The stability of the horizontal interface between conducting and non-conducting fluids under the influence of an initially uniform vertical electric field is discussed. To produce such a field when the conducting fluid is the heavier it is imagined that a large horizontal electrode is immersed in the non-conducting fluid. As the field increases the part of the interface below the electrode rises till at a voltage V, which depends on the interfacial tension, the height of the electrode above the interface and the density difference, the interface becomes unstable for vertical displacements Z which satisfy the equation $({\frac{\delta^2}{\delta x^2}} + {\frac{\delta^2}{\delta y^2}}+k^2) Z=0.$ The value of k consistent with the lowest value of V is found. When the electrode is situated above the interface at less than a certain distance the lowest value of V is attained when k = 0 so that the horizontal extent of an unstable crest is likely to be great. As the electrode height increases above this critical value k increases and the unstable crests become more closely spaced till an upper limiting value of k is obtained.

Experiments made with several pairs of fluids verify these theoretical conclusions. In some cases sparking occurs before the potential V is reached, but in others, air at atmospheric pressure over water, for instace, the instability occurs first and the jet of water which results permits the passage of a spark which may inhibit further development of the instability. The physical condition which determines the sparking voltage to a fluid may therefore be very different from that which is operative between solid electrodes. This consideration might be relevant to the performance of power-line insulators in wet weather.

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.

An analytical study is made of non-equilibrium effects on hypersonic, inviscid flow over slender, axisymmetric bodies. Also, two-dimensional results are obtained for the purpose of comparison. The rate process under consideration is that of molecular vibration of the gas. The exact problem is solved by successive approximations based on a double-expansion scheme involving two small parameters: one represents the fact that the bodies considered are slender; the other represents the facts that the vibrational internal energy is small in comparison to the total enthalpy. The exact differential equations and boundary conditions are simplified to the hypersonic-small-disturbance-approximation form. The unknown quantities in this approximate problem are expanded into series of the small parameter, (γ − 1)/(γ + 1), which is ⅙ for a diatomic gas. In this formulation it is found that the classical hypersonic similitude can be extended by slight modifications to cover the added consideration of vibrational non-equilibrium. The modifications introduced are the normalization of all lengths by the characteristic relaxation length of the gas and the addition of a new dimensionless parameter, which is a measure of the excitation level of the vibrational internal energy in the flow field. Explicit, uniformly valid solutions are obtained for the specific problems of flow over a slender cone and of that over a thin wedge. The successive approximations are carried as far as necessary to show the non-equilibrium effect, which differs in order of magnitude for the various flow quantities. One interesting feature of the solutions is the non-monotonic behaviour in the relaxation of the surface pressure of both the cone and the wedge, in contrast to intuitive expectation. The result for a 20° cone in a free stream of oxygen at 300° K and a Mach number of 15 is displayed and compared with the numerical solution of the exact problem using the method of characteristics.

General solutions are obtained for the long gravity wave equation from solutions of the wave equation in three dimensions. The method is applied to the theory of Tsunamis. It is also suggested that these waves are the cause of the shelf oscillations observed at Guadelupe.

The stability of the co-current stratified flow of oil and water was investigated experimentally in a horizontal rectangular conduit. Laminar-turbulent transitions were determined for both phases. With the two-phase system the transition to turbulence in the water phase occurred at a higher Reynolds number in the presence of a laminar oil layer provided the input water-to-oil ratio was relatively high, while the transition in the oil phase took place at a lower Reynolds number in the presence of a turbulent water layer. The appearance of first interfacial waves coincided with the transition to turbulence of the less viscous or water phase. This suggests that in the system investigated the resonance mechanism as proposed by Phillips (1957) was responsible for the generation of these first waves. However, at relatively high water flow rates and water-to-oil ratios more pronounced waves were observed which appeared to be generated by an instability in the mean flow.

The conically symmetric solution of the Eulerian equations of an incompressible fluid obtained by Hall, thought to be descriptive of flow properties in a leading-edge vortex, is generalized to include the effects of compressibility.

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.

The solution is obtained in general terms for the velocity fluctuations generated in a laminar boundary layer by an oscillating disturbance on the boundry wall. The form of excitation is chosen to represent a vibrating ribbon of the type used by Schubauer to force disturbance in boundary layers. The forced wave system generated by the ribbon is shown to be a spatially growing one, which is described far downstream by an eigenmode of the system which has a complex wave-number.

The stability of a uniformly rotating and infinitely conducting jet with twisted magnetic field is discussed. The dispersion relation is obtained for the non-axisymmetric perturbations; this involves a complex and implicit function of the growth rate. The complex growth rate implies that instability develops as an overstability. The effect of axial current is destabilizing for both the instabilities m = 0 and m = 1 discussed here. The effect of rotation on the stability of the jet is as follows: (a) for the m = 0 mode, rotation always has a destabilizing effect; (b) for the m = 1 mode, rotation has a stabilizing effect for very long-wave perturbations, but for short-wave perturbations it destabilizes the jet. In particular there exists a disturbance of a particular wavelength which is unaffected by the rotation of the jet.

