It is shown that when short wind-generated gravity waves lose energy by breaking (or other dissipative processes) near the crests of longer waves, the loss is supplied partly by the longer wave because of the second-order radiation-stress interaction. This process is discussed in detail analytically and also from energy considerations with use of the concept of radiation stress. The results are applied to the attenuation of swell by a local wind-generated wave field, and it is shown that the rate of decrease of the amplitude a" of the swell is constant and given by $\frac {da^{\prime\prime}}{dt} =- \frac {3\rho_a u_*^2 c }{2\rho _w c^{\prime\prime 2}},$ where ρa,ρw are the air and water densities, u* is the friction velocity of the wind in the interaction zone, and c", c are the phase velocities of the swell and the component of the locally generated field at the spectral maximum.

An example is presented which shows that the boundary of stability in an antisymmetric stratified shear flow is not necessarily marked by steady neutral waves with c = 0. The stability characteristics of stratified shear flow in the neighbourhood of the neutral curve are also discussed.

The study of wave propagation by geometrical optics is applied to a consideration of propagation through a non-uniform, statistically homogenous medium. Following the trajectory of a phase point, two effects are examined; the retardation of the phase point by the variable local wave speed along its trajectory and the further retardation and dispersion resulting from its meandering. Mean and mean-squared displacements are obtained to describe the retardation of the wave front, and the dispersion of the phase point from the incident direction.

The theory has application as a correction to the use of geometrical optics wherever the latter can be employed. In particular, it is shown by an estimate of the magnitude of the pertinent parameters that an application may well be found in the study of the tsunami (a long ‘shallow’ ocean wave).

A technique has been developed to detect very small amplitude fluctuations of concentration or temperature in aqueous electrolytic solutions. A platinized single-electrode conductivity probe is made one arm of an A.C. Wheatstone bridge, whose unbalance is then proportional to the incremental change of conductivity at the probe tip. A discussion of the sensitivity and spatial resolution of the probe and circuitry is given. This technique should have useful applications in oceanographic measurements of salinity or temperature, measurements of statistical parameters useful in the description of diffusion-controlled reactions in liquid-phase chemical reactors, and also the pure mixing of ionic materials and temperature.

Kolmogoroff's (1941) theory of local isotropy and universal similarity predicts that all turbulent velocity spectra are reducible to a single universal curve for the highest wave-numbers and that under certain conditions dimensional analysis may be used to predict spectral shapes. Identical arguments predict that the fine structure of conserved dynamically passive scalar fields mixed by turbulence will also be universally similar.

A single-electrode conductivity probe in a bridge circuit was used to measure the spectra and decay of a random homogeneous field of concentration and temperature behind a grid, and a Lintronic constant-temperature hot-film anemometer was used to measure the decay of velocity field. These experimental measurements of absolute turbulent velocity, temperature, and concentration spectra in salt water are here compared with the general predictions of universal similarity and local isotropy theories, as well as a prediction by Batchelor (1959) of the exact large wave-number spectral form for scalar mixing at high Schmidt number (v[Gt ]D. The spectral shapes are found to have the predicted similarity forms, and the data are consistent with Batchelor's predicted spectrum of the scalar field.

Coefficients of longitudinal and lateral dispersion were measured for steady uniform laminar flow through an isotropic porous medium. A unique experimental method for measuring lateral dispersion is described. It is found that the ratio of the coefficient of longitudinal dispersion D1 to the coefficient of lateral dispersion D2 is given by $\frac {D_1}{D_2} = \lambda \Re ^n$ where λ and n are dimensionless coefficients dependent upon the pore-system geometry, and [real ] is the Reynolds number based on the seepage velocity, the average grain diameter, and the kinematic viscosity.

An attempt has been made to establish the laws governing the flow in a turbulent line vortex. Up to the present time theoretical solutions for laminar flow have been used for comparison with experimental results for turbulent flow to find an ‘eddy viscosity’ term and its variation with various parameters. An approach is developed along lines similar to the methods used in turbulent boundary-layer theory and is found to be reasonably successful as far as the work has proceeded. It is predicted by theory, and confirmed by experiment, that the circulation in the vortex is proportional to the logarithm of radius under certain conditions. For the present experimental conditions, the vortices are found to be completely independent of viscosity effects when the parameter WZ/K0 exceeds 150, and above this value the experimental results may be correlated to give a universal distribution of circulation in the inner region of the vortex. Further experiments are necessary to verify and extend the results of these tests before any definite conclusions may be made regarding the circulation distribution in the outer core region of the vortex and the growth and development of the vortex.

A continuous-flow system is fed with a liquid which turns blue a specified time θ after entering. A more or less stationary pattern is thus set up, those parts of the liquid which have spent times longer than θ in the system being blue while the rest is colourless. The value of θ can be changed at will, enabling details of the flow-pattern to be deduced. The interpretation of the finer points of the colour-pattern is made difficult by the effects molecular interdiffusion of different parts of the liquid.

An experimental study has been made of transition to turbulence in the free convective flows on a heated plate. Observations have been made with the plate vertical and inclined at angles up to about 50° to the vertical, both above and below the plate. A fibre anemometer was used to survey the region of intermittent turbulence. Information has thus been obtained about the range of Grashof numbers over which transition takes place. Even when the plate is vertical the region of intermittent turbulence is long. When it is inclined, this region becomes still longer in the flow below the plate as a result of the stabilizing stratification, a Richardson number effect. It is possible to have a whole flow such that it should be described as transitional, not laminar or turbulent. It was noticed that in this flow and the vertical plate one, the velocity during the laminar periods could be either of two characteristic values, one of them close to zero. The behaviour above an inclined plate could be interpreted largely as a trend towards the behaviour described in a preceding paper.

The observations on the stably stratified flow help to explain a feature of glacier winds.

This paper discusses the general idea that in systems where a flexible solid is coupled with a flowing fluid three different types of instability are possible. These were originally designated by Brooke Benjamin (1960) as ‘class A’, ‘class B’ and ‘Kelvin-Helmholtz’ instability, and their collective significance has been clarified recently by Landahl (1962). Class A and class B disturbances are essentially oscillations involving conservative energy-exchanges between the fluid and solid, but their stability is determined by the net effect of irreversible processes, which include dissipation and energy-transfer to the solid by non-conservative hydrodynamic forces. Dissipation in the solid tends to stabilize class B distrbances but to destabilize class A ones. Class C instability (i.e. the ‘Kelvin-Helmholtz’ type) occurs when conservative hydrodynamic forces cause a unidirectional transfer of energy to the solid.

In § 2 this idea is examined fundamentally by way of the Lagrangian method of generalized co-ordinates, and in § 3 the example of inviscid-fluid flow past a flexible plane boundary is considered. The treatment of this example amplifies the work of Landahl, in particular by including the effect of non-conservative forces of the kind investigated by Miles in his series of papers on water-wave generation by wind.

Several years ago Dean (1948) showed how to solve the linearized potential problem of water waves passing over a submerged circular cylinder. He discovered the remarkable fact that there is no reflexion from the cylinder; the transmitted waves have the same amplitude as the incident waves, but they suffer a phase shift in passing the cylinder. Soon after the publication of Dean's paper, Ursell (1950) investigated the problem anew. He placed the solution on a rigorous basis, supplied a uniqueness proof, and developed a form of the solution with which it was reasonable to perform calculations.