A comparison is made between the effects of spreading the source (thus causing interference) and of viscosity in the Kelvin ship-wave problem. Two simple pressure distributions are considered and in both it is found that spreading, like viscosity, introduces a multiplicative damping factor into the inviscid pressure-point solution. In one case it is this factor, rather than that of viscosity, which dominates the decay of the wave profile, while, in the other, the effects alternate in importance as one travels along any particular wave crest.

Temperature and velocity fluctuations have been recorded in the open sea and in a tidal channel, and power spectra have been determined from the records. The one-dimensional spectra of temperature fluctuations are found to have an inertial subrange. At larger wave-numbers the data can be fitted by Batchelor's spectrum function for the viscous-convective range. The spectra are inconsistent with the form proposed by Pao for the viscous-convective range.

Estimates are given for the constants in Batchelor's spectrum function, but these depend upon knowledge of the rate of dissipation of kinetic energy, which is determined from the velocity spectra. There is doubt about the validity of some of the velocity spectra, and in other cases there is reason to suspect that the turbulence is not locally isotropic.

A hot film flowmeter, a thin film resistance thermometer and several thermistors were mounted on a submarine and used to study turbulence and temperature microstructure in the open sea. The surface layer is found to be continuously turbulent and patches of turbulence have been found in and below the main ocean thermocline.

Small-scale temperature fields in water were used to test the dynamic response of towed thermometers of the platinum film resistance type. Laminar buoyant plumes rising from submerged heaters below the line of motion were the test temperature fields. The analysis of results was based on an approximate ‘diffusion-layer’ model of the dynamic heat-transfer process occurring near the platinum film on the probe tip. The model represents the linear heat transfer into a two-layer semi-infinite medium, with the platinum thin film located at the interface between a water layer of thickness Δ and a semi-infinite substrate of glass. The differences of the thermal properties of water and glass were found to be negligible. The characteristic time Δ2/D, where D is the thermal diffusivity of water, was determined by the ratio of actual to film-indicated plume-peak temperature, assuming a sinusoid approximation to the plume profile. The frequency response for the same operating conditions as the plume tests could then be obtained from the diffusion-layer model.

Intermittency measurements have been performed within the first 100 virtual diameters of an axisymmetric compressible wake. The primary measurements, performed with the hot-wire anemometer, concerned the intermittency factor and the frequency of ‘zero crossings’. The intermittent flow covered most of the wake profile but for a narrow region about the axis, and was found to be normally distributed around the average front position. The latter, along with the extent of the front standard deviation, was found to agree numerically with expectations based on low speed wakes and to grow as the 1/3 power of axial distance. A weak periodicity of the front was detected at a wavelength about nine times greater than the longitudinal scale of turbulent velocity fluctuations. This periodicity affects the turbulent spectra.

The solution of the differential equation describing the equilibrium meniscus in a vertical right circular cylinder is obtained over the entire range of contact angles and Bond numbers (dimensionless ratios of gravitational to capillary forces) for which a stable meniscus exists. The first few terms of the asymptotic series valid for Bond numbers of small and large magnitude are given, and the numerical solution for intermediate values is computed. The behaviour of the solution as a function of contact angle and Bond number is depicted graphically.

Two-point time correlations up to eighth order of longitudinal velocity fluctuations in grid-generated turbulence have been measured using linearized hot-wire anemometry, digital sampling, and a high-speed digital computer. A novel feature of the present measurements is the adoption of digital Fourier analysis, using the recently developed fast-Fourier transform method. The joint probability density function for the velocity fluctuations at two points separated in time is found to be significantly non-Gaussian. All measured even-order correlations are nearly identical with those reported by Frenkiel & Klebanoff (1967 a, b), and higher-order correlations may be accurately predicted from the second-order correlation by assuming a Gaussian joint probability density. All individual odd-order correlations are substantially different from those reported by Frenkiel & Klebanoff. In particular, all mean values of odd powers of the fluctuating velocity are nearly zero, and the correlations are nearly antisymmetrical functions of the time delay as would be the case for purely isotropic homogeneous turbulence. In spite of the large difference between the individual measured odd-order correlations and previous measurements, quantities such as the skewness and skewness factor derived from certain combinations of the correlations are found to be quite insensitive to observed differences in the form of the correlations and are very similar to previous measurements.

