The particle pressure is the surface force that is exerted due to the motion of particles and their interactions. This paper describes measurements of the particle pressure exerted on the sidewall of a gas-fluidized bed. As long as the bed remains in a packed state, the particle pressure decreases with increasing gas velocity as progressively more of the bed is supported by fluid forces. It appropriately reaches a minimum fluidization and then begins to rise again when the bed is fluidized, reflecting the agitation of the bed by bubbles. In this fully fluidized region, the particle pressure scales with the particle density and the bubble size.

A previous study revealed that only maximization of the efficiency function, from among a large class of mean field moments, results in both a logarithmic law and a velocity defect law in turbulent Poiseuille channel flow. The efficiency function, [Escr ], is the product of a drag coefficient and the ratio of the fluctuation and mean dissipation rate integrals. Here, maximum [Escr ] is explored in Couette flow to test its generality as a statistical stability criterion for turbulent shear flows. The optimal flow exhibits a logarithmic law but does not have a velocity defect law. A decreasing velocity defect is predicted for Reynolds numbers up to 30 000. This prediction is shown to be supported by the existing data, which are limited to Reynolds numbers less than 20 000.

We consider the problem of steady Euler flows in a torus. We show that in the absence of a direction of symmetry the solution for the vorticity contains δ-function singularities at the rational surfaces of the torus. We study the effect of a small but finite viscosity on these singularities. The solutions near a rational surface contain cat's eyes or islands, well known in the classical theory of critical layers. When the islands are small, their widths can be computed by a boundary-layer analysis. We show that the islands at neighbouring rational surfaces generally overlap. Thus, steady toroidal flows exhibit a tendency towards Beltramization.

When a horizontal force is applied locally to some volume of a viscous densitystratified fluid, flows with high concentration of vertically oriented vorticity (vortex dipoles) are generated. The processes of generation and evolution with time of these unsteady flows in a stratified fluid are studied. A convenient way to produce and study these flows in the laboratory is to use a submerged horizontal jet as a ‘point’ source of momentum. The main governing parameter (the ‘force’) is easily controlled in this case. Two regimes were studied: starting jets with dipolar vortex fronts (the force acts continuously) and impulsive vortex dipoles (the force acts for a short period of time). A conductivity microprobe, aluminium powder, shadowgraph, thymol-blue and other techniques have been used to measure the velocity and density distributions in the flows. It is found that in both regimes the flows are self-similar: the lengthscale of the flows increases with time as t½ for starting jets and as t1/3 for vortex dipoles. Detailed information about the generation mechanism, kinematics and dynamics of the flows is obtained. On the basis of similarity principles a theoretical explanation of the experimental results is given. The theory is in good agreement with the results obtained.

Directional solidification experiments have been carried out using the analogue casting system of NH4Cl-H2O solution by cooling it from below with a constant-temperature surface ranging from - 31.5°C to + 11.9 °C. The NH4Cl concentration was 26% in all solutions, with a liquidus temperature of 15 °C. It was found that finger convection occurred in the fluid region just above the mushy layer in all experiments. Plume convection with associated chimneys in the mush occurred in experiments with bottom temperatures as high as + 11.0 °C. However, when the bottom temperature was raised to + 11.9 °C, no plume convection was observed, although finger convection continued as usual. A method has been devised to determine the porosity of the mush by computed tomography. Using the mean value of the porosity across the mush layer and the permeability calculated by the Kozeny-Carman relationship, the critical solute Rayleigh number across the mush layer for onset of plume convection was estimated to be between 200 and 250.

Nonlinear stability of core-annular flow near points of the neutral curves at which perfect core-annular flow loses stability is studied using Ginzburg-Landau equations. Most of the core-annular flows are always unstable. Therefore the set of core-annular flows having critical Reynolds numbers is small, so that the set of flows for which our analysis applies is small. An efficient and accurate algorithm for computing all the coefficients of the Ginzburg-Landau equation is implemented. The nonlinear flows seen in the experiments do not appear to be modulations of monochromatic waves, and we see no evidence for soliton-like structures. We explore the bifurcation structure of finite-amplitude monochromatic waves at criticality. The bifurcation theory is consistent with observations in some of the flow cases to which it applies and is not inconsistent in the other cases.

