The structure of turbulent boundary layers which develop with zero pressure gradient on a smooth wall and a k-type rough wall was examined using arrays of X-wires. Although the data were obtained only on two orthogonal planes, the technique provides some information on the three-dimensionality of the large-scale structures. The major effect of the roughness is to tilt the inclination of the structures towards the wall-normal direction. This is caused by the reduced damping of the wall-normal velocity fluctuations close to the rough surface and the break-up of structures whose scales are comparable to the size of the roughness elements. Both effects cause a reduction in the streamwise lengthscales, as suggested by all the measured two-point correlations. The correlations also show that the roughness tends to reduce the overall anisotropy of the large-scale motion. There is evidence to suggest that the magnitude of the vorticity field is larger over the rough wall.

A stably stratified interface, with strong turbulence below and quiescent air above, is studied in a wind tunnel with the aim of simulating the conditions at the inversion cap at the top of the atmospheric boundary layer. The interfacial layer was generated by means of a composite grid, with small mesh size above and a large one below (Veeravalli & Warhaft 1989). A temperature step generated in the plenum of the wind tunnel, was located at the centre of the layer. There is no shear and thus turbulence interactions, usually masked by turbulent production in traditional mixing layers, are highlighted. Close to the grid where the velocity fluctuations are strong, buoyancy effects are insignificant, but as the turbulence decays they become dominant. The bulk Richardson number, N2B/(〈u2〉2/L2u), where NB is the Brunt—Väisälä frequency across the layer, and 〈u2〉2 and Lu are the velocity variance and integral lengthscale, respectively, of the turbulence on the lower side of the layer, varied from approximately zero close to the grid to 80 far downstream. The stratification inhibited the turbulent penetration into the layer, reducing the high skewness and kurtosis of the velocity field for the neutral case, to Gaussian values. The layer, which initially thickened with downstream distance, thinned when buoyancy became pronounced, owing to the collapse of the heat flux. Significant regions of countergradient heat flux, and reversals in sign of the triple moment transport terms were observed in the upper part of the layer. An analysis of the value of the heat flux conditioned on the temperature fluctuations, showed that the large temperature fluctuations associated with weak turbulence became affected by stratification first. Cospectral analysis shows that these fluctuations are associated with large scales. We also show that although the joint normal approximation between velocity and temperature fluctuations is sound for a passive scalar field, it becomes less good with the onset of stratification, failing completely when the stratification is strong.

We consider the two-layer flow of immiscible, viscous, incompressible fluids in an inclined channel. We use long-wave theory to obtain a strongly nonlinear evolution equation which describes the motion of the interface. This equation includes the physical effects of viscosity stratification, density stratification, and shear. A weakly nonlinear analysis of this equation yields a Kuramoto–Sivashinsky equation, which possesses a quadratic nonlinearity. However, certain physical situations exist in two-layer flow for which modifications of the Kuramoto–Sivashinsky equation are physically pertinent. In particular, the presence of the second layer can mediate the wave-steepening instability found in single-phase falling films, requiring the inclusion of a cubic nonlinearity in the weakly nonlinear analysis. The introduction of the cubic nonlinearity destroys the symmetry-breaking bifurcations of the Kuramoto–Sivashinsky equation, and new isolated solution branches emerge as the strength of the cubic nonlinearity increases. Bistability between these new solutions and those associated with the Kuramoto–Sivashinsky equation is found, as well as the formation of a hysteresis loop from smaller-amplitude travelling waves to larger-amplitude travelling waves. The physical implications of these dynamics to the phenomenon of laminar flooding in a channel are discussed.

In the fundamental configuration studied here, a steady hypersonic free stream flows over a thin sharp aligned airfoil or flat plate with a leading-edge shock wave, and the flow field in the shock layer (containing a viscous and an inviscid layer) is steady laminar and two-dimensional, for a perfect gas without real and high-temperature gas effects. The viscous and inviscid layers are analysed and computed simultaneously in the region from the leading edge to the trailing edge, including the upstream-influence effect present, to determine the interactive flow throughout the shock layer and the positions of the shock wave and the boundary-layer edge, where matching is required. Further theoretical analysis of the shock layer helps to explain the computational results, including the nonlinear breakdown possible when forward marching against enhanced upstream influence, for example as the wall enthalpy increases towards its insulated value. Then the viscous layer is computed by sweeping methods, for higher values of wall enthalpies, to prevent this nonlinear breakdown for airfoils including the flat plate. Thin airfoils in hypersonic viscous flow are treated, for higher values of the wall enthalpies and with the upstream-influence effect, as are hypersonic inviscid flows, by modifying the computational methods used for the flat plate. Also, the behaviour of the upstream influence for bodies of relatively large thickness, and under wall velocity slip and enthalpy jump for flat plates, is discussed briefly from a theoretical point of view.

