Part I describes measurements of the drag on circular cylinders, made by observing the bending of quartz fibres, in a stream with the Reynolds number range 0·5-100. Comparisons are made with other experimental values (which cover only the upper part of this range) and with the various theoretical calculations.

Part II advances experimental evidence for there being a transition in the mode of the vortex street in the wake of a cylinder at a Reynolds number around 90. Investigations of the nature of this transition and the differences between the flows on either side of it are described. The interpretation that the change is between a vortex street originating in the wake and one originating in the immediate vicinity of the cylinder is suggested.

First, from a volumetric formulation of the momentum theorem of linearized theory, a general analytic proof is presented of the invariance of the drag of an arbitrary spatial distribution of horseshoe vortices and sources under reversal of the undisturbed flow. By consideration of the interference drag of two such singularity distributions, a reverse-flow relation for steady subsonic or supersonic flow is then obtained. This relation, a generalization of the Ursell-Ward theorem, may be applied to configurations with bodies whose surfaces are not quasi-cylindrical and whose surface pressures are quadratically related to the perturbation velocity.

The relation is used to discuss several interfering two-body arrangements in supersonic flow. It is shown that, in certain cases, the drag and lift may be determined without knowledge of the interference flow field associated with the arbitrarily prescribed body geometry. The simplicity of the results permits the formulation of optimum problems. The invariance of the drag under flow reversal with unchanged geometry is also established.

If a series of air trajectories is drawn from a fixed point at a certain height above the earth's surface, the end-points of the superimposed trajectories, after each has been followed for a time t, will have a standard vector deviation S. The purpose of this paper is to discuss the form of S. One expression is obtained by relating S empirically to the magnitude of the mean vector position [x] of the ends of the trajectories, so that $S = CL |[X|L]|^a,$

where L is a certain length and C and a are dimensionless constants; a is found to be about 0·870 and C is nearly proportional to $\surd T$, where T is the total period over which the series of trajectories is initiated.

A more satisfying expression for S connects it with the variability of the wind during the priod of initiation of the trajectories, i.e. with the standard vector deviation of wind (ω) which is itself dependent on T. The relationship involves the Lagrangian correlation coefficient r(t) of wind with time along the trajectories. It is found that the variation of S with time t agrees well with that deduced from the exponential formula r(t) = e-αt. Moreover, α, the reciprocal of the characteristic time of the ‘eddies’, is identified with ω2/K where K is the coefficient of eddy viscosity for lateral mixing.

The rise of a gas bubble in a viscous liquid at high Reynolds number is investigated, it being shown that in this case the irrotational solution for the flow past the bubble gives a uniform approximation to the velocity field. The drag force experienced by the bubble is calculated on this hypothesis and the drag coefficent is found to be 32/R, where R is the Reynolds number (based on diameter) of the bubbles rising motion. This result is shown to be in fair agreement with experiment.

The theory is extended to non-spherical bubbles and the relation of the resulting theory, which enables both bubble shape and velocity of rise to be predicted, to experiment is discussed.

Finally, an inviscid model of the spherical cap bubble involving separated flow is considered.

A previous analysis for the generation of surface waves by a parallel shear flow (Miles 1957 a) is extended by: (a) presenting results based on a more accurate solution of the differential equation; (b) imposing the boundary condition at the surface wave, rather than at the mean surface; and (c) including the dominant viscous term in the complete Orr-Sommerfeld equation. The modification (a) yields an energy transfer somewhat smaller than that predicted previously but of the same order of magnitude as, and in rather better agreement with, observation, while (b) has no effect and (c) only a small effect for gravity waves. The analysis is based on the equations of motion in intrinsic co-ordinates (rather than the usual Orr-Sommerfeld equation) and may be of interest in other problems of hydrodynamic stability.

Some ablating bodies entering the atmosphere will melt or soften. Under deceleration, the soft or melted surface will tend to develop instabilities of the Lamb-Taylor type. Two situations involving viscous incompressible fluids are investigated here: one where the liquid layer has constant viscosity and finite thickness, and the other, where the viscosity increases exponentially with distance away from the interface, and the layer is semi-infinite in extent.

It can be demonstrated, that if one neglects gradients in the flow direction, the rate of growth of interface disturbances in a plane normal to the axis of an axially symmetric blunt body is independent of the flow velocity. The fact that the deceleration and liquid thickness vary with time along a trajectory is also included in the analysis. Results of calculations for the amplification factor and the most amplified wavelength are given.

A mechanism due to the deceleration is postulated, which would cause the formation of longitudinal grooves on the surface of an axially symmetric blunt body while entering the atmosphere.

During the last few years, many experimental devices have been built in which strong shock waves are generated in gases by electromagnetic forces on currentcarrying gas particles. The general theory of these devices is discussed, taking external circuit inductance into account. It is shown that a shock wave of constant speed is finally attained. This shock wave is travelling at 90% of its final speed when the circuit inductance has increased to 3·0 times its initial value.

When a fluid which is lighter than its surroundings is emitted by a source under a sloping roof (or a heavier fluid from a source on a sloping floor), it may flow as a relatively thin turbulent layer. The motion of this layer is governed by the rate at which it entrains the ambient fluid. A theory is presented in which it is assumed that the entrainment is proportional to the velocity of the layer multiplied by an empirical function, E(Ri), of the overall Richardson number for the layer defined by Ri = g(ρa - ρ) h/ρaV2. This theory predicts that in most practical cases the layer will rapidly attain an equilibrium state in which Ri does not vary with distance downstream, and the gravitational force on the layer is just balanced by the drag due to entrainment together with friction on the floor or roof.

