Experiments on the two-dimensional turbulent wake generated by pairs of cylinders of unequal diameter have revealed some interesting flow characteristics. The wake width grew asymmetrically in the downstream direction, spread rate and entrainment coefficients proving larger on the small diameter cylinder side. Mean velocity profiles were also skewed to this side while maximum values of Reynolds stresses were larger on the other. Close to the cylinder, a region or turbulent ‘energy reversal’ was measured. The level of turbulence and the diffusion mechanism were high at this point and some comments are made concerning the structure of the flow under these conditions.

Extensive hot-wire auto- and cross-correlation measurements obtained in a fully developed compressible turbulent boundary layer are presented. A tentative mechanism of turbulence production and growth in hypersonic flow suggested by these measurements is developed. This flow model is consistent with previous observations in incompressible flows. Detailed measurements of the mean properties of the hypersonic turbulent boundary layer are also presented and compared with results from various transformation and finite-difference prediction methods. It is shown that none of the theories predict all the properties of the hypersonic turbulent boundary layer and that additional measurements are needed to provide more adequate physics of turbulent processes for use in the various theories.

The calculation of the pattern of waves produced by a point disturbance in a steady field which may be non-uniform can be performed straightforwardly by a single process of integration along the characteristic rays. For illustration, the method is applied to gravity waves produced by a source moving either in a straight line or in a circular path, to the symmetrical waves produced by a source in an expanding sheet and to the waves resulting from an instantaneous disturbance in :I stratified fluid.

The flow induced by the differential rotation of a cylindrical depression of radius a in one of two parallel rigid planes rapidly rotating about their common normal at speed Q is studied. A Taylor column bounded by the usual Stewartson layers arises, but the shear-layer structure is rather different from any previously studied. The Ei-layers (E = v/ωa2) smooth the discontinuity in the geostrophic flow, but the way in which this is accomplished is related to the possible singu-larities of the E1/3-layer solutions. The fact that the 1/4-layer is partially free and partially attached to a vertical boundary accounts for the new joining conditions for the 1/4-layer. The drag on a right circular cylindrical bump in uniform flow is given in addition to some general comments on the applicability of these joining conditions to the motion of an axisymmetric object of quite general shape.

New eigenvalue bounds are derived for the linear stability of inviscid parallel flows, both for homogeneous and for stratified fluids. The usefulness of these bounds, as compared with that of previous results, is assessed for several examples. For homogeneous fluids the new upper bounds for the imaginary part ci of the complex phase velocity are sometimes better than previous criteria. For both homogeneous and stratified flows, the new upper bounds for the wave-number α of neutrally stable disturbances improve on previous results, giving values within 10% of the known exact solution in several cases.

A number of mechanisms which transport dissolved constituents and maintain the salt balance in estuaries are described. Although some of these have already been analysed, two which appear to be the most important in many real estuaries have received little previous attention. The Mersey Estuary is used as an example in which to estimate the amount of mass transported by each mechanism. The computations show in part how little is known and how much hypothesis is still required in spit?e of the number of previous estuarine studies; one may conclude, however, that in many real estuaries the most important mass transport mechanism is the net (non-tidal) transverse circulation, which is induced in part by the boundary geometry and in part by the longitudinal density gradient.

The steady, inviscid, axisymmetric, rotating flow past a circular disk in an unbounded liquid is determined on the hypothesis that all streamlines originate in a uniform flow far upstream of the body. The characteristic parameter for the flow is k = 2ωa/U, where ω and U are the angular and axial velocities of the basic flow and α is the radius of the disk. Forward separation is found to occur for k > k = 1.9, in agreement with observation (Orloff & Bossel 1971). The length of the upstream separation bubble is determined on the hypothesis that the previous solution remains valid for k > k, despite the existence of closed streamlines within the upstream separation bubble (which may, but do not necessarily, inva,lidate the solution). This length increases rapidly for k > 3, in qualitative agreement with observation. The hypothesis of unseparated flow implies a singularity at the rim of the disk, just as in potential flow. The strength of this singularity departs only slightly from its potential-flow value for 0 ≤ k ≤ 2, but increases rapidly with k for k > 3, which suggests that (quite apart from the difficulties implied by the existence of closed streamlines) the solution cannot remain valid for sufficiently large k.

