The effect on an obliquely incident surface wave of a vortex sheet separating two uniform currents is considered. It is shown that the amplitude of the transmitted wave as a function of the angle of incidence and current strength is very close to that obtained by Longuet-Higgins & Stewart on the assumption of small smooth changes in current velocity. The difference is accounted for by a small amount of reflexion of the wave by the vortex sheet. It is suggested that, in the intermediate range where the change in current velocity over a wavelength is comparable with the wave velocity, the wave amplitude of the transmitted wave lies between the curves of Longuet-Higgins & Stewart and those found here.

Profiles of mean and fluctuating turbulent velocities and temperatures, of the time derivative of velocity and of intermittency have been measured in the wake of an unheated as well as a heated sphere in the low Reynolds number range 600–2500 at distances 80–1800 sphere diameters downstream. The wind-tunnel experiments exhibit a strong dependence on Reynolds number but they do not indicate the attainment of or an approach to the final period of turbulent decay which has been explored theoretically by Phillips and by O'Brien. The lowest turbulence Reynolds number obtained was Rλ, = 1·4.

Normal and tangential velocities in the boundary layer and out into the free stream have been obtained using a non-disturbing flow visualization technique for uniform laminar flow around a sphere. The non-similar data are available in tables at 2.5° intervals from 20° from the front to about 15° past the separation point a t Reynolds numbers of 290, 750, 1300 and 3000. Stream functions calculated by LeClair using a numerical solution of the Navier-Stokes equation at Re 21 300 are not in good agreement with measured values from 30° to 60°, but are in much better agreement around the separation point. Too few grid points near the sphere where the tangential velocities rise to a maximum above free-stream values may account for the difference.

The linear stability of non-planar shear flow of a stably stratified fluid is investigated. Howard's (1961) semicircle theorem, which places bounds on the range of the complex phase speed c, is derived, although sufficient conditions for stability of the (x-directed) basic flow $\overline{u}(y, z)$ have not been established. The stability properties of some particular shear-layer and jet flows for long-wave disturbances are examined. Much of the effort is directed to delineation of unstable properties of the flow $\overline{u}(y, z) = \tan h\,y \tan h\,z$ in terms of c, the wavenumber α and a local form J0, of the Richardson number. Limiting cases are inflexion-point instability (J0 = ∞) and two-dimensional instability of a vertically stratified shear flow ($J_0 < \frac{1}{4}$). The present numerical computations reveal that at least two modes of instability are present for each pair of values of α and J0 for α [les ] 0·2 and $J_0 < \frac{1}{4}$. The source of instability for each mode is examined by means of computed energy transformations. However, numerical difficulties prevent a detailed examination of these unstable modes for α > 0·2.

The linear stability of a rotating contained perfect gas flowing axially is shown to depend on a ‘centrifugal Richardson number’ when the ratio of the axial flow to the peripheral velocity, and the ratio of the peripheral velocity to the sound speed are both small. The Boussinesq approximation is not made. In the limit of infinite sound speed the known incompressible result (unstable, Pedley 1968) is reproduced. Comparison with computational results indicates that the asymptotic theory is pessimistic.

A two-dimensional horizontal flow is discussed, which is induced by other, buoyancy-driven flows elsewhere. It is an adaptation of the incompressible wall jet, which is driven by conditions a t the leading edge and has no streamwise pressure gradient. The relation of this flow to the classical buoyancy-driven boundary layers on inclined and horizontal surfaces is investigated, as well as its possible connexion with a two-dimensional buoyant plume driven by a line source of heat. Composite flows are constructed by patching various such solutions together. The composite flows exhibit $Gr^{\frac{1}{4}}$ scaling (Gr being the Grashof number).

The method of energy is used to study the stability of uniformly accelerated flows, i.e. those flows characterized by an impulsive change in boundary temperature or velocity. Two stability criteria are considered: strong stability, in which there is exponential decay of the disturbance energy, and marginal stability, in which the disturbance energy is less than or equal to its initial value. For the important case in which the critical stability parameter (measured by the Marangoni, Rayleigh or Reynolds number) decreases with time, it is proved that an onset time exists. Furthermore, it is shown that the experimental onset time is bounded below by the marginal stability limit, which in turn is bounded below by the strong stability limit.

The method is then applied to the problem of an impulsively cooled liquid layer susceptible to instabilities driven by interfacial-tension gradients. The strong stability and marginal stability boundaries are calculated and bounds on the onset time are given. These results represent the first rigorous bounds for convective instability problems of this class. Comparison with the limited available experimental data shows the calculated results to be lower bounds on the experimental onset times, and hence the theory is in agreement with available experimental results.

Gans' criterion is shown to be valid for all inviscid non-diffusive flows where the radial velocity is everywhere zero and the physical variables are functions of the radial distance only. That is, a modified form of the Miles-Howard theorem holds for a large class of helical gas flows.