Two series of laboratory experiments are described from which E(Ri) can be determined. In the first, the spread of a surface jet of fluid lighter than that over which it is flowing is measured; in the second, a study is made of the flow of a heavy liquid down the sloping floor of a channel. These experiments show that E falls off rapidly as Ri increases and is probably negligible when Ri is more than about 0·8.

The theoretical and experimental results allow predictions to be made of flow velocities once the rate of supply of density difference is known. An estimate is also given of the uniform velocity which the ambient fluid must possess in order to cause the motion of the layer to be reversed.

The Kelvin-Helmholtz model for the formation of surface waves at the interface between two fluids in relative motion is generalized for parallel shear flows. It is assumed that phase changes across the flow are negligible and hence that the aerodynamic pressure on the wave is in phase with its displacement (rather than its slope). A variational formulation is established and leads to the determination of appropriately weighted means for the velocity profiles. The principal application is to flow of a light inviscid fluid over a viscous liquid; it is shown that the principle of exchange of stabilities is applicable to such a configuration, and a critical wind speed in satisfactory agreement with observation is predicted for an air-oil interface. The results also are applied to an air-water interface and lead to the conclusion that Kelvin-Helmholtz instability of such an interface is unlikely at commonly observed wind speeds. A more general formulation of the Kelvin-Helmholtz boundary-value problem and variational principle, allowing for variations in both velocity and density, is given in two appendices.

For wings with supersonic edges and with arbitrary dihedral, twist, camber and thickness distribution, the pressure distribution on the wing exterior to and along the two Mach lines emanating from the vertex of the wing is equal to the corresponding pressure distribution for a planar wing. The problem is to find the pressure distribution inside the two Mach lines. In the present paper, the unknown pressure distribution is approximated by an elementary function of the two surface variables. The (as yet undetermined) constants in the function are then found by the conditions: (i) that the function takes on the corresponding planar values along the two Mach lines, (ii) that it fulfils certain generalized integral relationships (Ting 1959), and (iii) that it satisfies the averaging property of solutions of the wave equation to be developed in this paper. The generalized integral relationship relates the integral of the pressure distribution along the line of intersection of a Mach plane with the wing to the integral along the same line of the prescribed normal velocity. The averaging property relates the pressure distribution along the line of intersection of the surface of the dihedral wing to that on a planar wing.

A method, based on the measurement of attenuation of microwaves, which allows the electron density and the ionization rate of shock-heated gases to be obtained, is described. Results obtained for air in the shock Mach range 8·2-10·4, and for nitrogen containing 0·25% oxygen in the range 7·4-8·8, show that the electron density is in agreement with theoretical calculations based on thermodynamic equilibrium. Ionization time measurements in air are presented in this range and these results extend the measurements of Niblett & Blackman (1958) to a lower Mach range.

The motion of a fluid inside a rotating annulus of square cross-section, whose dimensions are small compared with the distance from the axis of rotation, is considered. The rigid side walls are held at different constant temperatures and the fluid motions that occur are strongly influenced by Coriolis accelerations. A detailed study is made of the azimuthally independent state, a Hadley cell, in the limit of small thermal Rossby number. It is convenient to employ a boundary layer type analysis, essentially with respect to the Taylor number and all the imposed boundary conditions are rigorously satisfied.

An entirely geostrophic thermal wind is found to obtain over the main body of the fluid. The circulation in the plane of the annular cross-section is entirely confined within narrow boundary layers and consists of a superposition of three cellular motions: a cell occupying the cross-section and two additional cells confined to the side-wall boundary layers. These motions are intimately related to the rotational constraint. The temperature distribution and its relation to the conductive and convective processes are determined.

The stability of a viscous fluid between concentric cylinders is analysed, for the case in which the basic velocity distribution is the sum of a velocity distribution due to the rotation of the cylinders (Taylor 1923), and a ‘pumping’ velocity distribution due to a pressure gradient acting round the cylinders (Dean 1928). The critical Taylor number is computed for a wide range of values of the ratio of average velocity of pumping to average velocity of rotation for the case in which the outer cylinder is stationary. It is assumed that the spacing between the cylinders is small.

The stability of plane shock waves was measured in a shock tube by perturbing the primary shock wave, formed on rupturing the diaphragm, by means of thin wedges. A time-record of the shape of the shock wave after it passed the wedges and travelled along a channel of constant cross-section was obtained by Schlieren photography. Analysis of the photographs enabled the rate at which the shock wave recovered its plane shape to be determined and this, together with the detailed shape of the wave at various instants, was compared with the first-order theory of Freeman (although all the conditions assumed in the theory could not be faithfully reproduced in the experiments).

For shock-wave Mach numbers of 1·165, 1·41 and 1·60, the time-rate of decay of the perturbations was found to agree quite well with the theoretical value, but the amplitudes of the perturbations were much larger than those given by the theory.

The experiments failed to give reliable information about the decay of the perturbations after a large time, owing, it is believed, to flow separation from the sharp corners of the wedges which constituted an additional source of disturbance to the shock waves.