A solution for the profile of a small drop or bubble symmetrical about a vertical axis and at rest in a second fluid is obtained as a first-order perturbation of a circle. At the end of the drop opposite the apex, the perturbation approach breaks down and a matching zero-gravity solution is used. The results agree with numerical solutions and indicate that the pendant-drop profile of maximum volume fitting a given small vertical tube intersects the exit plane at very nearly 90°. This enables the maximum volume to be determined accurately from a force balance.

The effect of tube elasticity on the stability of Poiseuille flow to infinitesimal axisymmetric disturbances is investigated. The disturbance equations for the fluid are solved numerically while those for the arbitrarily thick tube are solved analytically in terms of Bessel functions of complex argument. It is shown that an elastic tube can cause instability of Poiseuille flow, unlike a rigid tube, in which the flow is always stable. Neutral curves are presented for various values of the tube parameters. It is found that the critical Reynolds number varies almost as the square root of the Young's modulus of the tube material while the critical dimensionless frequency is almost invariant, being about 1·1 for the cases studied.

A linear stability analysis is presented for flow between concentric cylinders when a fully developed axial flow is present. Small perturbations are assumed to be nonaxisymmetric. This leads to an eigenvalue problem with four eigenvalues: the critical Taylor number, an amplification factor and two wavenumbers. The presence of the tangential wavenumber permits prediction of the stability of spiral flow. This made it possible to model the flow more accurately and to extend the range of calculations to higher axial Reynolds numbers than had previously been attainable. Calculations were carried out for radius ratios from 0·95 to 0·1, Reynolds numbers as large as 300 and cases with co-rotation and counter-rotation of the cylinders.

The experiment of Champagne, Harris & Corrsin in generating and studying a nearly homogeneous turbulent shear flow has been extended to larger values of the dimensionless downstream time or strain by the use of a larger mean velocity gradient in the same wind tunnel. The system appears to reach an asymptotic state in which scales and turbulent energy grow monotonically. Two-point covariances and tensor structure of one-point ‘Reynolds stress’ and ‘pressure/strain-rate covariance’ agree with the earlier case. However, the linear intercomponent energy exchange hypothesis due to Rotta, very roughly confirmed by the earlier experiment, is contradicted by the present data.

A numerical investigation of the problem of rotating disks is made using the Newton–Raphson method. It is shown that the governing equations may exhibit one, three or five solutions. A physical interpretation of the calculated profiles will be presented. The results computed reveal that both Batchelor and Stewartson analysis yields for high Reynolds numbers results which are in agreement with our observations, i.e. the fluid may rotate as a rigid body or the main body of the fluid may be almost at rest, respectively. Occurrence of a two-cell situation at particular branches will be discussed.

A photogrammetrical technique has been used to study the interaction of two identical explosively produced spherical shock waves and to compare this interaction with the reflexion of one of the spherical shocks from the ground. It is postulated that there was no energy loss in the interaction of the two shock waves and that the interaction therefore simulated the reflexion of a spherical shock from an ideal non-energyabsorbing surface. The ‘ideal’ reflexions were compared with real reflexions from two types of ground surface: one smooth and the other rough. Experiments were carried out with the centres of the spherical shocks at two separations so that observations could be made of the interaction of shocks of different strength. Significant differences were shown to exist in both the strengths of the Mach shocks and in the triple-point trajectories over the different surfaces. The results are intended to aid in the evaluation of computer codes being developed to simulate spherical-shock reflexions from real surfaces.

A subgrid model is presented for a passive scalar advected by a randomly prescribed frozen velocity field. In addition to an eddy diffusivity it has a term which describes the injection of noise from the subgrid scales, and a term which implicitly describes the coupling between the large eddies and the eddies just below the limit of resolution of the finite-difference grid. The construction of the model is based upon an iterative procedure which models away first the dissipation-range eddies and then the eddies of a slightly larger size, etc.

The unsteady creeping motion of a thin sheet of viscous liquid as it advances over a gently sloping dry bed is examined. Attention is focused on the motion of the leading edge under various influences and four problems are discussed. In the first problem the fluid is travelling down an open channel formed by two straight parallel retaining walls placed perpendicular to an inclined plane. When the channel axis is parallel to the fall line there is a progressive-wave solution with a straight leading edge, but inclination of the axis generates distortions and these are calculated. In the second problem a sheet with a straight leading edge travelling over an inclined plane penetrates a region where the bed is uneven, and the subsequent deformation of the leading edge is followed. The third problem considers the flow down an open channel of circular cross-section (a partially filled pipe) and the time-dependent shape of the leading edge is calculated. The fourth problem is that of flow down an inclined plane with a single curved retaining wall. These problems are all analysed by assuming that a length characteristic of the geometry is large compared with the fluid depth divided by the bed slope, and all the solutions display extreme sensitivity to the data.

The flows induced by the presence of an insulating sloping boundary in a doublediffusive system are examined. In the diffusive case, when the component with the larger diffusivity is unstably distributed, it is known that under certain circumstances horizontal motions are induced near the slope, and that a series of horizontal layers forms. We investigate the formation and properties of the layers, in particular their vertical scale and its dependence on the stratification and the slope angle. The scale of the layers is found to be a strong function of Gρ, the ratio of the vertical density gradient of the unstably distributed component to that of the stably distributed component. At low values of Gρ, no layering was observed; at larger values of Gρ layers were formed, and their scale increased as Gρ → 1. A weak dependence of scale on slope angle was also observed with the scale diminishing as the angle of the slope to the horizontal increased.

A new form of layering has been observed when the basic stratification is in the finger sense. At high enough values of Gρ the basic stratification is unstable to finger motions and these exist throughout the fluid. When a slope is introduced, horizontal motions are set up near the slope which cause the fingers to break down and layers are produced. There is considerable horizontal motion in these layers as well as convective motions driven by the fingers in the interfaces between the layers. The formation of these layers and some of their properties are documented.

The paper generalizes an earlier problem of Grundy (1972) by considering the expansion of a (uniform) initially contained gas into a low-density non-uniform ambient atmosphere of density ρ0r−k, where k > 0 and r is a non-dimensional radial co-ordinate. Regarding the flow as a perturbation of the perfect-vacuum expansion, we set up a boundary-value problem with boundary conditions on the contact front separating the two gases and on the strong shock which propagates into the ambient atmosphere. A large time solution to the problem can be developed by constructing an outer expansion valid near the contact front and an inner expansion valid near the shock. The matching process encounters two kinds of difficulty both of which imply that the large time solution is indeterminate from an asymptotic analysis alone.

The asymptotic analysis does show however that the shock velocity tends to a constant only for restricted values of k. For the remaining values the shock has a k-dependent power-law behaviour. The paper examines the location of the transition and determines the asymptotic power-law dependence of the shock velocity.