Subsequent to the present work, computations based on the Navier–Stokes and on the parabolized Navier–Stokes equations have yielded excellent and good agreement respectively with the present predictions for large Mach and Reynolds numbers.

The interactions between small dense particles and fluid turbulence have been investigated in a downflow fully developed channel in air. Particle velocities of, and fluid velocities in the presence of, 50 μm glass, 90 μm glass and 70 μm copper spherical beads were measured by laser Doppler anemometry, at particle mass loadings up to 80%. These particles were smaller than the Kolmogorov lengthscale of the flow and could respond to some but not all of the scales of turbulent motion. Streamwise mean particle velocity profiles were flatter than the mean fluid velocity profile, which was unmodified by particle loading. Particle velocity fluctuation intensities were larger than the unladen-fluid turbulence intensity in the streamwise direction but were smaller in the transverse direction. Fluid turbulence was attenuated by the addition of particles; the degree of attenuation increased with particle Stokes number, particle mass loading and distance from the wall. Turbulence was more strongly attenuated in the transverse than in the streamwise direction, because the turbulence energy is at higher frequencies in the transverse direction. Streamwise turbulence attenuation displayed a range of preferred frequencies where attenuation was strongest.

The generation and growth of single hairpin vortices created by controlled surface fluid injection were examined experimentally within a laminar boundary layer over a range of Reynolds numbers. Flow visualization, using both dye and hydrogen bubbles, was employed in conjunction with hot-film anemometry to investigate the growth characteristics and evolution of these single hairpin vortices. Hydrogen-bubble visualization results reveal that the passage of a hairpin vortex can give rise to a low-speed streak pattern adjacent to the surface, and a turbulent pocket-like pattern farther removed from the surface. When the displacement and injection Reynolds numbers exceed critical levels, regeneration processes occur, which result in the development of new hairpin-like vortices by both (i) lateral deformation of the vortex lines comprising the initial hairpin vortex and (ii) a process of vortex-surface interaction, which causes the ejection of surface fluid and subsequent hairpin formation by viscous-inviscid interactions. The combination of these processes results in both lateral and streamwise growth of the initial hairpin-vortex structure, yielding a symmetric turbulent-spot type of behaviour.

Near-critical states have been achieved downstream of a liquefaction shock wave, which is a shock reflected from the endwall of a shock tube. Photographs of the shocked test fluid (iso-octane) reveal a rich variety of phase-change phenomena. In addition to the existence of two-phase toroidal rings which have been previously reported, two-phase structures with a striking resemblance to dandelions and orange slices have been frequently observed. A model coupling the flow and nucleation dynamics is introduced to study the two-wave system of shock-induced condensation and the liquefaction shock wave in fluids of large molar heat capacity. In analogy to the one-dimensional Zeldovich–von Neumann–Döring (ZND) model of detonation waves, the leading part of the liquefaction shock wave is a gasdynamic pressure discontinuity (Δ ≈ 0.1 μm, τ ≈ 1 ns) which supersaturates the test fluid, and the phase transition takes place in the condensation relaxation zone (Δ ≈ 1–103 μm, τ ≈ 0.1–100 μs) via dropwise condensation. At weak to moderate shock strengths, the average lifetime of the metastable state, τ ∞ 1/J, is long such that the reaction zone is spatially decoupled from the forerunner shock wave, and J is the homogeneous nucleation rate. With increasing shock strength, a transition in the phase-change mechanism from nucleation and growth to spinodal decomposition is anticipated based on statistical mechanical arguments. In particular, within a complete liquefaction shock the metastable region is entirely bypassed, and the vapour decomposes inside the unstable region. This mechanism of unmixing in which nucleation and growth become one continuous process provides a consistent framework within which the observed irregularities can be explained.

Linear stability of incompressible flow in a circular pipe is considered. Use is made of a vector function formulation involving the radial velocity and radial vorticity only. Asymptotic as well as transient stability are investigated using eigenvalues and ε-pseudoeigenvalues, respectively. Energy stability is probed by establishing a link to the numerical range of the linear stability operator. Substantial transient growth followed by exponential decay has been found and parameter studies revealed that the maximum amplification of initial energy density is experienced by disturbances with no streamwise dependence and azimuthal wavenumber n = 1. It has also been found that the maximum in energy scales with the Reynolds number squared, as for other shear flows. The flow field of the optimal disturbance, exploiting the transient growth mechanism maximally, has been determined and followed in time. Optimal disturbances are in general characterized by a strong shear layer in the centre of the pipe and their overall structure has been found not to change significantly as time evolves. The presented linear transient growth mechanism which has its origin in the non-normality of the linearized Navier–Stokes operator, may provide a viable process for triggering finite-amplitude effects.

