Unsteady boundary-layer development over moving walls in the limit of infinite Reynolds number is investigated using both the Eulerian and Lagrangian formulations. To illustrate general trends, two model problems are considered, namely the translating and rotating circular cylinder and a vortex convected in a uniform flow above an infinite flat plate. To enhance computational speed and accuracy for the Lagrangian formulation, a remeshing algorithm is developed. The calculated results show that unsteady separation is delayed with increasing wall speed and is eventually suppressed when the speed of the separation singularity approaches that of the local mainstream velocity. This suppression is also described analytically. Only ‘upstream-slipping’ separation is found to occur in the model problems. The changes in the topological features of the flow just prior to the separation that occur with increasing wall speed are discussed.

The unsteady flow of a viscous incompressible fluid in a circular tube with an elastic insertion is studied numerically. The deformation of the elastic membrane is obtained by the theory of finite elasticity whose equations are solved simultaneously with the fluid equations in the axisymmetric approximation. The elastic wall expands outwards due to the positive transmural pressure and represents an idealized model for the response of pathologies in large arteries.

It is found that if either the fluid discharge or the reference pressure are imposed downstream of the insertion, the fluid–wall interaction develops travelling waves along the membrane whose period depends on membrane elasticity; these are unstable in a perfectly elastic membrane and are stabilized by viscoelasticity. In the reversed system, when the fluid discharge is imposed on the opposite side, the stable propagation phenomenon remains the same because of symmetry arguments. Such arguments do not apply to the originally unstable behaviour. In this case, even when the membrane is perfectly elastic, propagation is damped and two natural fluctuations appear in the form of stationary waves. In all cases the resonance of the fluid–wall interaction has been analysed. Comparisons with previously observed phenomena and with results of analogous studies are discussed.

This paper considers the stability of a horizontal liquid-metal free surface in the presence of a horizontal alternating magnetic field. A weak formulation is used to derive a generalized Mathieu–Hill equation for the evolution of surface perturbations. Previous studies which rely on time-averaging the electromagnetic force over one field cycle have predicted a generally weak instability, but we find much larger growth rates near the resonances, where the surface wave frequency is an integral multiple of the field frequency. The method can be extended to include viscous and ohmic damping; the former has little effect, while the latter damps all waves except those whose frequency is close to the field frequency. Growth rates can be closely approximated by simple algebraic formulae, as can the critical magnetic field strength for the onset of instability.

A study of the near-wake flow of castellated blunt-trailing-edge aerofoils at a Mach number of 2 was conducted to understand the nature of the flow and the mechanisms of base pressure recovery. The investigation has shown that strong gradients exist in the spanwise direction and that the formation of the wake recompression shock occurs further away from the wake axis. Also, the wake neck is broader and diffused. Detailed quantitative data involving pressure measurements, schlieren and holographic interferometry, and laser transit velocimetry, are presented. A theoretical model to predict the mean base pressure on a castellated base is also proposed. Comparison with experimental data shows that the model provides a qualitative description of the flow behind a castellated base at supersonic speeds.

The characteristics of turbulence caused by three-dimensional breaking of internal gravity waves beneath a critical level are investigated by means of high-resolution numerical simulations. The flow evolves in three stages. In the first one the flow is two-dimensional: internal gravity waves propagate vertically upwards and create a convectively unstable region beneath the critical level. Convective instability leads to turbulent breakdown in the second stage. The developing three-dimensional mixed region is organized into shear-driven overturning rolls in the plane of wave propagation and into counter-rotating streamwise vortices in the spanwise plane. The production of turbulent kinetic energy by shear is maximum. In the last stage, shear production and mechanical dissipation of turbulent kinetic energy balance.

The evolution of the flow depends on topographic parameters (wavelength and amplitude), on shear and stratification as well as on viscosity. Here, only the implications of the viscosity for the instability structure and evolution in terms of the Reynolds number are considered. Smaller viscosity leads to earlier onset of convective instability and overturning waves. However, viscosity retards the onset of smaller-scale three-dimensional instabilities and leads to a reduced momentum transfer to the mean flow below the critical level. Hence, the formation of secondary overturning rolls is sustained by lower viscosity.

The budgets of total kinetic and potential energies are calculated. Although the domain-averaged turbulent kinetic energy is less than 1% of the total kinetic energy, it is strong enough to form a patchy and intermittent turbulent mixed layer below the critical level.

