Measurements in three boundary layers, one with constant free-stream velocity and two with power-law variations of free-stream velocity giving ‘moderate’ and ‘strong’ adverse pressure gradients, are presented and discussed. Several unifying features of the turbulent motion, expected to appear in all boundary layers not too far from equilibrium, are identified. The intensity spectra at higher wavenumbers follow the Kolmogorov inertial-subrange law, although the Reynolds number is not particularly high even by laboratory standards: in addition the smaller-scale motion in the outer layer is determined entirely by the local shear stress and the boundary-layer thickness. The large eddy motion increases in strength relative to the general turbulence level as the general turbulence level increases, and the limited evidence available suggests that the large eddies are similar to those in the free mixing layer. In all cases the large eddies contribute a significant proportion of the shear stress in the outer layer.

As a contribution to the breakdown phenomenon of vortices in a two-dimensional free boundary layer, this paper deals with the question whether a single cylindrical (i.e. two-dimensional) vortex can become unstable. For this reason a single vortex, as it occurs in a free boundary layer, is approximated by an axisymmetrical vortex model. The inviscid stability theory of rotating fluids is then applied to this vortex model. By general stability criteria it was found that a vortex consisting of vorticity of one sign only is stable according to the Rayleigh criterion, but, if the vorticity has an extremum value outside the axis, may become unstable with respect to cylindrical disturbances. Furthermore, stability calculations for three special types of vortex were performed. It was found that they were more unstable with respect to cylindrical disturbances than to three-dimensional ones.

This paper considers the effect of a pressure point moving over the surface of a fluid which is composed of two layers of different densities, the lower layer being of infinite depth. The method is the same as that used by Crapper (1964) for the same problem with a uniform fluid. The resulting waves are in two sets, the first being the normal surface wave for the uniform ocean, with a slight change in amplitude, and the second an internal wave. The crests of the internal wave have a pattern similar to that of the surface wave for a shallow uniform fluid.

The equilibrium state of a rapidly rotating fluid, heated uniformly from above and cooled uniformly from below while contained in a cylinder with insulated side-walls is studied.

The circulations which are produced by the resulting stratification are studied over a wide range of parameters and it is shown that many of the features of the linear theory of rotating stratified fluid flows found in earlier studies reappear in this non-linear problem.

These include the gradual disappearance of Ekman layer suction and O(1) Ekman layers as the stratification increases, and the determination of the interior flow by the side-wall boundary layers in conjunction with the Ekman layers.

It is suggested therefore, that studies of rotating stratified flows which are unbounded laterally may frequently be defective and lead to solutions which are not the limit of any physically realizable experiment.

The wake of a disk at an angle to a stream contains marked periodic motions which arise from the regular shedding of vortices from the trailing edge. The vortices are in the form of a chain of irregular rings, each one linked to the succeeding one, and they move downstream at about 0·6 of free-stream velocity. The prominence of the vortex shedding increases as the angle of incidence (measured from the normal) increases up to at least 50°. The shedding frequency increases with the angle of incidence, but by a suitable choice of reference velocity and length scale, may be described by a wake Strouhal number which has the constant value 0·21 for all angles of incidence above zero, up to at least 40°.

Axially-symmetric bodies at zero incidence shed vortices in a similar manner, except that the orientation of the plane of vortex shedding is not fixed and varies from time to time.

The results of an experimental study of the diffraction of shock waves on plane-walled convex corners are given for a Mach number range from 1·0 to 5·0. The behaviour of the disturbances produced in the region perturbed by the corner are discussed. It is shown that the position of the slipstream and tail of the Prandtl-Meyer fan, and the velocities of the contact surface and second shock become independent of corner angle for angles greater than 75°. Comparisons with theoretical predictions of Jones, Martin & Thornhill (1951) and Parks (1952) are included. In most cases fair agreement is obtained.

Turbulence onset is considered in viscous incompressible flows. Development of fluctuations in an infinite flow with a constant gradient of mean velocity ∂U1/∂x2 = const., U2 = U3 = 0 is rigorously treated.

