The effect of the angle of divergence ϕ, the magnitude of the area ratio A21 and the specific-heat ratio of the gas γ on the attenuation of a shock in a two-dimensional area expansion has been experimentally determined. The results are compared with current theories relating shock strength and area ratio. At some distance from the expansion the change in shock strength, for shocks with strengths up to 10, is predicted reasonably accurately by an analysis of Chisnell (1957). Close to the area change surprisingly strong shocks were observed. This is shown to result from the diffracted shock undergoing a Mach reflexion at the end of the expansion.

A new class of analytic solutions to the problem of two-dimensional potential fnow is presented here. The method of solution has features of both direct and indirect solutions. The bodies about which flow is computed are semi-infinite and have forward regions that either are flat or consist of a circular arc, which may be convex or concave to the flow. Closed-form solutions are obtained for the surface velocity. Afterbody shapes are defined by implicit equations containing a quadrature. Certain analytic properties of the solutions are investigated. An interesting feature of the bodies is the presence of a ‘pseudo corner’ where the slope angle is continuous but the curvature is infinite. The surface velocity becomes logarithmically infinite at these points in contrast to the power-law behaviour at a true corner. One case of the convex circular arc has finite velocity everywhere, and in some sense represents flow over a circular cylinder with a ‘natural’ separation point. This point occurs at 77·45° from the front stagnation point, which is close to the separation point for incompressible laminar boundarylayer flow.

An experimental study of distributed air-injection from a porous section of a flat plate into a uniform incompressible airflow is described. The relative mass flow rates of the injection varied between 0·008 and 0·053 (strong injection) and the blowing was fairly uniformly distributed. In the resulting flow field, which was predominantly laminar except near the dividing streamline, where unsteadiness prevailed, velocity profile and pressure measurements were taken and the position of the dividing streamline thereby estimated. Overall the results agree fairly well with the steady laminar theory for strong normal blowing, outlined in §2, although for the strongest blow some signs of separation some way upstream of the blow are apparent.

A hypersonic gun tunnel has been used to measure the heat transfer to a sharpedged flat plate inclined at various incidences to generate local Mach numbers from 3 to 9. The measurements have been compared with a number of theoretical estimates by plotting the Stanton number against the energy-thickness Reynolds number. The prediction giving the most reasonable agreement throughout the above Mach number range is that due to Fernholz (1971).

The values of the skin-friction coefficient derived from velocity profiles and Preston tube data are also given.

The heat transfer due to forced convection from an isothermal sphere in a steady stream of viscous incompressible fluid is calculated for low values of the Reynolds number and Prandtl numbers of O(1). The mean Nusselt number is compared with the results of experimental measurements. At very low Reynolds numbers, both the local and mean Nusselt numbers are compared with the results obtained from the theory of matched asymptotic expansions.

In a horizontal convecting layer of fluid, several distinct transitions occur at certain distinct Rayleigh numbers R, for a given Prandtl number Pr. The regime diagram has been extended to include the Prandtl-number range

2·5 × 10−2 [les ] Pr [les ] 0·85 × 104.

In particular it is found that distinct changes in the slope of the heat-flux curve occur even for Pr = 2·5 × 10−2. The flow is steady up to R = Rt = 2·4 × 103. For R > Rt, the period of oscillation is compared with the theoretical values of Busse. For Pr = 0·71 decreases as well as increases in the slope of the heat-flux curve are observed.

For R just greater than Rc, the preferred orientation of rolls in various side-wall geometries is investigated. For high Prandtl number, the effect of curvature of the roll axis, forced by curved side walls, upon the second transition at RII is investigated. It is found that curvature, as well as previously discussed effects, leads to a lowering of RII. These results, along with the observed hysteresis, support the view that there are metastable states attainable by finite amplitude instability. Finally the nature of the time-dependent flow at large R and high Prandtl number is investigated in a Hele-Shaw cell. It is shown unequivocally that the observed periodicity at a fixed point is due to hot or cold plumes moving past the point.

The period of oscillations for the Bénard problem in a two-component system taking into account thermal diffusion is given. Schmidt-Milverton plots are presented for water-methanol and water-isopropanol systems. Anomalous heating curves are observed. Thermocouple responses are given for some heating powers and show oscillations in the temperature field. A qualitative agreement exists with the predicted values of the period given by the theory.

