It is suggested in this paper that axisymmetric holes in thin sheets of fluid in which surface tension forces predominate will open out if they are initially large in relation to the thickness of the sheet; but that small holes will close up. No exact criterion has been found for the critical hole size in a free falling sheet, but the behaviour of the sheet may be closely simulated by the suspension of a soap film between coaxial circular rings. Theoretical results and experimental observations on catenoid films so formed are described.

For a hole in a sheet standing under gravity on a horizontal plane an equilibrium configuration exists, which is shown to be unstable. It is suggested that in this case the equilibrium position serves to distinguish between holes which open and those which close. Experiments on the behaviour of holes in a mercury sheet reveal a well-defined critical size which is in good agreement with that predicted by the unstable equilibrium.

A further series of experiments on holes made in a sheet of water standing on paraffin wax gave no sharp distinction between opening and closing holes, and holes of a wide range of sizes could remain stationary. This behaviour is associated with changes in the angle of contact with the plane. Independent meniscus observations similar to those of Ablett for a steadily moving meniscus show that the angle of contact θa, for a meniscus about to advance is greater than the value θr for a meniscus on the point of receding. It is seen that this difference will produce a range of hole diameters within which a hole will be trapped and remain stationary. Observations on the minimum size of hole on a water sheet which will remain open are reported. But it was found that the largest holes which would remain stationary were too large in relation to the size of the sheet for reliable results to be obtained.

The motion of bodies through fluid at low Reynolds number is appreciably affected by the container walls. Consequently the Stokes-flow theory due to Batchelor (1970) and others for a slender body falling in an unbounded fluid is difficult to test experimentally unless it is extended to take account of nearby boundaries. Theoretical expressions are given here for certain drag coefficients of a circular cylindrical slender rod of finite length falling close to a single plane wall or falling midway between two parallel plane walls. Experiments with a very viscous liquid are described in which cylinders of small thickness-to-length ratios (ranging from 1:10 to 1:100 approximately) are made to fall in suitable orientations. From their times of fall over a measured distance experimental drag coefficients are determined and compared with the corresponding theoretical value from the extension of Batchelor's theory. For rods falling in a horizontal orientation the theoretical and experimental results are consistent within the order of accuracy of the experiments. However, when results are compared for rods falling in a vertical orientation there is a significant difference for which possible explanations are presented.

In recent years many problems concerned with the dispersion of a passive contaminant along pipes and channels have been investigated, and this paper is concerned with one such problem which arises in diverse applications. This is the study of the longitudinal dispersion of a contaminant whose concentration is prescribed as a harmonic function of time at one cross-section. On the basis of physical arguments and of detailed calculations for two laminar flows it is shown that for high frequencies the concentration pattern is transported downstream at the maximum fluid velocity but that for low frequencies it is transported at the discharge velocity, and that the fluctuations in concentration decay to zero in a much shorter downstream distance for high frequencies than for low frequencies. It is shown further that at high frequencies the concentration is exponentially small except near the places where the fluid velocity attains its maximum, whereas for low frequencies the variation in concentration over the cross-section is small. Some of these conclusions are compared with those made by others, and the agreement is in general satisfactory.

The eigenvalue equation for three-dimensional waves in parallel and cross flows parallel to a fluid discontinuity has been considered for spatially growing waves. The discontinuity plane (x, y plane) is perpendicular to the gravitational acceleration and consists in general of a jump in speed, in flow direction and in density. With the assumption of waves which are periodic in time and periodic in the y direction, the eigenvalue equation is solved for the complex wavenumber α in the x direction. These waves are used to Fourier synthesize the wave trails generated by a time-periodic disturbance with a Gaussian amplitude distribution e−δy2 along the y axis. Lines of constant phase and lines of constant amplitude within the wave trail have been illustrated for some examples.

The structure of shear layers due to bottom topography in a rotating stratified fluid is obtained under the restriction σS [Lt ] E½, where σS = ναgΔT/KΩ2L is a measure of the stratification and E = ν/Ω2L is the Ekman number. The layers are found to be similar to the side-wall layers discussed by Barcilon & Pedlosky (19673) if σS [Gt ] E½ and are Stewartson layers if $\sigma S \ll E^{\frac{2}{3}}$. Some comments are made on the possibility of Taylor column formation in a stratified fluid.