Marangoni convection in a differentially heated binary mixture is studied numerically by continuation. The fluid is subject to the Soret effect and is contained in a two-dimensional small-aspect-ratio rectangular cavity with one undeformable free surface. Either or both of the temperature and concentration gradients may be destabilizing; all three possibilities are considered. A spectral-element time-stepping code is adapted to calculate bifurcation points and solution branches via Newton's method. Linear thresholds are compared to those obtained for a pure fluid. It is found that for large enough Soret coefficient, convection is initiated predominantly by solutal effects and leads to a single large roll. Computed bifurcation diagrams show a marked transition from a weakly convective Soret regime to a strongly convective Marangoni regime when the threshold for pure fluid thermal convection is passed. The presence of many secondary bifurcations means that the mode of convection at the onset of instability is often observed only over a small range of Marangoni number. In particular, two-roll states with up-flow at the centre succeed one-roll states via a well-defined sequence of bifurcations. When convection is oscillatory at onset, the limit cycle is quickly destroyed by a global (infinite-period) bifurcation leading to subcritical steady convection.

An experimental study of transition from steady laminar to chaotic flow in a horizontal annulus between concentric cylinders is conducted for 0.90×105[les ]RaL[les ]3.37×105. Qualitative information on the averaged thermal field is obtained by an interferometric method, whereas the kinematics are visualized by using smoke lines. The transition from steady to unsteady mono- and multi-periodic regimes is accurately studied by a CTA and CCA combined hot-wire technique. Different data analyses are performed in order to differentiate the forms of transition.

The linear stability of doubly diffusive convection is considered for a two-dimensional, Boussinesq fluid in a tall thin slot. For a variety of boundary conditions on the slot walls, instability sets in through zero wavenumber over a wide range of physical conditions. Long-wave equations governing the nonlinear development of the instability are derived. The form of the long-wave equations sensitively depends on the thermal and salt boundary conditions; the possible long-wave theories are catalogued. Finite-amplitude solutions and their stability are studied. In some cases the finite-amplitude solutions are not the only possible attractors and numerical solutions presenting the alternatives are given. These reveal temporally complicated dynamics.

The modulation of isotropic turbulence by particles has been investigated using direct numerical simulation (DNS). The particular focus of the present work is on the class of dilute flows in which particle volume fractions and inter-particle collisions are negligible. Gravitational settling is also neglected and particle motion is assumed to be governed by drag with particle relaxation times ranging from the Kolmogorov scale to the Eulerian time scale of the turbulence and particle mass loadings up to 1. The velocity field was made statistically stationary by forcing the low wavenumbers of the flow. The calculations were performed using 963 collocation points and the Taylor-scale Reynolds number for the stationary flow was 62. The effect of particles on the turbulence was included in the Navier–Stokes equations using the point-force approximation in which 963 particles were used in the calculations. DNS results show that particles increasingly dissipate fluid kinetic energy with increased loading, with the reduction in kinetic energy being relatively independent of the particle relaxation time. Viscous dissipation in the fluid decreases with increased loading and is larger for particles with smaller relaxation times. Fluid energy spectra show that there is a non-uniform distortion of the turbulence with a relative increase in small-scale energy. The non-uniform distortion significantly affects the transport of the dissipation rate, with the production and destruction of dissipation exhibiting completely different behaviours. The spectrum of the fluid–particle energy exchange rate shows that the fluid drags particles at low wavenumbers while the converse is true at high wavenumbers for small particles. A spectral analysis shows that the increase of the high-wavenumber portion of the fluid energy spectrum can be attributed to transfer of the fluid–particle covariance by the fluid turbulence. This in turn explains the relative increase of small-scale energy caused by small particles observed in the present simulations as well as those of Squires & Eaton (1990) and Elghobashi & Truesdell (1993).

A general numerical method using the boundary integral equation technique of Pozrikidis (1994) for Stokes flow in an axisymmetric domain is used to obtain the first solutions to the Brinkman equation for the motion of a particle in the presence of planar confining boundaries. The method is first applied to study the perpendicular and parallel motion of a sphere in a fibre-filled medium bounded by either a solid wall or a planar free surface which remains undeformed. By accurately evaluating the singular integrals arising from the discretization of the resulting integral equation, one can efficiently and accurately treat flow problems with high α defined by rs/K1/2p in which rs is the radius of the sphere and Kp is the Darcy permeability. Convergence and accuracy of the new technique are tested by comparing results for the drag with the solutions of Kim & Russell (1985a) for the motion of two spheres perpendicular to their line of centres in a Brinkman medium. Numerical results for the drag and torque exerted on the particle moving either perpendicular or parallel to a confining planar boundary are presented for ε[ges ]0.1, in which εrs is the gap between the particle and the boundary. When the gap width is much smaller than rs, a local analysis using stretched variables for motion of a sphere indicates that the leading singular term for both drag and torque is independent of α provided that α = O(1). These results are of interest in modelling the penetration of the endothelial surface glycocalyx by microvilli on rolling neutrophils and the motion of colloidal gold and latex particles when they are attached to membrane receptors and observed in nanovid (video enhanced) microscopy. The method is then applied to investigate the motion of a sphere translating in a channel. The drag and torque exerted on the sphere are obtained for various values of α, the channel height H and particle position b. These numerical results are used to describe the diffusion of a spherical solute molecule in a parallel walled channel filled with a periodic array of cylindrical fibres and to assess the accuracy of a simple multiplicative formula proposed in Weinbaum et al. (1992) for diffusion of a solute in the interendothelial cleft.

