The streamlines due to a stokeslet on the axis in a finite, semi-infinite and infinite cylinder are obtained together with the case of a Stokes-doublet and source-doublet in an infinite cylinder. In the infinite and semi-infinite cylinder examples an infinite set of toroidal eddies are obtained. The eddies alternate in sign and the magnitude of the stream function decays exponentially with distance from the driving singularity. In the finite cylinder a primary interior eddy adjacent to the singularity is always obtained and, depending on location of the singularity within the cylinder and the ratio of cylinder length to radius, a finite number of secondary interior eddies. In the case of long cylinders, the eddies are generated along the axis, whereas, for squat cylinders, secondary eddies occur in the radial direction. The interior eddies emerge from the corner as the length of the cylinder is increased. Moffatt corner eddies exist but they are very much smaller than the interior eddies.

The far field of a lifting three-dimensional wing in transonic flow is analysed. The boundary-value problem governing the flow far from the wing is derived by the method of matched asymptotic expansions. The main result is to show that corrections which are second order in the near field make a first-order contribution to the far field. The present study corrects and simplifies the work of Cheng & Hafez (1975) and Barnwell (1975).

Solutions to Long's equation for a stably stratified incompressible fluid traversing a mountain range are obtained for various terrain shapes and amplitudes when the horizontal scale is large compared to the vertical wavelength. Nonlinear lower and upper (radiative) boundary conditions are utilized and found to have a strong influence on the wave structure at large amplitudes. The results for symmetric and asymmetric mountain profiles reveal that the wave amplitude and wave drag are significantly enhanced for mountains with gentle windward and steep leeward slopes. These results confirm and explain those obtained by Raymond (1972) using a different solution method. Several results obtained by Smith (1977) from perturbation analysis are also confirmed and extended to large amplitudes. The methods are also applied to investigate the nonlinear nature of the singularity predicted by linear theory for flow over a step.

In order to elucidate the general Stokes flow characteristics present for slender bodies of finite centre-line curvature the singularity method for Stokes flow has been employed to construct solutions to the flow past a slender torus. The symmetry of the geometry and absence of ends has made a highly accurate analysis possible. The no-slip boundary condition on the body surface is satisfied up to an error term of O(ε2 In ε), where ε is the slenderness parameter (ratio of cross-sectional radius to centre-line radius). This degree of accuracy makes it possible to determine the force per unit length experienced by the torus up to a term of O(ε2). A comparison is made between the force coefficients of the slender torus to those of a straight slender body to illustrate the large differences that may occur as a result of the finite centre-line curvature.

The existence of a liquefaction shock wave, a compression shock which converts vapour into liquid, has recently been predicted on physical grounds. The liquefaction shock was experimentally produced as the reflected shock at the closed end of a shock tube. Measurements of pressure, temperature, index of refraction and shock velocity confirm the existence of the shock and its general conformity to classical Rankine-Hugoniot conditions, with a discrepancy ∼ 10°C between measured and predicted liquid temperatures. Photographic observations confirmed the existence of a clear liquid phase and revealed the (unanticipated) presence of small two-phase torus-form rings. These rings are interpreted as vortices and are formed in or near the shockfront (∼ 50 rings/mm2 are visible near the shockfront at any given time). Separate experiments with the incident shock under conditions of partial liquefaction produced a fog behind the shock: measurements of laser-beam attenuation yielded the thickness of the condensation zone and estimates of the droplet size (∼ 10−7 m).

The fluctuating velocity components, u and w, and their gradients at the wall, \[ (\partial u/\partial y)|_{w}\quad {\rm and}\quad (\partial w/\partial y)|_{w}, \] were measured in a fully developed turbulent channel flow using hot-film probes. The data were taken in an oil channel at a low Reynolds number which allowed velocity measurements very close to the wall. From simultaneous measurements of these signals it could be deduced that coherent flow structures, inclined to the wall, travel downstream. Space-time correlations imply that these are rotating structures. The spanwise distance between these structures was found to be z+ ≈ 50 and they could be observed over a streamwise distance of Δx+ > 1000.

A numerical solution is obtained to describe the behaviour of a uniform bore over a sloping beach and the subsequent run-up and back-wash. The results exhibit features which have only previously been described in a qualitative manner. These include the formation’ of a landward-facing bore in the back-wash. A comprehensive set of results are presented for a typical initial subcritical bore height ratio.

The horseshoe vortex formed around the base of a cylinder by a separating laminar boundary layer has been investigated experimentally. Smoke flow visualization shows that both steady and unsteady vortex systems exist. Pressure distributions beneath both types of vortex system have been measured and the variation of the horseshoe vortex position on the plane of symmetry upstream of the cylinder has been determined. Unsteady horseshoe vortex systems are shown to have a complex oscillatory behaviour and the nature of this oscillatory behaviour is described. Using smoke flow visualization techniques some measurements have been made of the velocity distributions within horseshoe vortex systems.

This paper is concerned with the rate of transfer of heat or mass from a force-free couple-free particle immersed in fluid whose velocity far from the particle is steady and varies linearly with position. Asymptotic results for both small and large Péclet numbers are considered. There is at least a four-parameter family of different linear ambient velocity distributions, but nevertheless a comprehensive set of results for the transfer rate may be compiled by combining previously published work with some new developments. Some of these are exact results for particular linear ambient flow fields and some are approximate results for classes of linear flow fields.

For small Péclet number (P), the non-dimensional additional transfer rate due to convection is equal to αN20P½, where N0 is the Nusselt number for P = 0 and the proportionality constant α is a parameter of the concentration distribution due to a steady point source in the given linear ambient flow field. A general method of determining α is developed, and numerical values are found for some particular linear ambient flow fields. It is estimated that the value of α for any linear ambient flow field in which the vorticity does not dominate the straining motion lies within 10% of 0·34 when P is defined in terms of a particular invariant of the ambient rate-of-strain tensor E.

At large Péclet number the transfer rate N depends on the velocity distribution near the particle, and attention is restricted to the case of a sphere in low-Reynolds-number flow. For a rigid sphere $N = \beta P^{\frac{1}{3}}$ for any ambient pure straining motion, and the Levich concentration-boundary-layer method may be used to show that β = 0·90 for both axisymmetric and two-dimensional ambient pure straining, and probably for any other pure straining motion, when P is suitably defined. When the ambient vorticity ω is non-zero, the sphere rotates, and the Levich method cannot be used. However, it is shown that the part of the velocity distribution that varies sinusoidally with the azimuthal angle around the rotation axis does not affect the transfer rate and that N is asymptotically the same as for an ambient axisymmetric pure straining motion with rate of extension in the direction of the axis of symmetry equal to Eω(= ω. E. ω/ω2). In the exceptional case Eω = 0, N approaches a constant as P → ∞.

It is possible to interpolate between the asymptotic relations for small and large Péclet number with comparatively little uncertainty for any ambient pure straining motion and for any linear ambient flow field in which ω and Eω are non-zero.