The flow set up in an oblate cavity of a precessing rigid body is examined under the assumptions that the ellipticity of the spheroidal boundary of the fluid is large compared with Ω/ω and that the boundary-layer thickness is small compared with the deviations of the boundary from sphericity (ω is the angular velocity of the rigid body about the axis of symmetry, Ω is the angular velocity with which this axis precesses).

The motion of the fluid is found by considering an initial-value problem in which the axis of rotation of the spheroid is impulsively moved at a time t = 0; before that time this axis is supposed to be fixed in space, the fluid and envelope turning about it as a solid body. The solution is divided into a steady motion and transients, and, by evaluating the effects of the viscous boundary layer, the transients are shown to decay with time. The steady motion which remains consists of a primary rigid-body rotation with the envelope, superimposed on which is a circulation with constant vorticity in planes perpendicular to ω × (ω × Ω), the streamlines being similarly situated ellipses.

The possible effects of the luni-solar precession on the fluid motions in the Earth's core are discussed.

An account is given of photographic and pressure observations made on the oblique shock waves occurring in the wake of self-sustaining detonation waves in hydrogen-oxygen mixtures initially at atmospheric pressure. Four explosion tubes were employed, of which three are of circular cross-section with internal diameters of 10, 5 and 1·6 cm and the fourth is a square-section tube of side 1·5 in.

On the assumption that the oblique shocks are sufficiently weak to be regarded as Mach waves, the flow Mach number relative to the detonation front is determined; these are found to be substantially higher than the values predicted by deal one-dimensional theory. The measured flow Mach numbers in the rarefaction are then used to calculate the pressure distribution in this region on the basis of the supersonic nozzle model due to Fay (1959, 1962). The predictions of this model are found to disagree with with the observed static pressure profiles. Moreover, the pressure following the initial peak persists at a higher value than the theoretical for distances of the order of 5–10 cm behind the front. This phenomenon implies that the wall boundary-layer pressure remains higher than the C-J value and it is suggested that the pressure difference across the boundary layer can account for the formation of the oblique waves.

The supersonic features of the flow can be accounted for by the turbulent-structure hypothesis of White (1961). Some validation of this hypothesis is provided here by the observation of the absence of the oblique shocks in overdriven detonation waves caused by the diminished effects of turbulence. This observation is consistent with the view that the oblique shocks are generated by the pressure difference across the boundary layer near the front as this difference would also be diminished in an over-driven wave.

The simplest case of turbulent motion in a conductive fluid is studied. The turbulence is assumed incompressible, isotropic, homogeneous, charge invariant and free of fourth-order cumulants. The emphasis is placed on certain integrals of the correlation functions such as kinetic and magnetic energy, voticity, and current. A system of non-linear ordinary differential equations is derived which governs these integral quantities Several cases are solved numerically, illustrating the decay of ordinary turbulence, the buildup of magnetic energy by a linear or a non-linear process, the buildup of kinetic energy, as well as the destruction of vorticity by Lorentz forces.

In order to handle certain dissipative effects, a special hypothesis is introduced which seems to promote mathematical simplicity. In particular, it leads to a simple decay law very similar to the decay law of ordinary turbulence.

The stability of Couette flow between concentric, co-rotating cylinders in an axial magnetic field is examined for fluids of arbitrary magnetic Prandtl number Pm = ν/η, where ν is the kinematic and η the magnetic viscosity of the fluid. It is assumed that the gap spacing d between the cylinders is small compared to the mean radius and that no magnetic disturbances penetrate into the cylinder walls. The critical Taylor number at which non-oscillatory disturbances are marginally stable is determined as a function of the magnetic Prandtl number and the dimensionless parameter S = (Vad/v)2, where Va is the Alfvén velocity. Asymptotic formulas relating the critical Taylor number to the magnitude of the magnetic field are derived for the limiting conditions of very small and very large magnetic Prandtl number.

A general theorem for drag is given according to which the boundary-layer drag of a body is equal to the inviscid drag of the displacement surface together with a term which is given as an integral involving the ‘streamwise’ momentum and displacement thicknesses taken round the trailing edge. A less accurate result for thin slender wings is that the boundary-layer drag is equal to the line integral $\rho _\infty U^2_\infty \int \Theta d \sigma$ taken round the trailing edge, where Θ is the streamwise momentum thickness. This result leads to the possibility of finding boundary-layer drag by means of a traverse round the trailing edge. The extension of the results to wings with swept trailing edges is also given.