A closed form solution is obtained for the linearized problem of the diffraction of Kelvin waves by a sharp bend on a rotating earth. It is shown that for the frequency ω of the incoming wave less than f, where ½f is the angular velocity of rotation, the wave is transmitted around the bend without change of amplitude. For ω > f the amplitude is in general reduced but is unaltered for the special angles π/(2n + 1). For these special angles the solution is obtained in elementary terms.

Among a triad of gravity waves in a uniform shear flow, a remarkably powerful second-order resonant interaction may take place. This interaction is characterized by large growth rates of waves which propagate in directions oblique to that of the primary flow, and by a systematic transfer of energy from the primary flow to such waves. Most of the energy transfer takes place in the vicinity of a ‘critical layer’, where viscous forces are dominant.

Provided the resonance condition may be satisfied, a uniform shear flow which is perturbed by a two-dimensional wave of small but finite amplitude may be unstable, owing to the growth of two initially infinitesimal oblique waves which complete the resonant triad.

The nature of instability and disturbance amplification in the laminar natural convection boundary layer over a vertical flat surface with uniform heat flux has been theoretically investigated. The coupled Orr-Sommerfeld equation has been numerically integrated for a Prandtl number of 6·7, with the boundary condition that the disturbance heat flux be zero at the surface. The spatial amplification characteristics of disturbances convected downstream were analyzed, and constant amplification rate contours were determined. The relative amplification has been calculated from these contours and is presented in the form of amplitude ratio contours. An important feature of these results is that the low frequency disturbances, which become unstable first, amplify very slowly and also have wavelengths which are much longer than the distance to the leading edge. The higher frequency, shorter wavelength, disturbances amplify much faster and are, therefore, presumed to be the dominant ones in stability considerations. The nature of the velocity and temperature amplitudes and phase profiles across the boundary layer has also been examined.

Based on a dimensional consideration, the ‘−3 power law’ on the spatial spectrum of sand waves formed by flowing water Sηη(k) is derived for a large wave-number equilibrium subrange, S_{\eta\eta}(k)\sim \alpha k^{-3}, $$S_{\eta\eta}(k)\sim \alpha k^{-3},$$ where α is a constant depending on the angle of repose of sand particles and k denotes the wave-number.

Likewise, the frequency spectrum is shown to have the ‘−3 power law’ range for higher frequencies as well as the ‘−2 power law’ range for frequencies near a spectral peak.

These spectra are shown to agree with experimental data from various sources.

The work that follows considers the velocity profiles within the boundary layer at the wall of an arbitrarily converging funnel. The occurrence of super-velocities, i.e. components of velocity within the boundary layer exceeding their corresponding free stream component, is investigated and the relevance of such a phenomenon to the efficiency of discharge discussed.

It has been found experimentally that the turbulent pipe flow through a mitred, right-angle bend produces a downstream secondary circulation which does not conform to the twin-circulatory flow usually to be found in pipe bends. The secondary flow is dominated by a single circulation about the axis in either a clockwise or an anticlockwise sense, between which it switches abruptly at a low, random frequency. The phenomenon is explained in terms of the asymmetry of the inner wall separation and the turbulent axial circulation generated in the upstream flow.

A numerical examination has been made of the reflectivity of critical levels with low Richardson number to internal gravity waves propagating in stratified fluids with shear. At sufficiently low positive Richardson numbers the reflected wave may actually be stronger than the incident.

The normal mode instabilities of three simple models have also been computed. The results are presented in three dimensions: Richardson number, horizontal wave scale and real wave frequency.