The energy flux in a finite-depth gravity-wave spectrum resulting from weak non-linear couplings between the spectral components is evaluated by means of a perturbation method. The fifth-order analysis yields a fourth-order effect comparable in magnitude to the generating and dissipating processes in wind-generated seas. The energy flux favours equidistribution of energy and vanishes in the limiting case of a white, isotropic spectrum. The influence on the equilibrium structure of fully developed wave spectra and on other phenomena in random seas is discussed briefly.

It is the purpose of this paper to report an investigation concerning certain factors affecting transition from laminar to turbulent flow in boundary layers. The objectives of the investigation were to clarify further the effects of very small degrees of leading-edge bluntness, and to devise a means for estimating the effect of roughness on boundary-layer transition.

Stratford's method of computing the development of a turbulent boundary layer in a strong adverse pressure gradient, based on division of the layer into an inner equilibrium layer and an outer layer of almost constant total-head, is simple and is based on current knowledge of the properties of turbulent flows, but the correspondence with experiment is worse than would be expected. The causes of this are investigated, first by testing the basic assumptions against the measurements of Schubauer & Klebanoff and then by calculating from the theory properties of the layer at intermediate stages of the development towards separation. It is shown that the theoretical condition for zero wall stress (a relation between pressure rise and pressure gradient) is always satisfied twice, first at an intermediate stage of development with wall stress about one-fifth of the initial value and second at the real position of zero stress. This behaviour involves a rapid decrease of pressure gradient in the neighbourhood of separation, caused by rapid thickening of the layer, and it is shown that the pressure distribution near separation depends only on the pressure rise to separation and the characteristics of the initial boundary layer and not on the geometry of the flow. With more measurements of boundary layers separating in strong adverse pressure gradients, these characteristic distributions could be determined as a one-parameter family. Their use for the prediction of position and pressure rise to separation in flows with specified boundaries without prior knowledge of the pressure distribution is discussed.

In previous theoretical treatments of the stability of the compressible laminar boundary layer, the effect of the temperature fluctuations on the viscous (rapidly varying) disturbances is accounted for incompletely. A thorough re-examination of this problem shows that temperature fluctuations have a profound influence on both the inviscid (slowly varying) and viscous disturbances above a Mach number of about 2·0. The present analysis includes the effect of temperature fluctuations on the viscosity and thermal conductivity and also introduces the viscous dissipation term that was dropped in the earlier theoretical treatments.

Some important results of the present study are: (1) the rate of conversion of energy from the mean flow to the disturbance flow through the action of viscosity in the vicinity of the wall increases with Mach number; (2) instead of being nearly constant across the boundary layer, the amplitude of inviscid pressure fluctuations for Mach numbers greater than 3 decreases markedly with distance outward from the plate surface. This behaviour means that the jump in magnitude of the Reynolds stress in the neighbourhood of the critical layer is greatly reduced; (3) at Mach numbers less than about 2, dissipation effects are minor, but they become extremely important at higher Mach number, since for neutral disturbances they must compensate for the generally destabilizing effects of items (1) and (2); (4) the minimum critical Reynolds number for an insulated flat plate boundary layer decreases with increasing Mach number in the range 0 ≤ Me ≤ 3.A full list of symbols is given at the end of this paper.. Since the wave-number varies like 1/M2e when Me [Gt ] 1, the minimum critical Reynolds number is likely to increase sharply at hypersonic speeds.

Numerical examples illustrating the effects of compressibility, including neutral stability characteristics, are obtained and are compared with the experimental results of Laufer & Vrebalovich (1960) at Mach 2·2, and of Demetriades (1960) at Mach 5·8.

The two-dimensional steady flow of an incompressible viscous liquid round a circular cylinder is described in terms of matched expansions valid asymptotically at low Reynolds number, the velocity field at large distances being a combination of a uniform simple shear and a uniform stream, relative to axes moving with the centre of the cylinder (but not rotating with it).

An infinite number of terms are computed and summed. There is a transverse force on the cylinder, independent of its rate of rotation to the approximation considered here. At moderate and large distances the balance between convection and diffusion of vorticity is dominated by the shear, being quite different from that in a uniform stream alone.

The rate of longitudinal diffusion of a substance released from an instantaneous line source in a simple shear alone is enhanced. Round a maintained line source for which the local convection velocity is parallel to that of the shear the concentration falls only algebraically with distance in all directions, though it is largest in twin wakes extending directly both upstream and downstream. If there is superposed a lateral convection, however small, at sufficiently large distances the concentration is exponentially small outside a wake centred on half a parabola.

The two-dimensional perturbation velocity round any obstacle held in an unbounded simple shear at any Reynolds number is, at a sufficient distance, an irrotational cross flow decreasing as the inverse two-thirds power, associated with twin shear layers extending upstream and downstream. If there is a uniform lateral motion at large distances this conclusion is completely altered.

An investigation has been made of the flow over spiked cone-cylinders mainly at a Mach number of 10. Five distinct types of flow were discovered. The occurrence of each is defined in terms of spike length and cone angle.

Following a discussion of the flow mechanism, a semi-empirical separation relation is derived. This can be used to predict the flow pattern for the most common type of separated flow.

This paper is concerned with the magnetohydrodynamic boundary layer in uniform flow past a flat plate, when a uniform magnetic field in the stream direction is applied at the plate. For both large and small values of the electrical conductivity parameter, solutions in series are derived for the velocity and magnetic fields. In each of the cases it is shown that if the strength of the applied field exceeds a certain critical value, boundary-layer separation occurs.