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.

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.

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.

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.

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 $\overline {\rho^2} \sim \rho^{-2} {\frac {l^{3/2}}{r^{3/2}}}{\frac {M^{7/3}}{(M-1)^{1/2}}}$

The momentum and mass conservation equations derived in part 1 are used in the limiting case of large solids-to-fluid density ratio. Bubbles generally appear in such fluidized beds and solutions are obtained which describe the motion of the particulate and fluid phases in the presence of a fully developed bubble. The analytical solutions are shown to be in fair agreement with experiment.

The power spectrum of the wall pressure that would be measured by a transducer of vanishingly small size and the corrections to the power spectra measured by finite-size transducers are determined from the spectra measured by four transducers of different diameters. The root-mean-square wall pressure measured by a transducer of vanishingly small size is $\sqrt {p^2}| \tau_w = 2 \cdot 66$, approximately 13% higher than the root-mean-square pressure measured by the transducer used in the earlier investigations of Willmarth & Wooldridge (1962). Corrections to the power spectrum measured by a finite-size transducer are computed using the theory of Uberoi & Kovasznay (1952, 1953). The computations require information about the correlation of the wall pressure for very small spatial separation of the transducers. Unfortunately, these measurements have never been made. Corcos's (1964) similarity of the cross-spectral density is assumed to represent the missing information, but the computed corrections fail at high frequencies because the similarity expression is not valid when the spatial separation is small. The range of validity of the similarity is determined, and the average radial derivative of the cross-spectral density is inferred from the measured power spectra.

Whitham's treatment of the 'shock-shock’ diffraction of a shock wave advancing into a uniform, quiescent region is extended to a shock wave advancing into a region of uniform flow on the assumption that all velocities are approximately parallel. The result is applied to diffraction of a blast wave by a thin wedge travelling at supersonic speed. The prediction of the pressure on the wedge, just behind the diffracted blast wave, is qualitatively satisfactory.

Whitham (1957, 1958) has developed a method for treating the propagation of shock waves into non-uniform media, which has been widely and successfully used. In shock diffraction problems, he considers the medium ahead of the shock to be at rest. The purpose of this note is to generalize Whitham's technique to problems having a uniform flow ahead of the shock, in which the inclination of the shock normal to the direction of flow ahead of the shock remains small. This extension was suggested to the author by Miles (1964) who considered the problem of diffraction of a strong shock by a thin supersonic wedge.

A study has been made of the condition of the condensate layer on a plain cooled cylinder rotating in a steam atmosphere. Because the cylindrical surface was wettable, it was covered by what was essentially a film, from which, under the influence of centrifugal force, protrusions arose. The drainage of the film occurred by the growth and throwing off of these protrusions in the form of drops. The behaviour of the drops, the variation of their maximum size with speed, and their number per unit area were the subject of study.

In the first part of this work the stability of the erodible bed of a stream with a free surface is studied within the framework of classical hydraulics, in which the velocity variation with depth is reduced to a single mean velocity and the bed friction is related in a general way to the local depth and mean velocity. Only two-dimensional motions can be studied in this way. In considering bed friction and a difference in phase between deposition and the mean velocity gradient along the channel, this work combines aspects of earlier studies of Exner and Kennedy.

In the absence of a phase difference between erosion and mean velocity, the analysis proceeds without linearization. When the development from an equili- brium flow down a uniform slope is considered, the bed waves formed under subcritical flows are found to move downstream, while those under super-critical flows upstream; in both régimes bed waves are damped. In each case the side of a wave facing in the direction of motion is the steeper.

When a phase shift is introduced as well, the analysis is carried forward only after linearization. The primary effect of bed slope and friction is a shift in the ranges of phase angle for which growth can take place and a corresponding alteration in the wavelengths for maximum growth. Friction also reduces bed-wave celerity. Consideration is given to the physical processes represented by the artifice of a phase difference between erosion and mean velocity gradient.

The second section of this investigation concerns two-dimensional potential flow over a wavy stream bed. This problem is considered from a point of view different from that adopted previously by Kennedy; a modified criterion is proposed for the maximum Froude number at which bed waves will form. It is in better agreement with measured data.

