A uniform magnetic field is switched on at time t = 0 outside a body of conducting fluid. It is assumed that the field strength increases in time in proportion to 1 -e−αt, where α is a constant of the circuit generating the field. Under the assumption of small magnetic Reynolds number and small magnetic Prandtl number the equations governing the diffusion of the field into the fluid are derived and a simple expression is given for the initial vorticity distribution produced in the fluid. The situation in which an initially uniform field is switched off is also considered. It is shown that, for sufficiently symmetrically shaped bodies of fluid, the vorticity generated by the switching-on of the field is the same as that generated by the switching-off. The particular case of an infinitely long circular cylinder of conducting fluid is considered in detail and an explicit expression is derived for the vorticity distribution.

Large (gigajoule) amounts of energy can in principle be stored as kinetic energy in liquid metal circulating round a torus and can be extracted at the gigawatt level by Alfvén waves propagating along an imposed axial field. A major limitation on the energy that may be so stored is the disruption of these primary Alfvén waves by secondary flows in meridional planes, associated with out-of-balance centrifugal forces ahead of and behind the waves and non-uniform magnetic pressures at the wave fronts. Vorticity, created at the wave, itself propagates in secondary Alfvén waves.

This paper gives a linearized treatment of these secondary motions and the associated perturbations of the imposed axial field and compares the resulting disruption of the primary wave mode with crude estimates made in an earlier paper. The main case treated is the discharge of the stored energy into a matched resistor by an Alfvén step wave but the secondary consequences of standing primary waves are also explored. The nature of the solutions depends on the electromagnetic characteristics of the walls normal to the imposed field. The problem is mathematically interesting because it involves the joint solving of elliptic and hyperbolic equations that are coupled by the boundary conditions at these walls.

Treated in the present paper are the second-order effects, i.e. the effect of displacement thickness, longitudinal curvature, external shear and slip, on the two-dimensional laminar boundary-layer flow of incompressible fluid. The analysis is developed in terms of the stream-function co-ordinates proposed for the analysis of the rotational flow by the senior author previously. An inverse problem is set in the co-ordinates plane, and, within the framework of the second-order approximation, the problem is reduced to solving a parabolic partial differential equation for the total head. An implicit finite-difference scheme is then devised to solve the equation, and the practical computations are carried out for the flow along a flat plate or the one around a parabolic body, by making use of an electronic computer.

In this paper transonic small-disturbance theory is applied to a simplified model of the flow near the front of a ducted body. The body is assumed to consist simply of two parallel flat plates which extend from the inlet station to infinity downstream. The velocity far upstream is sonic, and the velocity far downstream in the duct, which is assumed to be known, is slightly subsonic. Air is therefore ‘spilled’ around the intake edges. An analytic solution is found for the resulting flow field up to the ‘limiting Mach wave’, and asymptotic solutions are found for the supersonic flow and for the shock wave far from, and near, the intake edges. The pressure distribution along the outside walls is then known at both ends, and its computation is completed by an empirical procedure. Distributions of pressure along the centre-line and along the inside and outside walls are shown. These results may be used to compute the drag of sharp-edged intakes with a very small frontal area.

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.

It is shown that for the steady isoenergetic rotational flow of an ideal gas, both the specific enthalpy and the speed of sound can be expressed as functions of the velocity. As a result, it is possible to formulate the equations of motion so that the velocity is the only dependent variable. For a gas whose enthalpy and sound speed are functionally related, the results are a generalization of those for a perfect gas. If the enthalpy and sound speed are independent variables, the new formulation leads to a single vector equation whose solution completely determines the flow.

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.

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.