It is shown that, in the flow of a viscous wall layer past a relatively steep obstacle at the wall, the Goldstein (1948) singularity generated in the classical boundary-layer approach to separation is removable in a physically sensible fashion. The removal is effected by means of a sequence of local double structures, the last of which arises just beyond separation owing to the occurrence of a further singularity which is also removable and describes the necessary complete breakaway of the viscous layer from the wall. The novel forms of the local pressure–displacement relations are the key elements allowing the solution to retain physical reality throughout. Beyond the breakaway the reattachment process takes place only at a relatively large distance downstream, before the motion returns to its original uniform shear form. The present flow configuration, the first we know of where Goldstein's singularity proves to be removable, has important applications in both internal and external flows at high Reynolds numbers and these are also discussed.

The ‘preferred mode’ of an incompressible axisymmetric free jet has been organized through controlled perturbation, and spatial distributions of time-average as well as phase-average flow properties in the near field are documented. The excitation produces noticeable changes in the time-average measures of the jet, although these changes are less dramatic than those for the excitation producing stable vortex pairing. For different stages in the evolution of the preferred-mode coherent structure, the phase-average vorticity, coherent Reynolds stress, and incoherent turbulence intensities and Reynolds stress have been educed through phase-locked hot-wire measurements, over the spatial extent of the structure and without invoking the Taylor hypothesis. For a particular stage of the evolution (i.e. when the structure is centred at x/D ≃ 3) the distributions of these quantities have been compared for both initially laminar and fully turbulent exit boundary layers, and for four jet Reynolds numbers. The relative merits of the coherent structure streamline and pseudo-stream-function patterns, as compared with phase-average velocity contours, for structure boundary identification have been discussed. The structure shape and size agree closely with those inferred from the average streamline pattern of the natural structure educed by Yule (1978).

These data as well as τ-spectra show that even excitation at the preferred mode cannot sustain the initially organized large-scale coherent structure beyond eight diameters from the jet exit. The background turbulence is organized by the coherent motions in such a way that the maximum rate of decrease of the coherent vorticity occurs at the structure centres which are the saddle points of the background-turbulence Reynolds-stress distributions. The structure centres are also the locations of peak phase-average turbulence intensities. The evolving shape of the structure as it travels downstream helps explain the transverse variations of the wavelength and convection velocity across the mixing layer. The coherent structure characteristics are found to be independent of whether the initial boundary layer is laminar or turbulent, but depend somewhat on the jet Reynolds number. With increasing Reynolds number, the structure decreases in the streamwise length and increases in the radial width and becomes relatively more energetic, and more efficient in the production of coherent Reynolds stress.

Turbulent spots evolving in a laminar boundary layer on a nominally zero pressure gradient flat plate are investigated. The plate is towed through an 18 m water channel, using a carriage that rides on a continuously replenished oil film giving a vibrationless tow. Turbulent spots are initiated using a solenoid valve that ejects a small amount of fluid through a minute hole on the working surface. A novel visualization technique that utilizes fluorescent dye excited by a sheet of laser light is employed. Some new aspects of the growth and entrainment of turbulent spots, especially with regard to lateral growth, are inferred from the present experiments. To supplement the information on lateral spreading, a surbulent wedge created by placing a roughness element in the laminar boundary layer is also studied both visually and with probe measurements. The present results show that, in addition to entrainment, another mechanism is needed to explain the lateral growth characteristics of a turbulent region in a laminar boundary layer. This mechanism, termed growth by destabilization, appears to be a result of the turbulence destabilizing the unstable laminar boundary layer in its vicinity. To further understand the growth mechanisms, the turbulence in the spot is modulated using drag-reducing additives and salinity stratification.

A closed-form solution of the coupled momentum and thermal energy equations is obtained for laminar gravitational circulation of water resulting from a longitudinal temperature gradient in a dead-end channel. The temperature gradient is determined by the rate of heat loss from the water surface. The solution is shown to be dependent on a modified Rayleigh number which involves the local surface heat-transfer coefficient. An experimental study was conducted, and the results are compared with the closed-form solution.

The European Mechanics Colloquium, Euromech 132, was held at the Ecole Centrale de Lyon from 2 to 4 July 1980. Specific areas of hot-wire or hot-film anemometry were presented and discussed, more especially the effect of the finite time constant of the wire supports, the use of yawed hot wires in supersonic flows, the possible improvement of vorticity meters, and multi-point measurements of wall-shear-stress fluctuations. Other subjects described during the meeting included a new technique for concentration measurements in flames, developments and new uses of digitization and conditional sampling, pattern recognition analysis of fluid flow from multi-point, multi-time velocity measurements, and new turbulence measurements in complex flows and in fluid-flow machinery.

An exhibition of hot-wire and hot-film anemometers and associated equipment was held during the colloquium.

The evolution of an infinitely long straight vortex filament in the presence of an approaching rigid sphere is considered. The fluid is regarded as being inviscid and incompressible. The shape of the vortex filament when the sphere is sufficiently far away from the vortex is determined approximately using linear theory. The subsequent evolution is followed numerically by integrating the nonlinear equation of motion.

