A solution is developed for the flow of a vapour in a liquid enclosure in which different portions of the liquid wall have different temperatures. It is shown that the vapour pressure is very nearly uniform in the enclosure, and an expression for the net vapour flux is deduced. This pressure and the net vapour flux are readily expressed in terms of the temperatures on the liquid boundary. Explicit results are given for simple liquid boundaries: two plane parallel walls at different temperatures and concentric spheres and cylinders at different temperatures. Some comments are also made regarding the effects of unsteady liquid temperatures and of motions of the boundaries. The hemispherical vapour cavity is also discussed because of its applicability to the nucleate boiling problem.

A second approximation is developed for the mass-transport velocity within the bottom boundary layer of cnoidal waves progressing over a smooth horizontal bed. Mass-transport profiles through the boundary layer are obtained by considering terms of up to third order in the perturbation parameter. A comparison with results based on a first approximation indicates that the effect of the third-order terms is to predict a smaller mass-transport velocity and that this difference is generally significant, particularly for waves extending to the intermediate depth range. The predicted correction to the first approximation is qualitatively supported by experimental evidence.

A surface gravity wave obliquely incident on a sloping beach is broken near the beach and has a smooth surface further out. Viewed in the frame of reference of the transition from the smooth to the broken part, the flow is steady, and the wave is oblique to the free stream. By placing a suitably shaped obstacle in a flume operated at high Froude number, such a wave can be generated. Experiments in which a wave of 18 cm height was generated are described and the wave shape and some of its characteristics presented. In particular, the dividing stream surface separating that part of the flow which curls over into the break from the part that flows smoothly over the obstacle is discussed.

Model surfboards can ride this wave unsupported, provided the correctly scaled weight loads them at the right centre-of-mass position. This makes it possible to determine the forces on the board without a balance. A comparison of the measured forces with estimates, particularly of the drag, indicate that viscous and surface-tension phenomena introduce only small scale effects in the Froude number modelling. While the results are not sufficiently accurate to draw definite conclusions about the effects of surf board shape, they indicate clearly that surf board flows may be modelled with quantitative success in the laboratory.

The motion of a bore over a sloping beach, earlier considered numerically by Keller, Levine & Whitham (1960), is studied by an approximate analytic technique. This technique is an extension of Whitham's (1958) approach for the propagation of shocks into a non-uniform medium. It gives the entire flow behind the bore and is shown to be equivalent to the theory of modulated simple waves of Varley, Ventakaraman & Cumberbatch (1971).

The time development of two-dimensional fluid motion induced by a line sink in a rectangular, density stratified reservoir with a free surface is given. It is shown that the initiation of such a sink gives birth to a spectrum of internal expanding shear fronts with a progressively decreasing vertical wavelength. These fronts move out from the sink and travel towards the far wall, where they are reflected. This process ceases once the front with a vertical wavelength equal to the steady withdrawal-layer thickness has reached the end wall. The fronts so introduced continue to move back and forth, expanding to standing waves if the viscosity of the fluid is small enough. The evolution and nature of the withdrawal layer are shown to depend critically on the relative magnitude of the convective inertia and viscous forces, the number of reflexions from the rear wall and the Prandtl number.

The two-dimensional thermal boundary layer over a finite hot film embedded in a plane insulating wall, with a shear flow over it which reverses its direction, is analysed approximately using methods similar to those previously developed for viscous boundary layers (Pedley 1976). The heat transfer from the film is calculated both for uniformly decelerated and for oscillatory wall shear, and application is made to predict the response of hot-film anemometers actually used to measure oscillatory velocities in water and blood. The results predict that the velocity amplitude measured on the assumption of a quasi-steady response will depart from the actual amplitude at values of the frequency parameter St greater than about 0·3 (St = ΩX0/U0, where Ω = frequency, U0 = mean velocity, X0 = distance of hot film from the leading edge of the probe). This is in good agreement with experiment. So too is the shape of the predicted anemometer output as a function of time throughout a complete cycle, for cases when the response is not quasi-steady. However, there is a significant phase lead between the predicted and the experimental outputs. Various possible reasons for this are discussed; no firm conclusions are reached, but the most probable cause lies in the three-dimensionality of the velocity and temperature fields, since the experimental hot films are only about 2·5 times as broad as they are long, and are mounted on a cylinder not a flat plate.

