The recent work on equilibrium (i.e. self-preserving) turbulent boundary layers in adverse pressure gradients is compared with theoretical predictions based on current generalizations about the turbulent shear flow. Using only assumptions of similarity, it is possible to show that an equilibrium layer can exist only if the free stream velocity varies as a power of distance downstream with an exponent greater than −$-\frac{1}{3}$ and if the velocity defect from the free stream is small. Assuming further that the effective eddy viscosity is independent of distance from the wall over the outer part of the layer, most of the properties of equilibrium layers may be computed from the known behaviour of layers in zero pressure gradient. The predicted values of skin friction and the predicted shape and magnitude of the mean velocity distribution are in fair agreement with the observations of Clauser. Finally, the modifications that are necessary if the velocity defect is not small are discussed briefly.

An analytical study is made of the resurgent wave motion induced by pressure distributions moving parallel to a straight coast line. The resurgence is shown to consist of an infinite number of edge wave modes; expressions for these modes are given and the wavelengths, frequencies and amplitudes are shown to be in agreement with experimental results. The effects of a Gaussian pressure distribution are analysed. For large-scale disturbances off the east coast of the United States only the fundamental mode is excited. Conditions, such as storm size, speed and distance from shore, for maximum induced wave amplitudes are derived.

The irrotational motions induced by, but outside of, the selfpreserving turbulent wake and jet are examined. It is found that there is a mean flow towards the centre of the jet, although there is no such flow in the case of the wake. Phillips's (1955) results on the nature of fluctuating irrotational flows are found to be largely unaffected by the introduction of simple inhomogeneities into the boundary conditions, but another mode of fluctuation with movement along the lines of mean flow is also shown to be likely. It is pointed out that, contrary to a statement of Corrsin & Kistler (1954), it is possible for the vorticity-free fluid between bulges of turbulent fluid to partake of the mean velocity of the turbulent fluid.

The generation of Aeolian tones is interpreted in terms of the theroy of aerodynamic sound. To do this, the intensity of the radiated sound is expressed in terms of the fluctuations in force upon a moving rigid body using the approximation that, at low mach numbers, these forces can be calculated assuming incompressibility of the flow. The fluctuations in lift and drag upon a circular cylinder at Reynolds numbers between 40 and 160 are calculated by integrating the fluctuations in momentum in the eddying wake, using the experimental data of Kovasznay (1949). It is found that the fluctuating lift per unit length is approximately $f_l = 0\cdot 38\rho U^2dcos2\pi nt$ where ρ is the density of the fluid and t the time, and that the magnitude of the fluctuations in drag is about 10% of this.

The axial length scale of these force fluctuations was found by an auxiliary experiment to be very large for Reynolds numbers below 100. When 100 < R < 160, the lenth scale is approximately 17d, the transition apparently occurring as a result of the instability to three-dimensional disturbances of the laminar eddying wake. Using this datum, the mean square acoustic pressure generated by the motion about the cylinder at these Reynolds numbers is found to be $\overline{P^2}(r) \sim 0\cdot 27 cos^2 \theta \frac {\rho ^2 ldU^6 S^2}{a^2r^2}$ where θ is the angle between the direction of observation and the incident stream, l the length of the cylinder and a the velocity of sound in the medium. Experiments undertaken to test this result directly, using sound intensity measurements from a whirling arm apparatus in an accoustically quiet room, gave very good agreement.

At higher Reynolds numbers, when the cylindg wake is turbulent, the theory leads to a, similar expression for $\overline{P^2}$ but with a smaller numerical factor. Analysis of previous experimental data on this basis gives good agreement, with a value of about 0·037 for the numerical constant. In view of this, it is likely that some of the earlier data which had appeared to give a Mach number dependence of M4, not M6, have been misinterpreted. Finally, mention is made of the conditions when the frequency of vortex generation is the same as the natural frequency of the wire, and the greatly increased intensity of the sound is seen to be the result of the greatly increased axial length scale of the force fluctuations.

The relative simplicity of this phenomenon makes possible perhaps the least ambiguous confirmation yet found of some of the essential ideas in the theory of aerodynamic sound.

This paper considers the flow due to a jet spreading out over a plane surface, either radially or in two dimensions. Solutions of the boundary layer equations are sought, according to which the form of the velocity distribution across the jet does not vary along its length. For laminar flow, such a similarity solution is obtained explicitly. For turbulent flow, an eddy viscosity is introduced, and it is eventually seen that complete similarity is not attainable, but that confident predictions can nevertheless be made about the nature of the velocity distribution and the rate of growth of the wall jet.

The flow rate of liquid metals is commonly measured by electromagnetic flowmeters. In these the fluid moves through a region of transverse magnetic field, inducing a potential difference between two electrodes on the walls of the pipe. The ratio of signal to flow rate is dependent on the velocity profile, and this is affected by electromagnetic forces.

In this paper the ultimate steady velocity profile and its associated pressure gradient and induced potential are calculated for the case of laminar flow in a circular pipe whose walls are conducting but without contact resistance. Laminar flow is encouraged by a transverse field. When the fluid conductivity and field strength are sufficiently high, boundary layers occur with a thickness inversely proportional to normal field intensity. The induced potential difference is then 0·926 of the value corresponding to the case of uniform velocity if the walls are non-conducting.

The distance the fluid must travel after entering the transverse field before the steady state is reached is next estimated by a Rayleigh approximation. The inlet velocity is taken to be uniform and effects which occur at the edge of the field are neglected. The process falls into two stages, first a boundary-layer growth and then an adjustment of the velocity away from the walls, occupying a much greater length of pipe. The entry length is shorter than it is in the case of flow in a rectangular pipe, but is still too long for appreciable distortion of the velocity profile to occur within practical flowmeters except at low flow rates. The pressure drop associated with the adjustment of the velocity profile is found to be independent of field strength, if this is high, and about one-eighth of the drop which occurs in the non-conducting case.

Experiments are described in which steady-state pressure gradients and induced potential differences were measured in mercury flowing along Perspex pipes of 0·5 and 0·25 in. bore in transverse fields up to 14500 gauss. The results confirmed the steady-state theory within the limitations of experimental accuracy and the assumption in the theory of high conductivity and an intense field. The experiments also covered the entry region in many cases, and showed that the theoretical entry lengths were correct in order of magnitude but over-estimated. However, the exact entry condition was uncertain, and steady readings were difficult to obtain in the entry region.