A semi-infinite body of liquid is in uniform rotation about a vertical axis for t < 0. A concentrated, vertical displacement of the free surface is imposed at t = 0. The motion of the free surface for t > 0 is calculated in linear approximation with the aid of Hankel and Laplace transformations, together with an intermediate transformation to parabolic co-ordinates. The result appears as an integral superposition of dispersive waves that divides naturally into two parts, corresponding to waves of the first and second class, with angular frequencies that are respectively greater or less than twice the angular speed of rotation. The waves of the first class, which are qualitatively similar to those in the classical (Cauchy–Poisson) problem, are found to dominate the asymptotic representation, as obtained through a stationary-phase approximation. The analysis is carried out in such a way as to separate the effects of Coriolis acceleration and free-surface curvature. Attention is focused on concave surfaces, such as would be realized in a laboratory experiment, but it is pointed out that striking differences exist between the dispersion laws for concave and convex surfaces, especially as regards waves of the second class.

Experimental measurements were made of the difference in pressure at large distances on either side of a spherical particle settling slowly along the axis of a long circular tube filled with viscous liquid. At low particle Reynolds numbers and for small sphere-cylinder diameter ratios, it was found that the product of the pressure difference and the cross-sectional area of the tube is equal to twice the drag on the particle, in accord with theory.

The boundary-layer flow over a semi-infinite flat plate is investigated. For time t < 0 there is the usual steady velocity boundary layer and, neglecting viscous dissipation, no thermal boundary layer. At t = 0 a temperature boundary layer is initiated without altering the velocity, and the subsequent temperature distributionn is studied for large and small t.

Heat transfer by convection from isothermal rotating cones is investigated experimentally by measuring the sublimation rate from naphthalene-coated cones and using the analogy between heat and mass transfer. Measurements are made for a range of conditions from entirely laminar flow to conditions when the outer 70% of the surface area is covered by turbulent flow. Mass-transfer measurements for laminar flow over cones of vertex angles 180°, 150°, 120° and 90° are in good agreement with the theoretical prediction. For turbulent flow, experimental results for cones of the above vertex angles also agree very well with the semi-empirical analogy calculations for the disk case. A different heat- and mass-transfer relationship with the rotational Reynolds number is observed in the measurements on the 60° cone, and is believed to be due to a change of flow characteristics. The instability and the transition of flows over different cone models are also discussed.

The increase in hypervelocity launcher velocities, the tendency for models to become more fragile and the use of sabot techniques has made it increasingly more important to reduce peak accelerations during the launch phase. At the same time a high acceleration must be maintained to enable a launcher barrel of reasonable length to be used. This paper considers the theoretical design of a launcher to give constant acceleration to the model. A similarity solution is found for the launcher barrel and the solution is extended to the first stage of the launcher. Departure from ideal gas laws is also discussed and the theory is extended to include the effect of molecular volume. The motion of the driving piston in the first stage is considered in detail and techniques to ensure that the piston motion results in constant base pressure on the model are presented.

Vibrationally relaxing flow through a nozzle is examined in the case when the amount of energy in the lagging mode is small. It is shown that there exists a ‘boundary-layer’ region in which relatively large departures from equilibrium occur. The position of this region is given by the type of criterion that has previously been used to predict the onset of ‘freezing’. An analytical solution for the distribution of the vibrational energy in the nozzle is obtained for a particular nozzle geometry, and an expression for the final asymptotic ‘frozen’ value of the vibrational energy far downstream is found. This asymptotic solution can be obtained from conditions at the ‘freezing’ point provided a suitable boundary condition is applied there.

The starting-point for this paper is the suggestion (Batchelor 1956b) that the wake behind a bluff body in a uniform stream may consist principally of two eddies rotating in opposite directions. The fluid is assumed to be incompressible and in two-dimensional steady motion at a very high Reynolds number. Along the boundary between the eddies, a viscous layer must form. This layer is unusual in that merely the vorticity, and not the velocity itself, varies appreciably across it. It will be shown that such layers can be treated theoretically much more simply than the general case, because it is possible to linearize the equation of motion. They may, of course, exist in flows other than that past a bluff body.

A discussion is also given of the flow near the rear stagnation point, where this boundary layer meets the body. It had been suggested that a large number of small eddies would have to exist there, but this seems not to be so.