The stability of an infinite layer of fluid of uniform thickness at rest with two horizontal boundaries is investigated when the difference between the temperatures at the top and bottom boundaries has a component which is a fluctuating periodic function of time in addition to a constant part. When both boundaries are free small fluctuations have a stabilizing effect on the layer, while large fluctuations tend to make it less stable, consistently with the numerical results of Yih & Li (1972); the effect is attributable entirely to the variation of the temperature gradient with time. An approximate relation between the mean Rayleigh number and the amplitude of the fluctuations is found which separates stable situations from unstable ones. This is compared with the criteria deduced by Homsy (1974) using energy arguments for disturbances of any amplitude.

The steady-state solution for the stratified flow over a bounded obstacle in a channel of finite height is obtained through the use of the inviscid unsteady Oseen equations; the body streamline encloses and is produced by a planar momentum sink. The calculations are compared with the experimental observations of Wei, Kao & Pao (1975) and Baines (1977). In a case where theoretical and experimental values match, good agreement was found. This suggests that the Oseen model with its columnar, wavelike and decaying solutions may provide a reasonable alternative to Long's model for subcritical flows.

Hot-wire measurements of second- and third-order mean products of velocity fluctuations have been made in the flow behind a backward-facing step with a thin, laminar boundary layer at the top of the step. Measurements extend to a distance of about 12 step heights downstream of the step, and include parts of the recirculating-flow region: approximate limits of validity of hot-wire results are given. The Reynolds number based on step height is about 105, the mixing layer being fully turbulent (fully three-dimensional eddies) well before reattachment, and fairly close to self-preservation in contrast to the results of some previous workers. Rapid changes in turbulence quantities occur in the reattachment region: Reynolds shear stress and triple products decrease spectacularly, mainly because of the confinement of the large eddies by the solid surface. The terms in the turbulent energy and shear stress balances also change rapidly but are still far from the self-preserving boundary-layer state even at the end of the measurement region.

In this paper we consider the stability of salt fingers to long wavelength internal wave perturbations. The Prandtl number of the fluid is assumed to be large, but the ratio of the two diffusivities (KS/KT) is allowed to be any size provided that KS < KT. This problem was first considered by Stern (1969), where several untested assumptions were made about the motion. Here we use a two-scale approach to separate the salt finger motions from the long-scale internal wave perturbations and to obtain the stability criterion. This collective instability of salt fingers succeeds in transferring energy from the small salt finger scales to the long internal wave scales.

Spatial stability results for the developing flow in a rigid circular pipe are presented for the velocity profile obtained by the Hornbeck (1963) method and compared with the available temporal stability results for the velocity profile obtained by Sparrow, Lin & Lundgren (1964). The disturbance is taken to be non-axisymmetric, and Gram–Schmidt orthonormalization is used to remove the parasitic errors during numerical integration.

It is found that the stability characteristics are very sensitive to the velocity field in the inlet region. At all axial locations investigated the critical frequency and critical wavenumber for the Hornbeck profile are larger than the corresponding values for the Sparrow profile while the critical Reynolds number is smaller. The minimum critical Reynolds number for the Hornbeck profile is only 13250 and occurs at $\overline{X} = 0.0032$ compared with 19780 at $\overline{X} = 0.0049$ for the Sparrow profile. The maximum difference between the two velocity profiles occurs near the boundary-layer edge but is within 5%. Results for the Hornbeck profile are found to be closer to the experimental data of Sarpkaya (1975).

The present study examines the steady, axisymmetric Stokes flow past a sphere coated with a thin, immiscible fluid layer. Inertial effects are neglected for both the outer fluid and the fluid film, and surface tension forces are assumed large compared with the viscous forces which deform the fluid film. Furthermore, the present analysis assumes that the mechanism driving the fluid circulation within the film is not too large. From force equilibrium on the film we find that a steady fluid film can only partially cover the sphere, i.e. the film must be held to the sphere by surface tension forces at the contact line. The extent of the sphere covered by the film is specified, in terms of the solid–fluid contact angle, by the condition of global force equilibrium on the fluid film.

Using a perturbation scheme based on the thinness of the fluid layer the solution to the flow field is obtained analytically, except for the fluid-film profile (i.e. the fluid–fluid interface) which requires numerical calculations. One of the principal results is an expression for the drag force on the fluid-coated particle. In particular, we find that the drag on a sphere is reduced by the presence of a fluid coating when the ratio of the film fluid viscosity to the surrounding fluid viscosity is less than ¼. Detailed numerical computations are conducted for a few typical cases. The calculations show that a film of prescribed areal extent, i.e. specified contact angle, is only possible when the magnitude of the driving force on the film is below some maximum value. A simple experiment was also performed, and photographs, which qualitatively illustrate the fundamental fluid-film configurations predicted by the theory, are presented.

Theoretical calculations show that the horizontal displacement of particles in the surface of steep solitary waves exceeds that predicted by the Korteweg–de Vries equation by as much as 100%.

Experimental evidence is given in support of the higher values.

