The way in which internal waves change in amplitude as they propagate through an incompressible fluid or an isothermal atmosphere is considered. A similarity solution for the small amplitude isolated viscous internal wave which is generated by a localized two-dimensional disturbance or energy source was given by Thomas & Stevenson (1972). It will be shown how summations or superpositions of this solution may be used to examine the behaviour of groups of internal waves. In particular the paper considers the waves produced by an infinite number of sources distributed in a horizontal plane such that they produce a sinusoidal velocity distribution. The results of this analysis lead to a new small perturbation solution of the linearized equations.

Experiments with a rotating source-sink annulus have shown that hot-wire probe supports can give rise to low-wavenumber, azimuthally propagating disturbances. These have been observed by a number of workers, and interpreted as Ekman boundary-layer instabilities and inertial eigenmodes of the annulus. The waves are associated with the wake downstream from the probe support; and a simplified model of the wake instability in cylindrical coordinates is presented. This model has a number of features in common with the observed disturbances. Extensive data have been obtained on wave frequencies and magnitudes, wavenumbers and phase relationships, and on wake structure and onset of the disturbances. The results of hot-wire anemometry experiments in an annulus are discussed in light of the present findings. It is concluded that the wave motions interpreted as type-II (class-A) Ekman instabilities and inertial eigenmodes by Tatro & Mollo-Christensen (1967) were probe-associated disturbances, while the boundary-layer waves observed by Caldwell & Van Atta (1970) were type-II disturbances, similar to those observed by Faller & Kaylor (1966a) using dye techniques.

The forced oscillations due to a point forcing effect in an infinite or contained, inviscid, incompressible, rotating, stratified fluid are investigated taking into account the density variation in the inertia terms in the linearized equations of motion. The solutions are obtained in closed form using generalized Fourier transforms. Solutions are presented for a medium bounded by a finite cylinder when the oscillatory forcing effect is acting at a point on the axis of the cylinder. In both the unbounded and bounded case, there exist characteristic cones emanating from the point of application of the force on which either the pressure or its derivatives are discontinuous. The perfect resonance existing at certain frequencies in an unbounded or bounded homogeneous fluid is avoided in the case of a confined stratified fluid.

This paper deals with two main problems concerning flow in curved alluvial channels. First, the large-scale bottom geometry that develops through the interaction of flow and sediment motion is determined. Second, experiments in an annular flume indicate that the bed is unstable and that this particular instability leads to the formation of a certain number of scour holes. This is explained by a linear stability analysis.

The inviscid transonic flow past a thin wing having swept leading edges, with smooth lift and thickness distributions, is shown to possess an outer nonlinear structure determined principally by a line source and a line doublet. Three domains (the thickness-dominated, the intermediate, and the lift-dominated), representing different degrees of lift control of the outer flow, are identified; a transonic equivalence rule valid in all three domains is established. Except in one domain, departure from the Whitcomb-Oswatitsch area rule is significant; the equivalent body corresponding to the source effect has an increased cross-sectional area depending nonlinearly on the lift. This nonlinear lift contribution results from the second-order corrections to the inner (Jones) solution, but produces effects of first-order importance in the outer flow. Of interest is an afterbody effect dependent on the vortex drag, which is not accounted for by the classical transonic small-disturbance theory.

The bounded solution of the unsteady Stokes equations is obtained for the flow of a viscous incompressible fluid about a circular cylinder which undergoes a linear translation starting from rest. A drag formula which consists of the known added-mass term and an additional term arising from the presence of viscosity is obtained. The drag obtained is applied locally in a study of damped vibration of a string. It is shown that the usual theory based on the quasi-steady drag formula overestimates considerably the period and the decay rate of damped vibration of a string in a viscous fluid.

The steady, inviscid, axisymmetric, rotating flow past a prolate spheroid in an unbounded liquid is determined on the hypothesis that all streamlines originate in a uniform flow far upstream of the body. The similarity parameters for the flow are κ = 2Ωa/U and δ = a/b, where 2a and 2b are the minor and major axes and Ω and U are the angular and axial velocities of the basic flow. Solutions are obtained both by separation of variables in prolate spheroidal co-ordinates and through the slender-body limit δ ↓ 0 with κ = O(1). Forward separation is found to occur for κ > κ*, where κ* lies between 2·2 and 2·3 for 0 < δ [les ] 1. The velocity on the body, the upstream axial velocity and the wave drag are calculated for κ < κ*.

The structure of turbulence of fully-developed flow through three concentric annuli with small radius ratios was investigated experimentally for a Reynolds number range Re = 2 × 104−2 × 105. Turbulence intensities were measured in three directions, and turbulent shear stresses in the radial and azimuthal direction, in annuli of radius ratios α = 0·02, 0·04 and 0·1, respectively. The results showed that the structure of turbulence for these asymmetric flows is not the same as that for symmetrical flows (tubes and parallel plates). The main difference between symmetrical and asymmetric flows is that, for the latter, the diffusion of turbulent energy plays an important role. This is the reason not only for the non-coincidence of the positions of zero shear stress and maximum velocity, but also for the failure of most turbulence models in calculating asymmetric flows.

A model equation is derived which approximately describes the propagation of periodic surface waves in water of slowly varying depth. Numerical solutions to the model equation are obtained for the scattering of an incident plane wave by a conical island.

An approximation to the profile of given area with smallest drag in laminar flow is obtained (for Reynolds numbers between 103 and 105). It was shown previously by Pironneau (1974) that the skin friction on such a profile has to satisfy certain optimality conditions; the method used is based on these results. It was found that the optimum profile is long and thin (thickness-to-chord ratio about 10%), the front end being shaped like a wedge of angle 90° and the rear end like a cusp. The drag is very close to the drag on a flat plate of equal length.

Cavitation bubbles were produced by focusing giant pulses of a Q-switched ruby laser into distilled water. The dynamics of the bubbles in the neighbourhood of a solid boundary were studied by means of high-speed photography using a rotating-mirror camera with framing rates of up to 300000 frame/s. Bubble motion was evaluated from the frames with the aid of a digital computer using a graphical input device. Smoothed distance-time curves of different portions of the bubble wall were obtained also, allowing a reliable calculation of bubble-wall velocities (except at the actual instant of collapse). One of the numerical examples of the collapse of a spherical bubble near a plane solid boundary obtained by Plesset & Chapman could be realized experimentally. A comparison of the bubble shapes shows good agreement.