The force acting on a fish-like body with combined thickness and lifting effects is analysed on the assumption of inviscid flow. A general expression is developed for the pressure force on the body, which is analogous to the momentum-flux analysis for non-lifting bodies in classical hydrodynamics. For bodies with constant volume, the mean drag (or propulsive) force is expressed in terms of a contour integral around the vortex sheet behind the body. Attention is focused on the case of steady-state motion with constant angle of attack, and the induced drag is analysed for finned axisymmetric bodies using the slender-body approximation developed by Newman & Wu (1973). Unlike earlier results of Lighthill (1970), the lift–drag ratio in this case depends on the body thickness.

It is shown in this note that the velocity of unstable or neutral waves in plane Poiseuille flow or plane Couette-Poiseuille flow, or of axisymmetric waves in Poiseuille flow, stable or unstable, must lie within the range of the velocity of the flow.

It is proved that a critical level, at which a wave packet is neither reflected nor transmitted, can exist only if the wave normal curve, which is formed by taking the cross-section through the wave normal surface in the plane of propagation, possesses an asymptote which is parallel to the direction of variation of the properties of the medium through which the wave packet moves. This condition, when applied to various types of hydromagnetic waves (such as hydromagnetic waves of the inertial or gravity type, or slow magnetoacoustic waves), shows that critical levels for such waves can exist only if the direction of spatial variations of the medium is perpendicular to the ambient magnetic field. Provided that the angle between the gravitational acceleration, or the rotation axis, and the magnetic field is not zero, hydromagnetic critical levels, characteristic of the gravity or inertial type, act like ‘valves’ in the sense that the wave packet can pierce the critical level from one side and is captured from the other side. It is also pointed out that critical-level behaviour is to some extent a consequence of the WKBJ approximation since the other limit, namely when the waves feel an almost discontinuous behaviour in the properties of the medium, gives markedly different results, particularly in the presence of streaming, which can give rise to the phenomenon of wave amplification.

A slightly stratified shear flow is considered when the effects of nonlinearity, viscosity and thermal diffusivity are in balance in the critical layer. Finite amplitude essentially non-diffusive neutral waves exist only if the mean temperature, velocity and vorticity profiles are distorted such that small jumps in these quantities occur across the critical layer.

Linearized wave-stress tensors derived from Hamilton's variational principle may be asymmetric. If interpreted as momentum fluxes, they would lead to lack of conservation of orbital angular momentum. It is shown that changes in internal angular momentum or spin of waves and torque coupling to external fields can adequately provide conservation of total angular momentum in such cases, Examples are given for acoustic, internal gravity, Rossby and plasma waves.

An experimental investigation was undertaken of the flow produced by the inviscid expansion of air through a hypersonic nozzle. Stagnation enthalpy levels up to 4 × 107 J/kg were used, with initial dissociation levels approaching 90%. By measuring the flow velocity and the frozen dissociation fractions of oxygen and nitrogen, it was found that existing theoretical models served adequately to define the nozzle flow, at least for the purpose of conducting experiments involving reacting inviscid hypersonic flows about blunt bodies.

To solve a mathematical problem involving a small parameter, it is customary to expand the solution in powers of that parameter. In singular cases the resultant linearized problem may be insoluble, and in some such cases it is appropriate to expand the solution in powers of the square-root of the small parameter. These cases are associated with bifurcation of the solution. The method is illustrated by applying it to the Falkner-Skan equation and to a problem in hydrodynamic instability. In particular, Hartree's conjecture, that near separation the skin friction vanes like the square-root of the appropriate parameter of the Falkner-Skan equation, is substantiated.

The magnetohydrodynamic and Boussinesq approximations are used on a fully ionized ideal fluid with a longitudinal magnetic field. The flow is in a direction normal to the gravity vector and all variations in velocity, density and magnetic field. The stability characteristics, mainly for normal-mode perturbations, are investigated. Two simple problems with discontinuous profiles are solved analytically. For a double shear layer, an appropriate range of magnetic field values destabilizes the flow. A long wave theory is presented and applied to several problems, some of which are destabilized by an appropriate magnetic field. Finally, the solution for continuous profiles is presented and shown to decay algebraically in time for any stable stratification.

The interaction of a gas cloud of specified mass, momentum and energy with an atmosphere in uniform motion is studied using the kinetic theory of gases. The Krook collision model is used to obtain analytically interpretable and numerically tractable results describing the spatial and temporal evolution of the cloud. The cloud originates from a continuum source and expands to a free molecular flow. It then begins to collide with the atmosphere, and is gradually transformed into a continuum flow diffusing through the atmosphere while being convected by the uniform motion.