Random fluctuations in sea level, ζ, in the frequency range 0·1-60 cycles per hour were measured along the coast near Oceanside, California, where the coastline and bottom contours are fairly straight and parallel for 30 km. The two-dimensional covariance $R(\eta, \tau) = \langle \zeta (y,t) \zeta (y + \eta, t+ \tau) \rangle$ was computed for points separated by various distances η along the coast. The Fourier transform $S(f,n) = \int \int R(\eta, \tau)exp [2\pi i (n \eta + f \tau)]d \eta d \tau$ gives the contribution towards the ‘energy’ $\langle \zeta ^2 \rangle$ per unit temporal frequency f per unit spacial frequency (long-shore component) n. It is found that most of the energy is confined to a few narrow bands in (f, n) space, and these observed bands correspond very closely to the gravest trapped modes (or edge waves) computed for the actual depth profile. The bands are 0·02 cycles per km wide, which equals the theoretical resolution of the 30 km array. Very roughly S(f,n) ≈ S(f, -n), corresponding to equal partition of energy between waves travelling up and down the coast. Theory predicts ‘Coriolis splitting’ between the lines f± (n) corresponding to these oppositely travelling waves, but this effect is below the limit of detection. The principal conclusion is that most of the low-frequency wave energy is trapped.

The wall-jet is the flow of fluid emanating from a narrow slot and blowing over a rigid wall. The configuration of the turbulent wall-jet is that of a very narrow, plane, turbulent half-jet investigated by Liepmann & Laufer (1947). The width of the slot is of the order of the boundary layer on the infinite wall and the jet, in this case, mixes with a stream moving with constant velocity. This flow has drawn considerable basic and applied interest in the past few years for it has the characteristics of both a boundary-layer and a free-mixing flow.

We consider here flow past an obstacle on the lower of two rotating horizontal planes which bound a viscous fluid. It is found that when the Taylor number is large viscous effects are confined to Ekman boundary layers on the solid surfaces and to a free shear layer coincident with the vertical cylinder circumscribing the bottom obstacle. The flow in the main body of the fluid outside the cylinder proves to be two-dimensional with zero relative vorticity, while inside the cylinder the fluid is stagnant in the rotating frame. The shear layer provides a continuous transition between the exterior and interior of the cylinder, and in addition provides a means by which fluid from the Ekman layers on the horizontal planes is exchanged with fluid outside the Ekman layers and exterior to the circumscribing cylinder. The predicted flow proves to be in agreement with many of the experimental results.

First- and second-order boundary-layer theory are examined in detail for some specific flow cases of practical interest. These cases are for flows over blunt axisymmetric bodies in hypersonic high-altitude (or low density) flow where second-order boundary-layer quantities may become important. These cases consist of flow over a hyperboloid and a paraboloid both with free-stream Mach number infinity and flow over a sphere at free-stream Mach number 10. The method employed in finding the solutions is an implicit finite-difference scheme. It is found to exhibit both stability and accuracy in the examples computed. The method consists of starting near the stagnation-point of a blunt body and marching downstream along the body surface. Several interesting properties of the boundary layer are pointed out, such as the nature of some second-order boundary-layer quantities far downstream in the flow past a sphere and the effect of strong vorticity interaction on the second-order boundary layer in the flow past a hyperboloid. In several of the flow cases, results are compared with other theories and experiments.

The problem of flow over a circular cone inclined slightly to a uniform stream is solved using the technique of matched asymptotic expansions. The outer expansion is equivalent to Stone's solution of the problem. The inner expansion, valid in a thin layer near the body, represents Ferri's vortical layer. The solution to first order in angle of attack so obtained is uniformly valid everywhere in the flow field. In the second-order expansion an additional non-uniformity appears near the leeward ray. This defect is removed by inspection. The first-order solution is in agreement with that of Cheng, Woods, Bulakh and Sapunkov. Formulas are given that may be used to render Kopal's numerical result uniformly valid to second order in angle of attack.

A characteristic feature of a steady trailing line vortex from one side of a wing, and of other types of line vortex, is the existence of strong axial currents near the axis of symmetry. The purpose of this paper is to account in general terms for this axial flow in trailing line vortices. the link between the azimuthal and axial components of motion in a steady line vortex is provided by the pressure; the radial pressure gradient balances the centrifugal force, and any change in the azimuthal motion with distance x downstream produces an axial pressure gradient and consequently axial acceleration.

It is suggested, in a discussion of the evolution of an axisymmetric line vortex out of the vortex sheet shed from one side of a wing, that the two processes of rolling-up of the sheet and of concentration of the vorticity into a smaller cross-section should be distinguished; the former always occurs, whereas the latter seems not to be inevitable.

In § 4 there is given a similarity solution for the flow in a trailing vortex far downstream where the departure of the axial velocity from the free stream speed is small. The continual slowing-down of the azimuthal motion by viscosity leads to a positive axial pressure gradient and consequently to continual loss of axial momentum, the asymptotic variation of the axial velocity defect at the centre being as x−1 log x.

The concept of the drag associated with the core of a trailing vortex is introduced, and the drag is expressed as an integral over a transverse plane which is independent of x. This drag is related to the arbitrary constant appearing in the above similarity solution.

The paper is concerned with formulation of the gas dynamic conservation equations for the individual species in a non-equilibrium partially ionized gas mixture. As an example, the conservation equations for the electrons and the overall conservation equations are developed for a three component plasma consisting of electrons, singly-ionized positive ions and neutral atoms. Non-elastic collisions are represented by the collisional-radiative decay mechanism of Bates, Kingston & McWhirter (1962a, b). Maxwellian velocity distributions are assumed, but the electrons are allowed to have a temperature different from the heavier particles and to drift relative to them. Particular attention is given to the electron energy balance equation which differs from that used by other investigators.

This paper considers the transient motion of a viscous fluid in a container rotating with constant angular velocity. The principal objective is to study the manner in which an arbitrary initial state of motion becomes a rigid rotation. In order to concentrate on the effects of viscosity, only the spherical container is studied here in great detail. A general theory will be presented in a subsequent publication.

Several sources of non-uniform behaviour make the analysis difficult and complex. In particular, there are three important time scales, viscous boundary layers, boundary-layer resonances at critical latitudes and intricate side-wall effects. The basic aproach consists of an expansion procedure by means of which the general inviscid solution is corrected for viscous effects and is made uniformly valid in time through the critical spin-up phase. Uniform validity is effected through the elimination of secular terms with unacceptable growth rates arising from the asymptotic perturbation series.

The interior (inviscid) motion leads to a non-self-adjoint partial differential equation eigenvalue problem with many intriguing properties. The general expansion theorem, orthogonality relationships, and viscous decay factors are deduced and used to solve the arbitrary intial-value problem. It is shown that the depth averaged circulation about circular contours, x2 + y2 = r2, is extracted from the fluid in the spin-up time scale T = L(Ωv)½. This is accomplished by a secondary non-oscillatory convective motion produced by suction into the Ekman layer. The excess circulation not eliminated in this way excites inviscid inertial oscillations which are also caused to decay by the boundary layers in the same time scale. Some very small residual effects decay in the ordinary viscous diffusion time, but all the essential processes are concluded in the much shorter interval. All modal oscillations in a sphere are determined and several specific calculations of frequency and decay rate are made and compared with experimental data. Perhaps the most important of these concerns the mode corresponding to rigid internal motion about another axis which can be produced by impulsively changing the rotation axis of the container. Agreement between theory and experiment is very good in all cases compared thus far.