This paper considers the surface response of a semi-infinite, uniformly rotating, constant depth, homogeneous ocean to a variable atmospheric force. For a general wind and pressure system it is shown that forced Kelvin-type waves can be generated and that only the longshore wind component and the pressure can generate them. In particular a semi-infinite wind and moving pressure pattern are shown to generate Kelvin waves that travel away from the force discontinuities at the speed of shallow-water waves. The waves in the latter case exhibit a frequency shift typical of non-dispersive waves from a moving source. Some numerical values for the amplitudes of the Kelvin waves are also given.

In this paper the interchange flow between two reservoirs connected by a contraction and containing fluid of different densities is considered. The effect of the boundary layers on the floor and walls of the contraction on the depth of flow in the contraction is discussed for the case of single layer flowing from one reservoir to the other. Next the theory for a denser layer plunging under a stationary layer is developed. In this case there is a discontinuity at the point of intersection of the surfaces of the flowing and the stationary fluids and there are three possible flow régimes depending on whether this discontinuity occurs at, downstream of, or upstream of the contraction.

Finally, the case where there is an interchange flow with fluid flowing from each reservoir into the other is introduced. This latter theory parallels that developed by Wood (1968) for the case of two layers flowing from one reservoir through a contraction into another reservoir and as in this case there are two points of control, one at the position of minimum width and one (the virtual point of control) away from this position of minimum width.

Experiments are described for a single layer flowing through the contraction and the results of these are used to obtain an indication of the accuracy that could be expected from the experiments with the more complicated exchange flow. The experiments with the exchange flow verified the major elements of the theory.

A technique is described for measuring the local phase speed in a turbulent flow. The technique has been used to measure the phase speed of the Fourier components of the longitudinal velocity fluctuations in grid turbulence. These measurements are unique in that the probe spacing is only twice the Kolmogoroff length scale. The velocity fluctuations were measured with linearized constant-temperature hot-wire anemometers, the outputs of which were digitally sampled and recorded in real time. Digital Fourier analysis techniques were then used to calculate the cross-spectral density of the two velocity measurements. From this, the phase, phase speed, and coherence were calculated. The coherence has been used to estimate the variance of these measurements.

An oscillating current such as a tidal stream or an inertial oscillation may have a horizontal scale of the order of many times the local depth of water. Thus an island projecting from an otherwise uniform sea bed will give rise to a local, periodic disturbance near the island. It is shown that this disturbance may be resolved into two waves travelling in opposite senses round the island. If the particle orbits at large distances are circular, then only one of these waves has non-zero amplitude.

In addition to the oscillatory motion, however, there is a steady d.c. streaming, or mass-transport velocity, whose magnitude is of order u2/σa where u denotes the magnitude of the oscillatory velocity at large distances, σ denotes the radian frequency, and a is the radius of the island. In this paper the profile of the streaming velocity is calculated for circular islands, with or without shoaling regions offshore. It is shown that resonance with the free modes trapped by the shoaling regions may greatly increase the streaming velocity. Viscosity (or horizontal mixing) also tends to increase the streaming velocity close to the shoreline.

The conclusions are supported by some simple model experiments. It is suggested that such streaming may partly account for the observed pattern of currents near Bermuda.

Two hypotheses concerning the turbulent flow over an infinitesimal-amplitude travelling wave are investigated. One hypothesis, originally made by Miles, is that the wave does not affect the turbulence and therefore the turbulent Reynolds stresses are dependent only on height above the mean wave surface. Alternatively, the proposal that turbulent stresses are primarily dependent on height above the instantaneous wave surface is examined. Numerical solutions of the appropriate equations are compared with Stewart's recent experimental results and with the approximate solutions employed by Miles and others. No definite conclusion can be reached from comparison with experimental results since the predicted flows are quite sensitive to details of the mean velocity profile near the wave surface where no data was taken. It is found that the asymptotic results do not apply for the conditions investigated.