A turbulent mixing layer in a water channel was observed at Reynolds numbers up to 3 × 106. Flow visualization with dyes revealed (once more) large coherent structures and showed their role in the entrainment process; observation of the reaction of a base and an acid indicator injected on the two sides of the layer, respectively, gave some indication of where molecular mixing occurs. Autocorrelations of streamwise velocity fluctuations, using a laser-Doppler velocimeter (LDV) revealed a fundamental periodicity associated with the large structures. The surprisingly long correlation times suggest time scales much longer than had been supposed; it is argued that the mixing-layer dynamics at any point are coupled to the large structure further downstream, and some possible consequences regarding the effects of initial conditions and of the influence of apparatus geometry are discussed.

The fluctuating lift and drag acting on a long, rigidly supported circular cylinder placed symmetrically in a narrow rectangular duct were investigated for various blockage percentages over a wide range of Reynolds numbers around the critical value. The data obtained permit a full assessment of the effect of confinement on the mean-drag coefficient, the root-mean-square values of both the drag and the lift fluctuations, the Strouhal number of the dominant vortex shedding, and the Reynolds number marking transition from laminar to turbulent flow separation. Besides experimental information on a subject on which little is known so far, the paper provides a basis for the deduction of better correction procedures concerning the effects of blockage.

The complete uniform asymptotic expansion of the velocity and pressure fields for Stokes flow past a slender body of revolution is obtained with respect to the slenderness ratio ε of the body. A completely general incident Stokes flow is assumed and hence these results extend the special cases treated by Tillett (1970) and Cox (1970). The part of the flow due to the presence of the body is represented as a superposition of the flows produced by three types of singularity distributed with unknown densities along a portion of the axis of the body and lying entirely inside the body. The no-slip boundary condition on the body then leads to a system of three coupled, linear, integral equations for the densities of the singularities. The complete expansion for these densities is then found as a series in powers of ε and ε log ε. It is found that the extent of these distributions of singularities inside the body is the same for all the singular flows and depends only upon the geometry of the body. The total force, drag and torque experienced by the body are computed.

Experiments were carried out to investigate the onset, size and shape of fingers in a salt–sugar two-component system. The results on the critical Rayleigh number ratio for the marginal state agree well with the prediction of the linear stability theory of Stern (1960). The theory also predicts that the fingers at the marginal state should be as wide as the layer thickness. In our experiments, in a layer of approximately 3·5 cm deep, the fingers, when they appeared, were always long and narrow, with typical lateral dimensions of approximately 1 mm.

An analytical–numerical analysis of the fluid motion induced by an impulsive change in the angular velocity of a rotating disk is presented. Separate solutions are derived for the early development and for the approach to the ultimate state. The superposed flow is found to have variations on two length scales, and is characterized by the generation and propagation of shear-type wave trains. These decaying wave trains ultimately lead to the new von Kármán state corresponding to the changed angular velocity of the disk.

A finite-amplitude model of baroclinic instability is studied in the case where the cross-stream scale is large compared with the Rossby deformation radius and the dissipative and advective time scales are of the same order. A theory is developed that describes the nature of the wave field as the shear supercriticality increases beyond the stability threshold of the most unstable cross-stream mode and penetrates regions of higher supercriticality. The set of possible steady nonlinear modes is found analytically. It is shown that the steady cross-stream structure of each finite-amplitude mode is a function of the supercriticality.

Integrations of initial-value problems show, in each case, that the final state realized is the state characterized by the finite-amplitude mode with the largest equilibrium amplitude. The approach to this steady state is oscillatory (nonmonotonic). Further, each steady-state mode is a well-defined mixture of linear cross-stream modes.