection for Taylor's theory to apply but that they are consistent with a description of the early stages of the dispersion process due to Sullivan (1968). It is subsequently argued that these observations suggest that Elder's estimate of the diffusivity is too low for two reasons. The first is the error caused by assuming the existence of an eddy diffusivity calculated by means of Reynolds analogy and the second is the neglect of the viscous sublayer. On the other hand it is shown that some of Taylor's observations in a circular pipe are consistent with his theory, although the values of the diffusivity which best fit the data are about 25% higher than Taylor's estimate, and it is suggested that this is for the same reasons as in the open channel. The paper concludes with a discussion of the effect of the viscous sublayer on the value of the longitudinal diffusivity. Partly on the basis of an approximate model it is argued that theoretical calculations which ignore the viscous sublayer are too low by amounts which depend on the Reynolds and Schmidt numbers and can be of the order of 20%.

The present study is motivated by a need to produce stability modes to assist in the understanding and control of unsteady separated flows. The flow configuration is a NACA 0015 aerofoil with laminar leading-edge separation and turbulent recirculation. In previous water tunnel experiments, this flow configuration was measured in an unperturbed (uncontrolled) separated state, and a harmonically perturbed (controlled) reattached state. This study presents numerical data of the unperturbed case, and recovers stability modes to describe the evolution of perturbations in this environment. The unperturbed flow is numerically generated using large eddy simulation. Its temporal properties are quantified via a Fourier analysis of the velocity time history at selected points in space. The leading-edge shear layer instability is characterized by instantaneous vortex structures, and the bluff body shedding is illustrated by proper orthogonal decomposition modes. Statistical measures of the velocity field agree well with the water tunnel measurements. Finally a stability analysis is undertaken using a triple decomposition to distinguish between the time averaged field, the unsteady scales of motion, and a coherent wave (perturbation). This analysis identifies that perturbations in the region immediately downstream of the separated shear layer have the highest spatial growth rates. The associated frequency is of the order of the sub-harmonic of the shear layer instability.

This paper presents the results of an experimental study of fluid dynamics around an inclined circular cylinder with and without water running over its surface, covering water rivulet formation, fluid forces on the cylinder, near wake and their interrelationships. The cylinder inclination angle (α) with respect to incident flow was between 55° and 80°. It has been found that water running over the cylinder surface may behave quite differently, depending on the Reynolds number (Re), and subsequently impact greatly upon the fluid dynamics around the cylinder. As such, five flow categories are classified. Category A: one water rivulet was observed, irrespective of α, at the leading stagnation point at a small Re. Category B: the rivulet splits into two, symmetrically arranged about the leading stagnation line, once Re exceeds a critical value that depends on α. The two rivulets may further switch back to one, and vice versa. Category C: two symmetrical straight rivulets occur. Category D: the two rivulets shift towards the flow separation line with increasing Re and oscillate circumferentially. The oscillation reaches significant amplitude when the rivulets occur at about 70° from the leading stagnation point. This increased amplitude is coupled with a rapid climb in the mean and fluctuating drag and lift, by a factor of near 5 for the fluctuating lift at α = 80°. Meanwhile, the flow structure exhibits a marked variation. For example, Strouhal number and vortex formation length decrease, along with an increase in spanwise vorticity concentration, velocity deficit, and coherence between vortex shedding and fluctuating lift. All these observations point to the occurrence of a ‘lock-in’ phenomenon, i.e. the rivulet oscillation synchronizing with flow separation. A rivulet–vortex-induced instability is proposed to be responsible for the well reported rain–wind-induced vibration associated with the stay cables of cable-stayed bridges. Category E: the two rivulets shift further downstream just beyond the separation line; the shear layers behind the rivulets become highly turbulent, resulting in weakened vortex shedding, flow fluctuating velocities and fluctuating fluid forces. Based on the equilibrium of water rivulet weight, aerodynamic pressure and friction force between fluid and surface, an analysis is developed to predict the rivulet position on the cylinder, which agrees well with measurements.