In 1964, Yeh & Cummins demonstrated that coherent light sources could be used for the measurement of steady fluid velocities by observing the Doppler shift in the frequency of light scattered from small particles moving with the fluid. Since 1964 many investigators have attempted to extend this technique to the measurement of turbulent velocity fluctuations.

A fundamental limitation on this type of velocimeter is the Doppler ambiguity introduced by the finite transit time of particles through the scattering volume, turbulent velocity fluctuations across the scattering volume, mean velocity gradients and electronic noise. A unified account of the effect of the Doppler ambiguity on the measurement of the instantaneous velocities is presented and results are interpreted using the power spectrum. The influence of the ambiguity on the measurement of other statistical quantities is also examined.

Limitations on the spatial and temporal resolution imposed by the finite sampling volume are examined using the power spectrum and criteria for optimization of the response are proposed.

An operational laser-Doppler velocimeter is described and measurements of spectra in both laminar and turbulent flow are presented. The experimental results are seen to be in excellent agreement with theoretical predictions.

A two-dimensional unsteady transonic flow of a perfect gas with constant specific heats is considered, solutions being found in the form of perturbations from a uniform, sonic, isentropic flow. Longitudinal viscous stress terms are retained so that shock waves can be included. The case where the characteristic time of a temporal flow disturbance is large compared with the time taken by a sonic disturbance to traverse the transonic regime is studied. A similarity solution involving an arbitrary function of time is employed, such that the channel walls are in general not stationary. Solutions are presented for thick (shock fills transonic region) and thin (shock tends to a discontinuity) shock waves for both decelerating and accelerating channel flows. For the thin-shock case, both numerical and asymptotic solutions are given. Flow pictures illustrating variations in shock position and structure as well as velocity distributions are shown for exponentially decreasing and for harmonic temporal flow disturbances.

Approximate equations are derived for the slow variation in amplitude of free oscillations at the inertial frequency in a slightly stratified ocean. In an ocean of constant depth with horizontally uniform stratification the evolution equation for waves of small vertical mode number can be reduced to a Schrödinger equation, with the increment in Coriolis parameter playing the role of the potential. An exact solution of the Schrödinger equation is presented which demonstrates the transience of inertial oscillations.

Considering the barotropic instability problem of the mean westerly current in the atmosphere we have performed a series of experiments in a rotating vessel (using water and a barotropic model) to study the behaviour of a zonal asymmetric basic current with respect to small perturbations. In the centre of a rotating cylindrical vessel (of large diameter and rotation rate ω) a smaller cylinder was installed, the rotation of which relative to the vessel, at a rate Δω, generates a nearly two-dimensional field of mean relative motion within a sharply defined region. The dominant zonal velocity component $\overline{v}$ shows monotonic radial decrease within this so-called friction zone. Now what happens if the relative rotation of the inner cylinder, the source of momentum, suddenly vanishes, i.e. δΩ = 0? The main result is that the basic zonal current $\overline{v}$, which now has an asymmetric radial profile ($\overline{v} = 0 $ at the inner cylinder and the outer edge of the friction zone), breaks down into vortices, the number of which, the integer wavenumber n, is a function of the parameter ε = δω/ω alone: n = n(ε); increasing ε eff effects a decrease of n. For a theoretical discussion of the experimental results we assume this to be a problem of barotropic instability and base our analytical considerations on the two-dimensional non-divergent vorticity equation, frictional forces being neglected. By applying a perturbation method and prescribing a realistic asymmetric basic current we can derive the relation ν = {[¾π/ln (ε + 1)½]2 + 1}½, which yields the real wavenumber v as a function of the parameter ε = δω/ω. The analytical results are in good agreement with the experiments.

Experiments are described in which the vortex shedding from a bluff body and the base pressure coefficient have been measured in a shear flow. It is shown that the shedding breaks down into a number of spanwise cells in each of which the frequency is constant. The division between the cells is thought to be marked by a longitudinal vortex in the stream direction and this is supported by evidence from experiments where a longitudinal vortex was generated in an otherwise uniform flow.