A smoke plume that has become nearly horizontal at some distance from the source behaves much like a ‘line-thermal’, for which, using a perturbation method, a solution in laminar flow may be obtained, on the supposition that excess temperatures are small and buoyant movements slow, i.e. that the Rayleigh number of the problem is suitably low. In analogy with some other problems in turbulent flow and turbulent diffusion, the laminar solution is then assumed to approximate what is observed in the turbulent case, provided that the rate of growth of the diffusing cloud is assessed realistically.

The so-calculated pattern of streamlines in a cross-section of the plume agrees qualitatively with the observed behaviour of hot plumes and puffs, consisting of two vortex-like structures of opposite sense of rotation, lying on either side of the plume centre. The bodily upward movement of the plume is found to depend critically on the rate of growth of the plume. Thus when the plume diameter grows faster than linearly with distance (such behaviour characterizes the ‘quasi-asymptotic’ stage of relative diffusion predicted by Batchelor, 1952, for which Richardson's (4/3)-power law of eddy diffusivity holds) the plume tends to reach an asymptotic height. A crude theoretical estimate of the asymptotic height attained shows fair agreement with observations reported elsewhere. Although the plume nearly reaches this asymptotic height in the quasi-asymptotic phase, it retains a small gradient in the final phase which may be of importance at large distances from the source. The small-Rayleigh-number criterion restricts the validity of the solution to ‘weakly buoyant’ plumes.

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.

The empirical description of turbulent wall layers across which the shear stress varies is considered. The description given by Townsend for zero-stress layers is found to be inapplicable to uniform pressure flows in pipes and two-dimensional channels, and to a boundary layer developing in the absence of a pressure gradient.

In a barotropic fluid, a free turbulent flow induces a fluctuating potential flow which is determined by the instantaneous flow near the edge of the turbulent flow. If the surrounding fluid is stably stratified, internal wave-motions are possible and, in general, wave-energy accumulates until it is sufficient to modify the turbulent flow. Here the growth of wave-motion from rest is examined with particular reference to the atmospheric problem of wave excitation by the surface boundary layer. Wind shear is supposed negligible outside the turbulent flow and the disturbances from the boundary layer are assumed to travel with a convection velocity V relative to the upper air. For times large compared with {−g/ρ(dρ/dz)}−½ (ρ is the potential density), most of the wave-energy resides in components of phase-velocity near the convection velocity. For a model atmosphere with increased stability above a tropopause, this resonance mechanism leads to the formation of wave-groups with crests at right-angles to the convection velocity and wavelengths near 2πV[−g/ρ(dρ/dz)]−½. Using likely values for the surface disturbances, wave-amplitudes of order 100 m can develop within several hours of the initiation of the boundary layer but sufficient amplitude to produce overturning or breaking is unlikely within a reasonable time.

A general linear theory is developed to describe the manner in which rigid fluid rotation is established from a prescribed initial state of motion in a container of arbitrary shape. The container rotates with uniform angular velocity and is filled with a viscous incompressible fluid.

A new mean circulation theorem is proved and used to separate the flow into geostrophic motion and inertial oscillations. The basic eigenvalue problem is studied and important properties concerning spectrum, orthogonality and completeness are deduced. The effect of viscosity on the inviscid modes is calculated in a manner that maintains the solution uniformly valid through the spin-up time. All modes decay in this time scale which characterizes the entire transition to rigid rotation in all configurations.

The wave drag of a Hovercraft is calculated as the horizontal force associated with a pressure distribution moving over the free water surface. A general formula is derived for the wave drag due to any pressure distribution moving over water of finite depth. This is then applied to rectangular and elliptical planform Hovercraft, and results are presented for a range of Froude numbers and water depths.

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.

The problem considered is that of the diffraction of the field of a point source in a fluid of infinite depth by an infinite vertical cylinder. It is shown that the surface wave component of the velocity potential may be expressed in terms of the solution to a classical electromagnetic (or acoustic) diffraction problem.

An asymptotic solution to the Navier-Stokes equation is obtained for the incompressible flow of a viscous fluid past a semi-infinite flat plate when a slip boundary condition is applied at the plate. The results for the shear stress (and hence the slip velocity) on the plate differ basically from those obtained by previous authors who considered the same problem using some form of the Oseen equations.

Mach wave radiation studies have, so far, been concentrated on the sound radiated to large distances from the flow. Then, both a turbulent eddy and the distance it may travel during its coherent life, appear small to the distant observer, so that the sound arrives from one direction. When that direction is the Mach angle, a Mach wave is heard. This paper deals with a different situation, where, although a turbulent eddy appears small, the distance it travels does not. Sound arriving at the observer then comes from different directions at different times in the eddy's life, so that Mach waves can only be radiated over a relatively small range, where the radiation angle corresponds to the Mach angle. In that range the far field equations no longer apply. It is shown that, whereas the distant field increases with the cube of convection Mach number, M, and inversely with the square of distance travelled, 1/r2, this particular near field is of a type where the mean square density, $\overline {\rho^2}$, has the proportionality $\overline {\rho^2} \sim \rho^{-2} {\frac {l^{3/2}}{r^{3/2}}}{\frac {M^{7/3}}{(M-1)^{1/2}}}$