The mean-velocity field over monochromatic, 1·96 Hz, deep-water waves was measured by means of hot-wire anemometers for a range of wind speeds (relative to wave speed) of 0·4 to 3·0. The mean-velocity profile, over waves 0·64 cm in amplitude, was the same as that over a rough plate; that is, the mean velocity varied as the logarithm of the height above the mean-water level, except very close to the water, where the effect of the viscous sublayer became important. The wave-induced perturbation-velocity field and its associated Reynolds stresses were also measured and compared with numerical solutions of various linear equations governing shearing flow over a wavy boundary. The comparison showed that the measured velocity field was not well predicted by these theories.

An experimental investigation has been made of the flow patterns at the initiation of convection in a layer of a high Prandtl number liquid confined between rigid, horizontal surfaces and heated from below. The experiment was designed to overcome the limitations of earlier experiments and to correspond closely to the conditions of the theory. In particular, the upper and lower rigid surfaces which enclosed the layer were made of copper which has a high thermal conductivity. To aid in the analysis of the experimental results some supplementary observations of the flow patterns were made using a glass upper plate. For small fluid depths and large temperature differences between the upper and lower surface the initial flow was in the form of hexagonal cells as predicted theoretically. With increasing Rayleigh number the cellular flow appeared to transform into rolls as predicted. For large fluid depths and small temperature differences only circular plan-form rolls were observed. This is in agreement with the results of other experimenters. It is tentatively proposed that this non-appearance of an initial cellular flow is due to the shape of the test chamber having a dominating influence on the flow pattern when the temperature gradient in the fluid is small. Measurements were also made of the development time for the flow patterns and the critical Rayleigh number.

An extension to Coles's (1956) ‘law of the wall–law of the wake’ formulation for incompressible unblown boundary layers with momentum thickness Reynolds number Reθ > 6000. is made for Reθ < 6000. It is found that κ = 0·40, the von Kármán constant for Reθ > 6000, is replaced by Ω = 0·40 (Reθ/6000)⅛ for Reθ < 6000. Based upon the data of Simpson (1967) this formulation is extended to injection and undersucked (dθ/dx > 0) flows in ‘law of the wall’ and ‘velocity-defect’ representations. This law of the wall for the logarithmic turbulent region and Reichardt's sublayer variation of εM/ν are used to obtain a continuous expression for εM/ν as a function of U+, V+w, and Reθ for the wall region. This expression is in reasonable agreement with the generated εM/ν blowing results and in less agreement with the unblown and suction results. Eddy viscosity and mixing length results confirm that εM/δ*U∞ ∝ Ω2 and l/δ ∝ Ω for the outer region and that εM/δ*U∞ and l/δ are substantially independent of blowing and moderate suction, as also reflected by the velocity defect representation for injection and suction.

The Korteweg–de Vries equation is shown to govern formation of solitary and cnoidal waves in rotating fluids confined in tubes. It is proved that the method must fail when the tube wall is moved to infinity, and the failure is corrected by singular perturbation procedures. The Korteweg–de Vries equation must then give way to an integro-differential equation. Also, critical stationary flows in tubes are considered with regard to Benjamin's vortex breakdown theories.

An experiment is reported, in which turbulent shear-stresses as well as mean velocities have been measured in a three-dimensional turbulent boundary layer approaching separation. It is shown that even very close to the wall the stress vector does not align itself with the mean velocity gradient vector, as would be required by a scalar ‘eddy viscosity’ or ‘mixing length’ type assumption. The calculation method of Bradshaw (1969) is tested against the data, and found to give good results, except for the prediction of shear-stress vector direction.

The problem considered is that of absorbing two-dimensional water waves in a channel by means of a moving termination at the end of the channel. The problem is formulated for a semi-infinite channel and solutions are determined according to a linearized theory. The motion of the termination that is needed for absorption is determined in the form of a linear operation on the measured surface elevation at a fixed point in the channel so a self-actuating wave-absorbing system can be devised. A theoretical method of studying the stability of such a system is presented. A system of this type was built and experiments with it are described. Wave absorption is demonstrated both for monochromatic waves and for wave pulses. The absorption of a wave pulse is compared with the absorption of the same pulse by a fixed beach making a ten degree angle with the horizontal direction.