The focusing of a weak and nearly plane shock wave at an axisymmetric arête is examined. The initial-value problem governing the flow in the focal region is derived. A similitude is introduced which shows that the details of the flow depend on the initial shape and strength of the shock only through a simple rescaling of the variables. The dependence of the pressure coefficient on the physical parameters is given. It is seen that the maximum pressure coefficient is proportional to a parameter measuring the rate of focusing of the shock and to the square root of a parameter measuring the initial strength of the shock.

The stress tensor in a granular shear flow is calculated by supposing that binary collisions between the particles comprising the granular mass are responsible for most of the momentum transport. We assume that the particles are smooth, hard, elastic spheres and express the stress as an integral containing probability distribution functions for the velocities of the particles and for their spatial arrangement. By assuming that the single-particle velocity distribution function is Maxwellian and that the spatial pair distribution function is given by a formula due to Carnahan & Starling, we reduce this integral to one depending upon a single non-dimensional parameter R: the ratio of the characteristic mean shear velocity to the root mean square of the precollisional particle-velocity perturbation. The integral is evaluated asymptotically for R [Gt ] 1 and R [Lt ] 1 and numerically for intermediate values. Good agreement is found between the stresses measured in experiments on dry granular materials and the theoretical predictions when R is given the value 1·7. This case is probably the one for which the present analysis is most appropriate. For moderate and large values of R, the theory predicts both shear and normal stresses that are proportional to the square of the particle diameter and the square of the shear rate, and depend strongly on the solids volume fraction. A provisional comparison is made between the stresses predicted in the limit R → ∞ and the experimental results of Bagnold for shear flow of neutrally buoyant wax spheres suspended in water. The predicted stresses are of the correct order of magnitude and yield the proper variation of stress with concentration. When R [Lt ] 1, the shear stress is linear in the shear rate, and the analysis can be applied to shear flow in a fluidized bed, although such an application is not developed further here.

Experiments have been carried out to investigate the phenomenon of vortex shedding from the blunt trailing edge of an aerodynamic body in transonic and supersonic flow. The effect of a discharge of bleed air from a slot in the trailing edge has been included and the relationship between the vortex formation and base pressure has been considered.

In transonic flow a small amount of bleed air was found to produce a rearward shift in the point of origin of the vortices with a consequent substantial increase in base pressure. The effect was less marked in supersonic flow. At higher rates of bleed two different regimes of vortex shedding were identified and increase in bleed rate caused a reduction in base pressure. For bleed rates giving near-maximum base pressure no vortex shedding occurred.

The unstable conclusion drawn by Ortloff & Ives of the cylinder motion in a viscous stream is shown to be incorrect. Furthermore, a region of stable solution is derived in the parameter space defined by the normal and tangential drag coefficients.

High-resolution measurements have been performed of the convective heat current as a function of time when a Rayleigh-Bénard cell is swept through its threshold with a specified time-dependent heat input. The results are interpreted in terms of the amplitude equation which exactly describes the slow variations in space and time of hydrodynamic quantities near the threshold. A phenomenological forcing field is added to this equation, and its form and magnitude are fitted to the onset time of the convective heat current. A deterministic model in which the field is an adjustable constant yields a good fit to the data for both a step and a linear ramp in the heat input. An alternative stochastic model, in which the field is a Gaussian variable with zero mean and a white-noise spectrum, is adequate for the ramp experiments, but cannot fit the step data for any value of the mean-square field. The systematics of the field and onset time versus ramp rate are studied in both the deterministic and stochastic models, and attempts are made to interpret the field in terms of physical mechanisms. When the data for long times are analysed in terms of the amplitude equation, it is found that the state first excited at onset is not the roll pattern which is stable in steady state. Instead, the system goes first to an intermediate state, which we tentatively identify as a hexagonal configuration. The decay of this state is governed by a further adjustable field in the amplitude equation.

An analysis is presented for the propagation of water waves past a rectangular submarine trench. Two-dimensional, linearized potential flow is assumed. The fluid domain is divided into two regions along the mouth of the trench. Solutions in each region are expressed in terms of the unknown normal derivative of the potential function along this common boundary with the final solution obtained by matching. Reflection and transmission coefficients are found for various submarine geometries. The result shows that, for a particular flow configuration, thereexists an infinite number of discrete wave frequencies at which waves are completely transmitted. The validity of the solution in the infinite constant-water-depth region is shown by comparing with the results using the boundary integral method for given velocity distributions along the mouth of the trench. The accuracy of the matching procedure is also demonstrated through the results of the boundary integral technique. In addition, laboratory experiments were performed and are compared with the theory for two of the cases considered.

The translational and rotational drag coefficients for a cylinder undergoing uniform translational and rotational motion in a model lipid bilayer membrane is calculated from the appropriate linearized Navier–Stokes equations. The calculation serves as a model for the lateral and rotational diffusion of membrane-bound particles and can be used to infer the ‘microviscosity’ of the membrane from the measured diffusion coefficients. The drag coefficients are obtained exactly using dual integral equation techniques. The region of validity of an earlier asymptotic solution obtained by Saffman (1976) is elucidated.