A new criterion for the direct initiation of cylindrical or spherical detonations by a localized energy source is presented. The analysis is based on nonlinear curvature effects on the detonation structure. These effects are first studied in a quasi-steady-state approximation valid for a characteristic timescale of evolution much larger than the reaction timescale. Analytical results for the square-wave model and numerical results for an Arrhenius law of the quasi-steady equations exhibit two branches of solutions with a C-shaped curve and a critical radius below which generalized Chapman–Jouguet (CJ) solutions cannot exist. For a sufficiently large activation energy this critical radius is much larger than the thickness of the planar CJ detonation front (typically 300 times larger at ordinary conditions) which is the only intrinsic lengthscale in the problem. Then, the initiation of gaseous detonations by an ideal point energy source is investigated in cylindrical and spherical geometries for a one-step irreversible reaction. Direct numerical simulations show that the upper branch of quasi-steady solutions acts as an attractor of the unsteady blast waves originating from the energy source. The critical source energy, which is associated with the critical point of the quasi-steady solutions, corresponds approximately to the boundary of the basin of attraction. For initiation energy smaller than the critical value, the detonation initiation fails, the strong detonation which is initially formed decays to a weak shock wave. A successful initiation of the detonation requires a larger energy source. Transient phenomena which are associated with the intrinsic instability of the quasi-steady detonations branch develop in the induction timescale and may induce additional mechanisms close to the critical condition. In conditions of stable or weakly unstable planar detonations, these unsteady phenomena are important only in the vicinity of the critical conditions. The criterion of initiation derived in this paper works to a good approximation and exhibits the huge numerical factor, 106–108, which has been experimentally observed in the critical value of the initiation energy.

A computational study has been performed to identify the onset of transverse buoyancy-driven recirculations during laminar flow of hydrogen and nitrogen in horizontal ducts with cool upper walls, and lower walls consisting of three sections: a cool upstream section, a heated middle section and a cool downstream section. The motivation for this work stems from the need to identify operating conditions maximizing the thickness uniformity, the interface abruptness and the precursor utilization during growth of thin films and multi-layer structures of semiconductors by metalorganic chemical vapour deposition (MOCVD). A mathematical model describing the flow and heat transfer along the vertical midplane of MOCVD reactors with the above geometry has been developed and computer simulations were performed for a variety of operating conditions using the Galerkin finite-element method. At atmospheric pressure and low inlet velocities, transverse recirculations form near the upstream and downstream edges of the heated section. These can be suppressed either by increasing the inlet velocity of the gas, so that forced convection dominates natural convection, or by decreasing the operating pressure to reduce the effects of buoyancy. The onset of transverse recirculations has been determined for Grashof (Gr) and Reynolds (Re) numbers covering the following ranges: 10−3 < Re < 100 and 1 < Gr < 106, with Gr and Re computed using fluid properties at the inlet conditions. The computations indicate that, for abrupt temperature changes along the lower wall (worst-case scenario), transverse recirculations are always absent if the following criteria are satisfied: \[(Gr/Re) < 100\quad {\rm for}\quad 10^{-3} < Re \leqslant 4\quad {\rm and}\quad (Gr/Re^2) < 25\quad {\rm for}\quad 4 \leqslant Re < 100.\]

The predicted critical values of Re, which correspond to the onset of transverse recirculations, agree well with reported experimental observations. The above criteria can be used for optimal design and operation of horizontal MOCVD reactors and may also be useful for heat transfer studies in horizontal ducts with differentially heated lower walls.

This paper reports the results of a two-dimensional finite element simulation of the motion of a circular particle in a Couette and a Poiseuille flow. The size of the particle and the Reynolds number are large enough to include fully nonlinear inertial effects and wall effects. Both neutrally buoyant and non-neutrally buoyant particles are studied, and the results are compared with pertinent experimental data and perturbation theories. A neutrally buoyant particle is shown to migrate to the centreline in a Couette flow, and exhibits the Segré-Silberberg effect in a Poiseuille flow. Non-neutrally buoyant particles have more complicated patterns of migration, depending upon the density difference between the fluid and the particle. The driving forces of the migration have been identified as a wall repulsion due to lubrication, an inertial lift related to shear slip, a lift due to particle rotation and, in the case of Poiseuille flow, a lift caused by the velocity profile curvature. These forces are analysed by examining the distributions of pressure and shear stress on the particle. The stagnation pressure on the particle surface are particularly important in determining the direction of migration.

