A pulsating sphere, which performs a sequence of virtually impulsive changes in its radius with time, is completely surrounded by an inviscid, incompressible fluid whose velocity field is generally rotational. This paper indicates how it is possible, by means of Helmholtz's theorem, to relate the corresponding vorticity and velocity fields immediately before and after such expansions or contractions.

The method is then applied to the case of a spherical mass of fluid initially in uniform rotation in which a spherical core undergoes a single sudden expansion, followed after a short interval by an equally rapid contraction back to the original radius. An interesting meridional flow is thereby induced, which tends to decrease the angular velocity of rotation of the fluid near the poles at the outer surface, relative to that of the equatorial fluid. It is perhaps significant that this is in qualitative agreement with the variation of angular velocities observed at the surface of the sun.

An experiment has been performed, using pulsed dye injection on an aerofoil in a Hele-Shaw cell. The purpose was to observe the form of the trailing-edge flow when the Reynolds number was high enough to permit separation and the initiation of a Kutta condition. The experiment provides a successful confirmation of the existence of a ‘viscous tail’ as predicted by Buckmaster (1970) although there is an unexplained quantitative discrepancy.

The rotating system of an infinite disk beneath an unbounded fluid can exhibit resonance if the disk performs torsional oscillations at a certain frequency. This effect is examined in detail, and the solution is shown to depend crucially upon the existence of a small, steady departure from the basic rotational state in the far field.

The flows caused by a uniformly expanding circular cylinder or sphere in a perfect gas at rest at various (from small to very large) expansion velocities are analysed by a method of successive approximations in which the first approximation represents the incompressible flow. The shock waves which form around the bodies are also treated. The results for a sphere, even up to the third approximation, agree closely with Taylor's (1946) calculations for all the expansion rates.

For the understanding of longshore currents along a natural beach, the effects of bottom unevenness are considered to be important, especially for the flow in the swash zone. Currents in the swash zone are strongly influenced by the bed slope because the effect of gravity overwhelms the effect of the depth change. In the present paper, we investigate these effects and focus on waves propagating from offshore over a flat ocean basin of constant depth to a beach with a sloping wavy bottom. The waves are incident at a small angle to the beach normal, and the bed slope in the alongshore direction is varied slowly. To simplify the problem, only cnoidal waves and solitary waves are considered and the bed level is varied sinusoidally in the longshore direction.

A perturbation method is applied to the two-dimensional nonlinear shallow water equation (two-dimensional NLSWE) for the wave motion in order to generate a more simplified model of wave dynamics consisting of a one-dimensional NLSWE for the direction normal to the beach and an equation for the alongshore direction. The first equation, the one-dimensional NLSWE, is solved by Carrier & Greenspan's transformation. The solution of the second one is found by extending Brocchini & Peregrine's solution for a flat beach. Two methods for the solution of the one- dimensional NLSWE are introduced in order to get a solution applicable to large-amplitude swash motions, where the amplitude is comparable to the beach length. One is the Maclaurin expansion of the solution around the moving shoreline, and the other is Riemann's representation of the solution, which exactly satisfies the one-dimensional NLSWE and the boundary conditions. After doing a consistency check by confirming that Riemann's method, a numerical solution, agrees with the exact solution for an infinitely long, sloping beach, we assumed that the Maclaurin series solution can also describe wave motion in the swash zone properly not only for this model but also for our ‘wavy’, finite beach model.

The solution obtained from the Maclaurin series is then plugged into the equation for the alongshore direction to calculate the shore currents induced by wave run-up and back-wash motions, where a ‘weakly two-dimensional solution’ is derived from geometrical considerations. The results show that since the water depth near the shoreline is comparable to the bed level fluctuations, the flow is strongly affected by the bed unevenness, leading to recognizable changes in shoreline movement and the time-averaged velocity and the mass flux of the flow in the swash zone. More specifically, the inhomogeneity of the alongshore mass flux generates offshore currents because of the continuity condition for the fluid mass.

In this paper we solve some model problems by the method of matched expansions and deduce some features of Green's function using the reciprocal theorem to demonstrate that scattering by density gradients can enhance the radiation efficiency of quadrupoles to that of dipoles. If a fluid is subjected to body forces close to and on both sides of a density interface, then the source system degenerates to a quadrupole only if the components of the forces perpendicular to the interface are equal in magnitude and opposite in direction and, additionally, the components of the forces per unit fluid density parallel to the interface are equal but opposite. In other cases dipole rather than quadrupole radiation efficiency is achieved. But we also show that, despite published assertions to the contrary, the radiation efficiency is not enhanced further and there is no monopole contribution to the radiated sound.

General solutions for the linearized three-dimensional unsteady motion of a relaxing gas, including the effects of direct heat addition, are obtained using a Green's function technique. The possibility of direct heat addition into each separate mode of energy storage must be catered for, and the solutions have some bearing on the question of the heating of a gas by radiation.

Examples are given of initial-value and heat-source solutions in an unbounded domain and the boundary-value problem is exemplified by a study of the motion created by a spherical piston.

Detailed measurements of the flow over a compression corner were taken using hot-wire probes. The experiments were performed in supersonic flow (M = 2·64) under adiabatic wall conditions. The incompressible analogues of the boundary-layer profiles were obtained and their integral characteristics and shape factors correlated. Comparison with the self-similar profiles used by Lees & Reeves (1964) to describe interaction problems showed some similarities between the shape factors, but the measured negative shears in the separated bubble proved to be much less.

The waves propagating from an oscillating plane piston into a vibrationally relaxing gas are calculated by an exact numerical method ignoring viscosity and heat conduction. Secondary effects due to the starting of the piston from rest and to acoustic streaming can be eliminated from the calculated flows, leaving a truly periodic progressive wave which can be analysed and compared with approximate solutions. It is found that for moderate amplitude waves nonlinearity is only important as a convective effect which produces higher harmonics, whereas dissipation is adequately described by linear theory.