The steady movement of a liquid meniscus in a circular capillary tube has been examined theoretically for dynamic contact angles close to 90° with minute slippage of the liquid on the solid, thus relaxing the conventional no-slip boundary condition. The resulting flow field does not produce an unbounded force at the contact line, contrary to that with the no-slip condition. The interfacial velocity, wall stress, fluid pressure and the meniscus shape are calculated, and the significance of dynamic contact-angle measurements is discussed. A modified version of the classical Washburn equation which takes account of the meniscus also reveals the importance of slippage.

The hydrogen-bubble technique has been used to measure the velocities of pulsating water flow in a rigid circular pipe. Mean flows with Reynolds numbers between 1275 and 2900 were superimposed on an oscillating flow produced by moving the pipe axially with simple harmonic motion. While the velocities in the oscillating boundary layers on the pipe wall were found to be close to those predicted by laminar flow theory, at the higher Reynolds numbers the velocities near the centre of the pipe were lower than those predicted and more uniformly distributed.

The intermittency of the periodic bursts of turbulent motion at the higher Reynolds numbers was measured. At each mean-flow Reynolds number the turbulent intermittency of the flow was found to be a function of a single parameter: the harmonicflow Reynolds number.

A conditioning function is generally used to discriminate between the turbulent and non-turbulent zones in intermittent flows. Any fluid-mechanical property is conditioned by multiplying it by the intermittency function. A formalism is developed in which some integrals of the fluid-mechanical variables at the interface are important ingredients with a precise physical meaning. The present ideas may prove to be useful in turbulence dynamics and turbulent mixing of scalars.

The effect of a drag-reducing additive on the structure of wall turbulence in pipe flow was investigated experimentally. Real-time hologram interferometry was used for flow visualization and turbulence measurements. The real-time modulation of interference fringes by a refractive-index enhancer infused into the near-wall flow was recorded by medium-speed motion photography. The spanwise direction and the direction normal to the wall were studied to investigate the ‘streaks’ and ‘bursts’ that originate in the sublayer. A region of the flow was sampled for spatial and temporal correlations of concentration fluctuations to detect the scales of eddy interaction.

The addition of 50 p.p.m. by weight of Separan AP30 to water significantly altered the Newtonian wall-flow structure. The drag-reducing additive suppressed the formation of streaks and the eruption of bursts. When compared at the same wall shear, the sublayer period increased over the Newtonian value by a factor almost equal to the ratio of the corresponding non-dimensional streak spacings.

These results suggest a stabilized wall layer in the drag-reducing solution as compared with that of the Newtonian solvent, resulting in less turbulence production and reduced frictional drag. The role of the extensional viscosity of the dilute polymer solution is discussed as a possible mechanism for explaining the visualized and measured phenomena.

A series of experiments designed to reveal the properties of high Reynolds number vortex rings, using flow-visualization and laser-Doppler techniques, has uncovered several interesting and unexpected results. Starting at the beginning of the motion, at a nozzle, and proceeding downstream, these include the following.

1. A formation process that is strongly Reynolds number dependent.

2. The amount of vorticity that appears downstream is very close to that predicted by a simple ‘slug’ model. However flow-visualization studies show that such a model is an oversimplification and that an excess of ring vorticity is probably cancelled by the ingestion of vorticity of opposite sign at the nozzle lip.

3. (iii) A new, bimodal form of vortex-core instability has been observed at moderate but not high Reynolds numbers.

4. Azimuthal inhomogeneities in the breaking of these, and the normal instability waves, create an ‘axial’ flow along the vortex core in the turbulent ring. This axial flow takes the form of a propagating wave that has many characteristics of a solitary wave. It is hypothesized that this axial flow prevents further ring instability.

5. The long-term behaviour of the turbulent ring is marked by dramatic changes in its growth rate, which are probably related to changes in the ‘organization’ of the vortex core. The descriptive turbulent-ring model developed in Maxworthy (1974) is substantially confirmed by these experiments and by observation of ring propagation through a stratified ambient fluid.

High-speed motion pictures (2000 frames/s) of saltating spherical glass microbeads (of diameter 350–710 μm and density 2·5 g/cm3) were taken in an environmental wind tunnel to simulate the planetary boundary layer. Analysis of the experimental particle trajectories show the presence of a substantial lifting force in the intermediate stages of the trajectories. Numerical integration of the equations of motion including a Magnus lifting force produced good agreement with experiment. Typical spin rates were of the order of several hundred revolutions per second and some limited experimental proof of this is presented. Average values and frequency distributions for liftoff and impact angles are also presented. The average lift-off and impact angles for the experiments were 50° and 14° respectively. A semi-empirical procedure for determining the average trajectory associated with given conditions is developed.

