In the steady-state counterpart of the wake behind a totally immersed, self-propelled body, simulated in an air tunnel by a concentric nozzle and disk, measurements were made of mean-flow velocity and pressure, turbulence intensities in the three co-ordinate directions, turbulent shear, and mean temporal gradient and auto-correlation of the axial-velocity fluctuations. Through the equations of momentum and energy for the mean and the turbulent motion, the experimental data were used to verify the condition of self-propulsion and the accuracy of measurement, and to provide a picture of the force field and the process of energy transformation.

The variation of the principal flow characteristics was analysed with the aid of appropriate hypotheses as to the transport mechanism and the structure of the turbulence. Two hypotheses proved to be most useful: a more general concept of self-preservation than is known from elementary free-turbulence flows; and the assumption that beyond an intial shear zone the turbulence can be regarded as having originated at a point source in the flow. Extension of the analysis to flows past line and plane sources of turbulence then permitted its validity to be tested with the extensive experimental information available on decaying homogeneous turbulence behind a grid. The rates of diffusion and decay were first deduced in terms of the conventional power laws and thereafter, on the assumption of proportionality of all length scales for any one flow, in terms of more elaborate relationships. The most noteworthy results of the latter approach are the asymptotic development of wake widths and eddy scales toward constant values and the elimination of the subdivision of the flow field into a number of decay zones of vaguely defined limits that has been customary in the theory of homogeneous turbulence. Agreement with corresponding experimental results for a self-propelled body and a grid (i.e. for a point and a plane source of turbulence) was obtained over the entire available ranges of measurement.

Approximate methods are used in a theoretical investigation of piston acceleration, peak pressure and piston oscillations in a gun tunnel. Behaviour in all these respects, at a given ratio of initial driver and test gas pressures, is related to the value of a ‘gun tunnel parameter’, Λ, and the ratio of the speeds of sound in driver and test gases. It is shown that large values of Λ must be combined with an enhanced speed of sound in the driver if high performance is to be achieved with manageable peak pressures. With air as test gas, using values of Λ achieved in current practice and a suitable driver gas, the analysis indicates that piston speeds approaching four times the speed of sound in air may be obtained.

Film-thickness measurements on some liquids flowing down vertical surfaces gave values higher than those given by Nusselt's theory. This was shown to be due to the presence of waves on the film surface, and the discrepancy is thought to be due mainly to the omission from Nusselt's theory of the factors causing wave motion. The authors have investigated flow in films of water on a rotating disk to find whether or not this discrepancy between the actual and theoretical thickness, as calculated by laminar-flow film theory, occur in this case also.

Spanwise variations of surface shear stress, amounting to 10% or more, may be produced in nominally two-dimensional boundary layers by a spatial instability of the flow through the wind-tunnel damping screens: boundary layers are shown theoretically to be very sensitive to variations of free-stream direction. Screens with open-area ratios more than about 0·57 do not produce appreciable spanwise variations in the boundary layer, and it is recommended that tunnels for boundary-layer measurements should be fitted with such screens. The critical open-area ratio does not seem to depend noticeably on Reynolds number in the usual range encountered in wind tunnels, but the figure of 0·57 should not be taken as general until measurements have been made in representative selection of wind tunnels in other laboratories.

The ‘switch-on’ ionizing shock wave, initiated by a strong radial discharge between electrodes at one end of a cylindrical tube placed in a solenoid, moves along the tube with a speed that depends principally on the parameter $\xi = B_{\theta } B_0|(2e_0 \rho _1),$ where Bθ is the jump in the transverse magnetic field caused by the discharge current, B0 is the applied axial field, ρ1 is the upstream (neutral) gas density, and e0 is the ionization energy. This simple result, established by Kunkel & Gross (1962) with the aid of the Chapman-Jouguet hypothesis and for fully ionizing shocks in an infinite-slab plasma, is here extended to cylindrical plasmas and to partially ionizing shocks. The effect of dissociation energy is also taken into account. The degree of ionization is determined by applying the Saha equation downstream of the shock. Most reported experiments fall into the partially ionized region, and are found to be in good agreement with the theory given in this paper.

This paper gives the theory of the motion of a finitely conducting, viscous liquid between long, concentric, rotating cylinders under a radial magnetic field in the case of high Hartmann number. Because the current and vorticity contents of a Hartmann layer are related, it is easy to predict the behaviour in both steady and unsteady states. Experiments with mercury which confirm the theory closely are described. As these were developed for an educational film on magnetohydrodynamics, they have the attraction that the results are immediately obvious to the observer.

The terminal velocities, drag coefficients, and orientations of single cylinders falling in a large tank of viscous liquid have been determined for Reynolds numbers Re ranging from > 0·01 to 1000 to 1000. Stationary eddies appear in the wakes of cylinders at 26 > Re > 50, and the shedding of a Kármán vortex street at Re > 50 causes them to oscillate as they fall.

The interaction of two long, thin cylinders, which is largely determined by their initial relative positions, has been studied in some detail. One interesting result is that two equal cylinders, initially non-parallel and vertically separated by about 50 diameters, catch up and slide along each other until they bisect at right angles. When several cylinders are released in random orientations, they tend to cluster and then separate into pairs crossed at right angles and into trip-lets in the form of a symmetrical ++.