Experiments in ionizing neon are described in which heavy-particle and electron densities are measured and compared with the current kinetic model. The experimental results allow a determination of the atom-atom collisional excitation cross-section constant, giving a value of (8±2) × 10−20 cm2/eV for the range of conditions examined. The population of two of the excited-state levels of the atom are measured and compared with theoretical predictions. The experimental populations are found to follow the expected behaviour in the quasi-equilibrium region, but are several orders of magnitude higher than predicted in the nonequilibrium zone. These findings suggest that the depopulation of excited states through ionizing collisions occurs more slowly than expected. Absorption linewidths and line shifts are also measured in the quasi-equilibrium region and found to compare well with theory. A small precurson population is also observed and population measurements in this region are compared with other experimental results in argon and krypton.

The interactions between longitudinal vortices and accompanying waves considered here are strongly nonlinear, in the sense that the mean-flow profile throughout the boundary layer is completely altered from its original undisturbed state. Nonlinear interactions between vortex flow and Tollmien-Schlichting waves are addressed first, and some analytical and computational properties are described. These include the possibility in the spatial-development case of a finite-distance break-up, inducing a singularity in the displacement thickness. Second, vortex/Rayleigh-wave nonlinear interactions are considered for the compressible boundary layer, along with certain special cases of interest and some possible solution properties. Both types, vortex/Tollmien-Schlichting and vortex/Rayleigh, are short-scale/long-scale interactions and they have potential applications to many flows at high Reynolds numbers. Their strongly nonlinear nature is believed to make them very relevant to fully fledged transition to turbulence.

The third Euromech Colloquium on this topic was held at FISBAT in Bologna in August 1990, in succession to those in 1979 at Munich (No. 113) and 1983 at Delphi (No. 173). About 30 participants came from 10 countries. At the Colloquium it became clear that there have been some significant developments since 1983 in theoretical analysis, computational modelling and field experiments, with new kinds of measurement. As well as papers on improvements in the quantification and understanding of the main, well-known features of these flows, there were also papers on phenomena that had not previously been studied; for example new computations of flows over undulating surfaces driven by buoyancy forces, caused by heating the surface, showed that secondary flows are produced with vorticity parallel to the undulations, while wind tunnel experiments on flows perpendicular to the crests showed secondary flow with vorticity perpendicular to the crests, and with a scale consistent with Craik's (1982) theory which predicted these novel kinds of Langmuir cells. The magnitude of the net drag force on undulating surfaces in neutrally stratified turbulent flows now appears to be moderately well established by different methods, including computations, laboratory experiments, and theoretical analyses. These have clarified the relative magnitudes of a number of contributing mechanisms. The role of Coriolis accelerations (f) in atmospheric flow over simple terrain features (lengthscale L, height H) on the mesoscale (order 30 km upwards) is now better understood. For stratified air flow impinging onto hills rising from a flat plain the Rossby radius (lR = HN/f) is the relevant lengthscale (where N is the buoyancy frequency), but in neutral or convective conditions, such as those which occur when southerly winds are channelled down the Rhine valley, the turning of the wind on a scale of the terrain less than the Rossby radius can also be significantly influenced by Coriolis accelerations.

The recent field measurements by Doppler-sodar (which are installed in several French power stations) produce useful data for comparing with computational models; they also emphasize the need to solve the theoretical question of how best to combine model calculations and measurements within the flow field that exceed the number required to specify the flow in the model. Models of the mean flow and the turbulence have improved to the extent that they can be used in other scientific and practical problems, such as being incorporated into models of dispersion of pollutants, or in models of microphysics and chemical processes in polluted clouds over hills.

Following the Colloquium an ERCOFTACt Workshop was held in which the computer codes of such models were presented and compared in detail. It was decided that i t is necessary to have a systematic intercomparison of such codes, and also detailed comparisons with the extensive sets of data now available from recent field and laboratory experiments.

The wide range of scales that occur in these complex atmospheric flows (10−2 m to 105 m) all have to be considered and calculated in detail, because simple assumptions about the flow (such as that the mean velocity has a logarithmic profile up to a significant height above the surface) are erroneous. Computational models were described that range in complexity from those based on analytical solutions (at low computational cost) to those based on solving discretized equations with large variations in grid sizes to accommodate the range of scales. Novel interactive software was used that enables graphs from different models to be requested and then rapidly displayed simultaneously on a screen for comparisons to be made. This software opens out significant new possibilities for scientific meetings and workshops involving computational fluid dynamics.