The essential difference, from the theoretical point of view, between an externally excitedlciody and a fish is that the latter can apply lateral vibratory movements at any part of its surface, whereas in the ‘artificial fish’ lateral vibrations are applied only at the point where the external force acts on the body. A good example which illustrates how the artificial fish swims is the ‘Pod’. The Pod is a medical device consisting of a small magnet attached to a plastic ‘tail’. If the Pod is placed in a patient's blood vessel, and an alternating magnetic field is applied, the magnet oscillates angularly and the plastic tail causes it to swim. The purpose of the device is to deliver medicaments at any desired location in the circulatory system.

In this paper the theory of swimming of elastic slender bodies excited by an external force is presented. Special reference is made to the hydrodynamic forces acting on a swimming cylinder in viscous fluctuating flow. The results obtained are used in the analysis of the propulsion mechanism of the Pod.

The flow driven by variations in surface tension round a hemispherical gas or vapour bubble on a heated wall has been investigated numerically for steady-state conditions over a wide range of values of dimensionless parameters, and experimentally for one set of conditions. Although six parameters are needed to specify the flow conditions, the magnitude of the liquid flow normal to the heated wall is determined primarily by tihe Marangoni number, Prandtl number and the Biot number based on the effective heat-transfer coefficient at the liquid-gas interface. The interior temperature of the bubble depends in addition on the thermal conductivity ratio of the liquid and the wall material. The flow is very sensitive t o the presence of surface-active contaminants. For water, calculations and experimental observations both indicate that contamination which lowers the static surface tension by only 0.1% may suppress the thermocapillary motion.

An experimental study of the structure of the internal layer which grows down-stream from a rough-to-smooth surface change shows it to be essentially different from that studied by Antonia & Luxton (1971 b) for the case of a smooth-to-rough perturbation. The rate of growth of the internal layer is less than that for the smooth-to-rough step and it appears that the more intense initial rough-wall flow dictates the rate of diffusion of the disturbance for a considerable distance. Inside the internal layer the mixing length I is increased relative to the equilibrium distribution I = KY. A turbulent energy budget shows that the advection is comparable with the production or dissipation, whilst there seems to be some diffusion of energy into the internal-layer region close to the wall. The boundary layer, as a whole, recovers much more slowly following a rough-to-smooth change than following a smooth-to-rough change, and at the last measuring station (16 boundary-layer thicknesses from the start of the smooth surface) the distributions of mean velocity and Reynolds shear stress are far from self-preserving.

Experimental measurements of the advancing head of a gravity current are described. The head, of depth d in mean cross-section and advancing at mean speed U, has an elevated nose whose mean height h satisfies h/d = 0·61 Re-0·23±0·01 through the range 300 < Re < 10000 (Re = Ud/ν). A shifting pattern of lobes and clefts ranges across the head, in which the mean lobe width $\overline{b}$ is found experimentally to satisfy $\overline{b}/d = 7.4\,Re^{-0.39\pm 0.02}$. By moving the floor in the direction of the current, or by introducing a thin dense layer beneath it, the lobes and clefts can be suppressed and a purely two-dimensional flow obtained. It is concluded that the lower boundary plays an essential role in determining the substructure of the head and that this originates in convective instability as the head rides over less dense fluid.

We consider the propagation of a weak nonlinear wave whose energy is concentrated in a narrow band of wavenumbers in a fluid which is both dispersive and dissipative. We use the small amplitude equations of Whitham's theory of slowly varying wave trains, modified slightly to include dissipation, to show that the modulation of the wave may be described by a nonlinear Schrödinger equation. For long waves which are purely dispersive we obtain the Kortewegde Vries equation, and for long waves which are dissipative we obtain Burgers’ equation by suitable transformations of the nonlinear Schrödinger equation. We mention the problem of Stokes waves in deep water and comment briefly upon invariant far-field theory.