The shear-induced particle self-diffusivity in a concentrated suspension (20%–50% solids volume fraction) of non-colloidal spheres (90 μm average diameter) was measured using a new correlation technique. This method is based on the correlation between the positions of tracer particles in successive images and can be used to determine the self-diffusivity in non-colloidal suspensions for different time scales. These self-diffusivities were measured in the velocity gradient and vorticity directions in a narrow-gap Couette device for values of the strain γΔt ranging from 0.05 to 0.5, where γ is the applied shear rate and Δt is the correlation time. In both directions, the diffusive displacements scaled linearly with γΔt over the range given above and the corresponding diffusivities were found to be in good agreement with the experimental results of Leighton & Acrivos (1987a) and of Phan & Leighton (1993), even though these earlier studies were performed at much larger values of γΔt. The self-diffusivity in the velocity gradient direction was found to be about 1.7 times larger than in the vorticity direction. The technique was also used to determine the shear-induced fluid tracer by measuring the mean square displacement of 31.5 μm diameter tracer particles dispersed in concentrated suspensions (30%–50% solids volume fraction) of much larger spheres (325 μm average diameter). These fluid diffusivities were found to be 0.7 times the corresponding particle diffusivities when both were scaled with γ a2 (2a = 325 μm).

We are concerned here with forced steady recirculating flows which are laminar, two-dimensional and have a high Reynolds number. The body force is considered to be prescribed and independent of the flow, a situation which arises frequently in magnetohydrodynamics. Such flows are subject to a strong constraint. Specifically, the body force generates kinetic energy throughout the flow field, yet dissipation is confined to narrow singular regions such as boundary layers. If the flow is to achieve a steady state, then the kinetic energy which is continually generated within the bulk of the flow must find its way to the dissipative regions. Now the distribution of u2/2 is governed by a transport equation, in which the only cross-stream transport of energy is diffusion, v∇2 (u2/2). It follows that there are only two possible candidates for the transport of energy to the dissipative regions: the energy could be diffused to the shear layers, or else it could be convected to the shear layers through entrainment of the streamlines. We investigate both options and show that neither is a likely candidate at high Reynolds number. We then describe numerical experiments for a model problem designed to resolve these issues. We show that, at least for our model problem, no stable steady solution exists at high Reynolds number. Rather, as soon as the Reynolds number exceeds a modest value of around 10, the flow becomes unstable via a supercritical Hopf bifurcation.

When two particles collide in a liquid, the impulsive acceleration due to the rebound produces a pressure pulse that is transmitted through the fluid. Detailed measurements were made of the pressure pulse and the motion of the particles by generating controlled collisions with an immersed dual pendulum. The experiments were performed for a range of impact velocities, angles of incidence, and distances between the wall and the pairs of particles. The radiated fluid pressure was measured using a high-frequency-response pressure transducer, and the motion of the particles was recorded using a high-speed digital camera. The magnitude of the impulse pressure was found to scale with the particle velocity, the particle diameter and the density of the fluid. Additionally, a model is proposed to predict the impulse field in the fluid based on the impulse pressure theory. The model agrees well with the experimental measurements.

X-ray lithography and micro-machining have been used to study gas-assisted liquid atomization in which a liquid film was impinged by a large number of sonic micro-gas jets. Three distinct breakup regimes were demonstrated. Two of these regimes share characteristics with previously observed atomization processes: a bubble bursting at a free surface (Newitt et al. 1954; Boulton-Stone & Blake 1993) and liquid sheet disintegration in a high gas/liquid relative velocity environment (Dombrowski & Johns 1963). The present work shows that suitable control of the gas/liquid interface creates a third regime, a new primary atomization mechanism, in which single liquid droplets are ejected directly from the liquid film without experiencing an intermediate ligament formation stage. The interaction produces a stretched liquid sheet directly above each gas orifice. This effectively pre-films the liquid prior to its breakup. Following this, surface tension contracts the stretched film of liquid into a sphere which subsequently detaches from the liquid sheet and is entrained by the gas jet that momentarily pierces the film. After droplet ejection, the stretched liquid film collapses, covering the gas orifice, and the process repeats. This new mechanism is capable of the efficient creation of finely atomized sprays at low droplet ejection velocities (e.g. 20 μm Sauter mean diameter methanol sprays using air at 239 kPa, with air-to-liquid mass ratios below 1.0, and droplet velocities lower than 2.0 m s−1). Independent control of the gas and the liquid flows allows the droplet creation process to be effectively de-coupled from the initial droplet momentum, a characteristic not observed with standard gas-assisted atomization mechanisms.