Thermocapillary convection in an infinite liquid layer driven by a temperature gradient parallel to the interface in the absence of gravity is considered. It is demonstrated that the temperature field has to satisfy restrictive conditions in order for a continuous layer to exist. It is further shown that the same conditions apply to long finite layers. Such layers, when subject to heating that does not satisfy the existence conditions, undergo large deformations and possible break up if the layer is sufficiently long.

Reflections of weak shock waves over wedges are investigated mainly by considering disturbance propagation which leads to a flow non-uniformity immediately behind a Mach stem. The flow non-uniformity is estimated by the local curvature of a smoothly curved Mach stem, and is characterized not only by a pressure increase immediately behind the Mach stem on the wedge but also by a propagation speed. In the case of a smoothly curved Mach stem as is observed in a von Neumann Mach reflection, the pressure increase behind the Mach stem is approximately determined by Whitham's ray-shock theory. The propagation speed of the flow non-uniformity is approximated by Whitham's shock-shock relation. If the shock-shock does not catch up with a point where a curvature of the Mach stem vanishes, a von Neumann Mach reflection appears. The boundary on which the above-mentioned condition breaks results in the transition from a von Neumann Mach reflection to a simple Mach reflection. This idea leads to a transition criterion for a von Neumann Mach reflection, which is algebraically expressed by χ1 = χs where χ1 is the trajectory angle of the point on the Mach stem where the local curvature vanishes and is approximately replaced by χg—θw (χg is the angle of glancing incidence, and θw is the apex angle of the wedge) and χs is the trajectory angle of Whitham's shock-shock, measured from the surface of the wedge. For shock Mach numbers of 1.02 to 2.2 and a wedge angle from 0° to 30°, the domains of a von Neumann Mach reflection, simple Mach reflection and regular reflection are determined by experiment, numerical simulation and theory. The present transition criterion agrees well with experiments and numerical simulations.

A direct numerical simulation, based on spectral methods, has been used to compute the time-dependent, axisymmetric viscous flow past a rigid sphere. An investigation has been made for oscillatory flow about a zero mean for different Reynolds numbers and frequencies. The simulation has been verified for steady flow conditions, and for unsteady flow there is excellent agreement with Stokes flow theory at very low Reynolds numbers. At moderate Reynolds numbers, around 20, there is good general agreement with available experimental data for oscillatory motion. Under steady flow conditions no separation occurs at Reynolds number below 20; however in an oscillatory flow a separation bubble forms on the decelerating portion of each cycle at Reynolds numbers well below this. As the flow accelerates again the bubble detaches and decays, while the formation of a new bubble is inhibited till the flow again decelerates. Steady streaming, observed for high frequencies, is also observed at low frequencies due to the flow separation. The contribution of the pressure to the resultant force on the sphere includes a component that is well described by the usual added-mass term even when there is separation. In a companion paper the flow characteristics for constant acceleration or deceleration are reported.

A new theoretical formulation is presented for mass transport across the dynamic interface associated with a spherical bubble undergoing volume oscillations. As a consequence of the changing internal pressure of the bubble that accompanies volume oscillations, the concentration of the dissolved gas in the liquid at the interface undergoes large-amplitude oscillations. The convection-diffusion equations governing transport of dissolved gas in the liquid are written in Lagrangian coordinates to account for the moving domain. The Henry's law boundary condition is split into a constant and an oscillating part, yielding the smooth and the oscillatory problems respectively. The solution of the oscillatory problem is valid everywhere in the liquid but differs from zero only in a thin layer of the liquid in the neighbourhood of the bubble surface. The solution to the smooth problem is also valid everywhere in the liquid; it evolves via convection-enhanced diffusion on a slow timescale controlled by the Péclet number, assumed to be large. Both the oscillatory and smooth problems are treated by singular perturbation methods: the oscillatory problem by boundary-layer analysis, and the smooth problem by the method of multiple scales in time. Using this new formulation, expressions are developed for the concentration field outside a bubble undergoing arbitrary nonlinear periodic volume oscillations. In addition, the rate of growth or dissolution of the bubble is determined and compared with available experimental results. Finally, a new technique is described for computing periodically driven nonlinear bubble oscillations that depend on one or more physical parameters. This work extends a large body of previous work on rectified diffusion that has been restricted to the assumptions of infinitesimal bubble oscillations or of threshold conditions, or both. The new formulation represents the first self-consistent, analytical treatment of the depletion layer that accompanies nonlinear oscillating bubbles that grow via rectified diffusion.