Characteristics of the turbulent motion in a cylinder wake have been measured during passage through a distorting section of a wind tunnel, the overall effect of the distortion being considerable lateral extension and compression without a considerable change of flow velocity. However, the sectional area is not constant and rates of longitudinal extension are comparable with the rates of lateral straining. Hot-wire anemometers, mostly in X-configurations, are used to measure mean velocities, turbulent intensities, Reynolds stresses, intermittency factors and spectra, and velocity correlations have been calculated from digital recordings of the outputs from arrays of eight single-wire anemometers. In contrast to previous investigations, the direction of compression is parallel to the axis of the cylinder, and the original entrainment eddies of the plane wake are suppressed rather than amplified.

The results show that substantial changes in stress-intensity ratios, entrainment rates, dissipation rates and turbulence length-scales occur in response to the three-dimensional distortion. In particular, the ratio of Reynolds stress to total intensity increases during the initial acceleration of the flow before decreasing as the flow is strained laterally, and correlations show that length-scales do not change in proportion to the lateral extension and become relatively small compared to the flow width.

Three-dimensional finite-amplitude thermal convection in a fluid layer is considered in the case where the boundaries of the layer are much poorer conductors than the fluid. It can be shown that if the conductive heat flux through the layer is not too large, the horizontal scale of motion is much greater than the layer depth. Then a ‘shallow water theory’ approximation leads to a nonlinear evolution equation for the leading-order temperature perturbation, which can be analysed in terms of a variational principle. It is proved that the preferred planform of convection is a square cell tesselation, as found in a rather more restricted parameter range by Busse & Riahi (1980), in contrast to the roll solutions that obtain for perfectly conducting boundaries. It is also shown that the preferred wavelength of convection increases slowly with amplitude.

By using the technique of multiple scaling a theory of gas-bubble oscillations in a liquid is developed. Collections of bubbles of arbitrary shape under the action of surface tension, buoyancy and solid surfaces are considered. In the absence of thermal conduction in the bubbles and compressibility of the liquid a conserved ‘action’ is defined for each of the modes of oscillation. The equation governing the decay of the action with time is found by carrying the analysis to second order. The geometrical configuration of the bubbles, in which the oscillations take place, evolves in time under convection by an underlying ‘basic’ flow for which the governing equations are derived. The bubble pulsations influence the development of the basic motion. Later in the work a source of gas bubbles is brought in and its effects on the oscillations discussed. The results of the interaction of pulsating bubbles with the liquid surface are also briefly considered. The determination of the amplitude of oscillations induced by the splitting up of bubbles and by the generation of bubbles from the gas source is described. Finally, several applications of the theory to specific problems are given.

The results of experiments involving instability, known as fingering, in a circular Hele Shaw cell with inward and outward flow are presented. The width of fingers in this situation is examined, and an approximate equation for the growth of fingers is proposed. The equation rα = cos (nθ) is shown to fit the shape of long fingers.