Cones with a flat base fall with apex upwards if the vertex angle θ < ¼π and with apex downwards if θ > ¼π. Double cones, cemented base to base, and with apex angles θ1 and θ2(θ2 > θ1), fall with acute apex upwards if $2\theta _1 + \theta_2 \textless \frac {3}{2} \pi$, the stable orientation being apex downwards if this condition is not satisfied. At Re ≃ 100, the shedding of a Kármán vortex street causes the cones to oscillate, while at Re > 800, the flow becomes highly turbulent and they tumble as they fall.

Some experimental results are presented for the motion of small rigid spherical particles suspended in a Newtonian viscous liquid flowing under steady laminar conditions in a vertical tube of circular cross-section. When the particles were neutrally buoyant, the Segré & Silberberg (1961, 1962) effect was confirmed, the particles moving into a narrow annular zone with a diameter about two-thirds of the tube diameter. When the particles were slightly denser than the fluid, they migrated relatively rapidly to the wall of the tube for downward fluid flow and to the axis of the tube for upward fluid flow. Individual particle trajectories were obtained (necessarily approximately) from photographic records, and statistical techniques used to obtain ‘universal’ paths for given flow conditions. A complete set of relevant dimensionless parameters is given by the tube flow Reynolds number, the ratio of the tube diameter to the particle diameter, and the ratio of the Stokes free-fall velocity of the particle to the maximum fluid velocity. An attempt has been made to study the dependence of the trajectories on each of these parameters, the ranges being 10–200, 10–20 and 0–0.2 respectively. Detailed results can be found in Jeffrey (1964). Some comments are made on the relevance for this situation of certain theoretical solutions given elsewhere.

This paper is concerned with forced oscillations of fluid in a rectangular container. From the linearized approximation of the equations governing these oscillations, resonance frequencies are obtained for which the amplitude of the oscillations becomes infinite. Observation shows that under these circumstances a hydraulic jump is formed, which travels periodically back and forth between the walls of the container. This hydraulic jump is a non-linear phenomenon, analogous to the shock wave appearing in one-dimensional gas flow under similar resonance conditions.

A theory developed by previous authors for one-dimensional gas flow is applied to the fluid oscillations in order to calculate the strength and the phase of the jump. The moment exerted on the container is also calculated. These quantities were measured experimentally at the lowest resonance frequency and the results are in good agreement with the theoretical values.

The effect of Coriolis force on the onset of thermal convection in a shallow layer of viscous liquid is studied in the limit of rapid rotation of the layer. Existing results which apply when the fluid lies between free boundaries are extended to the case where the boundaries are rigid.

Using a method due to Davies & Taylor (1950), a simple model is employed to derive the velocity of a two-dimensional gas bubble rising in liquid along the axis of a channel of finite width. The asymptotes of the solution agree well with previous results and an experimental investigation confirms the effect of channel width on bubble velocity. Measured values of velocity are, however, approximately 9% higher than theoretical values due to the three-dimensional nature of the real flow.

If a thick, turbulent boundary layer is disturbed near the rigid boundary, the flow changes are confined initially to a thin layer adjacent to the boundary. Elliott (1958) and Panofsky & Townsend (1964) have attempted to calculate the flow disturbance caused by an abrupt change in surface roughness by assuming special velocity distributions which are consistent with a logarithmic velocity variation near the boundary. Inspection of their distributions shows that the deviations from the upstream distribution are self-preserving in form, and it is shown that self-preserving development is dynamically possible if log l0/z0 (l0 being depth of modified flow, z0 roughness length) is fairly large and if l0 is small compared with the total thickness of the layer. Other kinds of surface disturbance may lead to self-preserving changes of the original flow and the theory is developed also for flow downstream of a line roughness, for the temperature distribution downstream of a boundary separating an upstream region of uniform roughness and heat-flux from a region of different or possibly varying roughness and heat-flux, and for the return of a complete boundary layer to self-preserving development after a disturbance. The requirement that the distributions of velocity and temperature should conform to the logarithmic, equilibrium forms near the surface makes the predictions of surface stress and surface flux nearly independent of the exact nature of the turbulent transfer process, and the profiles of velocity and temperature are determined within narrow limits by the surface fluxes. To provide explicit profiles, the mixing-length transfer relation is used. Its validity for the self-preserving flows is discussed in an appendix.

In a previous paper, it was shown that abrupt changes in the surface conditions under a very deep boundary layer cause changes of mean velocity and temperature that satisfy the dynamical conditions for self-preserving development. Here the theory is extended to predict the development of the modified flow in the moderately deep layers that occur in nature and the laboratory. The problems considered are the changes in the velocity profile produced by an abrupt change of surface roughness and also by a line of concentrated roughness such as a fence, the changes in temperature produced by change of roughness combined with changes of heat flux at the surface, and diffusion of heat or a scalar pollutant from a line source at or near ground level. The predictions are compared with observations by Rider (1952) of the flow downwind of a hedge, by Rider, Philip & Bradley (1963) of temperature and humidity downwind of a change in surface, and of vertical diffusion from a line-source at ground level.

The modification of a turbulent wind profile owing to momentum transfer from wind to surface waves is calculated in terms of the power spectrum of the surface-wave slope. The reduction in profile curvature, and hence of the wind-to-wave energy-transfer coefficient, is estimated on the basis of a Neumann spectrum. It appears that this reduction is likely to be small for typical wind speeds.