It is shown that two-dimensional eddy fluctuations, with infinitesimal initial amplitude A and scale of initial eddies l, increase in this flow so that the maximum ratio max ε(t)/ε(0) of their energy at the moment t to the initial energy exceeds any prescribed value as the Reynolds number R = (∂U1/∂x2) l2/v increases. The analysis of the non-linear equations obtained in the paper which describe development of fluctuations with a finite amplitude leads to the conclusion that there exists a’ stability barrier’ Ã (R) for the initial amplitude of eddy fluctuations. If A < Ã (R), then fluctuations decay as t → ∞, and if A > Ã(R) the energy of fluctuations does not decay. As R → ∞, Ã(R) → 0 according to the inequalities \[ l(\partial U_1/\partial x_2)K_2/R^{\frac{2}{3}}\leqslant \tilde{A}(R)\leqslant l(\partial U_1/\partial x_2)\,K_1/R^{\frac{2}{3}}. \] It is shown that the non-linear mechanism of preventing turbulence from decay involves generation of large-scale turbulent oscillations which then transmit energy to small-scale motions.

The described mechanism of turbulence onset from small eddies in shear flows appears to be of universal character. It is interesting that several qualitative characteristics of turbulence observed in various shear flows can be rigorously deduced even in a model where disturbances remain two-dimensional.

The flow of a viscous fluid through axially symmetric pipes and symmetrical channels is investigated under the assumption that the Reynolds number is small enough for the Stokes flow approximations to be made. It is assumed that the cross-section of the pipe or channel varies sinusoidally along the length. The flow is produced by a prescribed pressure gradient and by the variation in cross-section that occurs during the passage of a prescribed sinusoidal peristaltic wave along the walls. The theory is applied in particular to two extreme cases, peristaltic motion with no pressure gradient and flow under pressure along a pipe or channel with fixed walls and sinusoidally varying cross-section. Perturbation solutions are found for the stream function in powers of the ratio of the amplitude of the variation in the pipe radius or channel breadth to the mean radius or breadth respectively. These solutions are used to calculate, in particular, the flux through the pipe or channel for a given wave velocity in the first case and for a given pressure gradient in the second case. With a suitable notation it is possible to combine the analysis required for the two cases of pipe and channel flow.

Laminar boundary layer on a flat plate with zero pressure gradient was excited by a solitary three-dimensional disturbance. The growth of the disturbance was studied using a 10-channel linearized d.c.-coupled hot-wire system. The development of the disturbance flow field was studied and compared with theory by Criminale & Kovasznay (1962). The experimental results indicate a departure from the theory on account of the simplifying assumptions made in the theory. Certain new results were also obtained.

The shock curvature and flow variable gradients at the tip of a pointed body caused by non-equilibrium effects are considered. Co-ordinates introduced by Chester (1956) are used since they offer a convenient way of treating the boundary conditions. The desired functions are obtained by solving numerically a system of linear ordinary differential equations. These equations have a singularity; the nature of the singularity is found analytically, and its numerical treatment is discussed. The specific non-equilibrium effect considered is vibrational relaxation in a pure diatomic gas. Representative results are given for flow of N2 over a cone for a comprehensive range of Mach number and cone angle. There is a point analogous to the Crocco point. The exact results are compared with predictions from (i) a hypersonic, small disturbance theory; (ii) the application of an integral method; (iii) characteristic calculations. In an appendix, a comparative discussion is given of results for frozen flow over ogival bodies.

It is shown that islands can trap long-wave energy in a way similar to the capture of a particle by an atomic nucleus. The frequencies of the captured waves form a discrete set, being determined by the shape of the island and the contours of the surrounding sea bed. If the depth at great distances tends to a constant value, the trapped modes must leak some energy to infinity, though the consequent rate of decay may be exceedingly small. The initial energy of the trapped modes may be absorbed from incident radiation of the same frequency or from a sharp pulse. The particular example of a rectilinear pulse incident on a circular island is discussed in some detail.

The effect of the rotation of the Earth is to split the frequencies of a pair of waves progressing in opposite directions round the island. The splitting of the frequencies produces slow beats in the waves as seen at any fixed point. Slight asymmetry in the island induces a slow exchange of energy between each pair of progressive modes.

The present investigation was suggested by the occurrence of regular oscillations having a period of 6 min and a beat period of about 3 h in long-wave records taken at Macquarie Island, in the Southern Ocean.