In the third part of this paper, the potential analysis is extended to include class of three-dimensional motions. The conditions are found for the formation of dunes (bed waves 180° out of phase with the surface waves above) and anti-dunes (the two in phase). The criterion separating dunes and antidunes for two dimensions is found to give a lower limit on the Froude number for antidunes of the more general three-dimensional class. In the antidune regime the streamwise perturbation to the velocity can change sign between surface and stream bed; the limit for this is determined.

The erosion equation relating changes in bed level to local stream speed is generalized to include sediment convection in two dimensions. With this equation, three distinct regimes of bed-wave motion are found: at low Froude numbers, dunes moving downstream; at higher Froude numbers, antidunes moving upstream; and, finally, antidunes moving downstream. The criterion separating the last two r6gimes is just that mentioned above as the limit of flows whose velocity perturbation has the same sign from surface to stream bed. It is argued that this fundamental change in the flow marks also the end of the region of growth of small bed waves. It is found that three-dimensional dunes and upstream-moving antidunes can exist beyond the two-dimensional limit, but that the latter applies for all bed waves such that the ratio of stream depth to wavelength (d/λ) is small. This explains why the modified criterion for two dimensions provides for small d/λ an envelope for data obtained from observations of a wide variety of bed forms, but fails to do so for larger d/λ. The celerity of bed waves beneath three-dimensional flows is discussed. It is suggested that a class of waves occurring in natural streams will move more slowly than would two-dimensional waves in similar conditions.

The work concludes with a comparison of several methods of modelling erosive flows.

The effect of a uniform and constant rate of strain imposed upon a turbulent wake which is generated behind a circular cylinder has been examined experimentally. The strain field, produced by passing the flow through a distorting duct of constant cross-sectional area, simultaneously compresses the wake in the plane of the cylinder and extends it in the other lateral direction but applies no strain in the direction of the main stream. The investigation shows the existence of a large-scale, periodic eddy structure within the strained wake, similar to, but more intense than, that which was observed for the undistorted wake. These large lateral convective motions appear to be the primary mechanism controlling the development of the flow, and are responsible for the failure of the wake to attain the theoretically predicted self-preservation state. It is shown that the strain rate, which acts favourably upon these large eddies, is sufficient to produce a net increase in vorticity in spite of the ordinary processes of turbulent viscous decay. At the same time, however, the rate of viscous dissipation of the smallest eddies in the flow is augmented by the strain, and the resulting wake structure is almost entirely dominated by the large-eddy motions. A possible means by which the large eddies are initiated is discussed.

An attempt has been made to predict the mean velocity field of turbulent jets immersed in secondary streams confined by constant-area ducts. The calculations have employed empirical data derived solely from the turbulent free jet. The conditions under which ducted jets may be considered approximately self-preserving have been examined by comparison of results of momentum-integral calculations with data from various sources on two-dimensional and axisymmetric jets immersed in secondary streams of constant velocity. For flows in which confining walls have significant effects, it is shown that the velocity field may be determined fairly well from free-jet data using the assumption of approximate self-preservation. Before the jet spreads to the wall, both the mean-velocity and turbulent shear stress are assumed self-preserving. Afterward only the shear stress is subject to this condition. Improvement of the methods used appears mainly to require a better model of the zone of recirculation.

The change by an order of magnitude of the oscillating properties of the flow past a circular cylinder in the Reynolds number range 2*103 to 5*104 is demonstrated experimentally. It is shown that in this range these properties are highly susceptible to small disturbances of the frequency of the transition waves which precede turbulence in the shear layers just downstream of the cylinder. It is suggested that this susceptibility is responsible for the different lift coefficient values measured by various workers.

The effect of disturbances on the mean flow properties is also described.

The frequency-determining mechanism and the characteristic length of the oscillating flow are discussed.

Howarth's transformation is applied to the compressible laminar boundary-layer equations for the flow at a point of attachment on a general curved surface. It is shown that the boundary-layer equations yield similarity solutions for the case when the viscosity varies linearly with the temperature, the Prandtl number is unity and the surface is maintained at constant temperature. The resulting eighth-order boundary-value problem is solved numerically for various surface temperature conditions and for various values of b/a, where a and b are constants representing the local velocity gradients in the principal directions of flow at the edge of the boundary layer.

Flow and heat transfer properties of the similar solutions at both nodal and saddle-points of attachment are given in graphical and tabular form.