A linear stability analysis is applied to a system consisting of a horizontal fluid layer overlying a layer of a porous medium saturated with the same fluid, with uniform heating from below. Surface-tension effects at a deformable upper surface are allowed for. The solution is obtained for constant-flux thermal boundary conditions.

Recent work (Hunter & Riahi 1975) on nonlinear convection in a rotating fluid is extended to a multi-modal regime. The schematic multi-boundary-layer method of Busse (1969) and the upper-bound technique of Howard (1963) are used to obtain upper bounds on the Nusselt number N. It is shown that there are infinitely many modes in the range $Ta \ll R^{\frac{3}{2}}$, where Ta is the Taylor number and R is the Rayleigh number, and different types of mode optimize N in different regions of the parameter space (R, Ta). While the optimal N is independent of Ta for Ta [Lt ] R, it is found that it increases with Ta in $R \ll Ta \ll (R \log R)^{\frac{4}{3}}$ and decreases as Ta increases in $(R \log R)^{\frac{4}{3}} \ll Ta \ll R^{\frac{3}{2}}$, and that the functional dependence of the optimal N on R and Ta is continuous (within a logarithmic term) throughout the region of R, Ta space.

The generation, and thence the dissipation, propagation and radiation, of waves in a compressible fluid subjected to a magnetic field is studied as an extension of the ‘acoustic analogy’ (Lighthill 1952) to magneto-acoustics. A formal theory of magneto-acoustic waves introduces (i) a single differential operator describing propagation, (ii) a dynamic and a magnetic tensor modelling generation and (iii) a dissipation tensor to complete the wave equation. The interpretation of these tensors indicates the magnitude of the physical processes of wave generation, by turbulence and inhomogeneities, and of wave dissipation, by viscous and electrical resistance and heat conduction. The total quadrupole components are classified according to the mode of emission. If the magnetic field or compressibility is neglected we obtain, respectively, ‘aerodynamic acoustics’ and a corresponding theory for Alfvén waves. These hydrodynamic and hydromagnetic results contrast with magnetodynamics, when the magnetic field is dominant. The magneto-acoustic far field implies a law of directivity and intensity of radiation. The main results have been collected in three summary tables (see appendix).

In a slow linear shear flow over a cylinder in contact with a plane, there is an infinite set of eddies within the cusps at the point of contact. If the cylinder is not in contact with the plane, there is a flux of fluid between the cylinder and the plane, no matter how small the gap. When the gap is approximately 0·685 times the cylinder radius or less, the flow separates from the boundaries. Single eddies form alternately on the plane and the cylinder. These interlace as the cylinder approaches the plane and force the fluid which flows through the gap to take a tortuous path. The expressions for the force and torque acting on the cylinder are also given.

This paper is a theoretical and experimental investigation of the onset of the buoyancydriven longitudinal roll cells that occur when a liquid layer flows over a heated horizontal plate. Linear stability theory is applied under the assumption that the spatially developing temperature profile can be treated locally, that is at each axial position, as being ‘frozen’. Using the film thickness as the length scaling factor, the critical Rayleigh numbers associated with the onset of longitudinal rolls are found to be considerably lower than measured values. A modified local stability analysis using the thermal boundary-layer thickness as the scaling factor is shown to agree with experiments. Predicted wavenumbers and the position of the onset of cellular convection are in agreement with wavenumbers measured by flow-visualization techniques. The position of the onset of cellular convection is also obtained from heat-transfer measurements at the heated surface. In the asymptotic limit of a linear undisturbed temperature profile the classical solutions of the Rayleigh-Bénard problem for the critical Rayleigh number and wavenumber are recovered, the only effect of the flow being the structure of the secondary flow that occurs when the system is unstable. Amplification theory is also compared with experimental data for the position at which the thermal effects of the convection are detectable and for the wavenumbers measured by flow visualization. The thermal amplification ratio $\overline{Nu}$ and a velocity-disturbance amplification ratio $\overline{w}$ are used to interpret the onset of discernible cellular convection. The data are not consistent with any single amplification ratio over the range of Rayleigh numbers studied (103 < Ra < 3 × 105), and the theoretical and experimental results suggest that a band of wavenumbers rather than a single wavenumber is encountered when cellular convection occurs.

This paper presents an inviscid bluff-body wake model which correctly takes into account the displacement effect of the far wake by means of an appropriate source–sink system located behind the body. The separating streamlines, which in previous inviscid wake models have been regarded as the time-averaged shear layers emanating from the separation points within a small distance downstream of the body, can be interpreted as the displacement surface of the wake throughout the whole region of flow behind the body. The solutions for a normal flat plate, a circular cylinder and a 90° wedge are worked out and compared with experiments, where possible. The theoretical pressure distributions agree fairly well with the experimental ones. The shape of the separating streamlines obtained from the present theory is physically reasonable and compares well with experimental results for a normal plate and a 90° wedge.