Laminar throughflow between finite parallel disks, one stationary and the other rotating, can be characterized by four dimensionless parameters in the general case. But, if the ratio of disk spacing to disk radius is small, an approximate definition of the flow may be made with reference to a single parameter, the Ekman number. The equations of motion and the equation of continuity in this ‘thin-film’ approximation are reduced here to an initial-value problem for nonlinear ordinary differential equations, by a Galerkin-type procedure. Hamming's modified predictor-corrector method is employed subsequently to solve for the stream functions. Radial pressure profiles of this solution are compared with published experimental data. The calculated results may be applied to the design of hydrostatic bearings and face seals.

This paper presents the results of experiments on plane shock waves refracting at air/SF6 and He/CO2 interfaces. These are called fast-slow gas combinations because the speed of sound in the incident shock gas is greater than that in the transmitting shock gas. Our work was based on a generalization of the von Neumann (1943) classification of shocks into two classes called weak and strong. We introduced two subclasses of each of these, giving in all four groups of phenomena for study. This is possibly an exhaustive list, at least for conditions where the gases are approximately perfect. We present data on all four groups and study various transition conditions both within and across the groups. Our results appear to conflict with a previously reported irregular refraction; in fact we could apparently completely suppress this wave system by attention to our gas purity and boundary conditions. In its place we found a different system which appears to be a new phenomenon. We found another new system which has the appearance of a Mach-reflexion type of refraction but with its shock dispersed into a band of wavelets. It is interesting that the wavelets remain intense enough to induce identifiable vortex sheets in the flow. Finally we found yet another refraction of the Mach-reflexion type which had no detectable vortex sheet emanating from the triple point: such a system was foreshadowed by von Neumann.

In the first part of this paper the nonlinear development of the most unstable mode is numerically studied for a bounded shear layer with a hyperbolic-tangent profile. It is found that the vortex nutation, discovered by Zabusky & Deem (1971) for a jet profile, is a manifestation of strongly coupled oscillations in the vortex amplitude and the phase. In the second part, with the aid of the numerical result we devote ourselves to deriving coupled nonlinear equations that describe the amplitude oscillation, the vortex nutation and the momentum transport. The approximate oscillatory solution for the vortex amplitude and phase in the nonlinear stage is compared with the numerical solution and agreement is found.

The problem of heat transfer (or mass transfer at low transfer rates) to a strip of finite length in a uniform shear flow is considered. For small values of the Péclet number (based on wall shear rate and strip length), diffusion in the flow direction cannot be neglected as in the classical Leveque solution. The mathematical problem is solved by the method of matched asymptotic expansions and expressions for the local and overall dimensionless heat-transfer rate from the strip are found. Experimental data on wall mass-transfer rates in a tube at small Péclet numbers have been obtained by the well-known limiting-current method using potassium ferrocyanide and potassium ferricyanide in sodium hydroxide solution. The Schmidt number is large, so that a uniform shear flow can be assumed near the wall. Experimental results are compared with our theoretical predictions and the work of others, and the agreement is found to be excellent.

The existence of universal similarity of the fine-scale structure of turbulent velocity fields and the validity of the original Kolmogorov local similarity theory and the later reformulations were investigated. Recent studies of the fine-scale velocity field for many different flows, e.g. grid flows, wakes, jets and the atmospheric boundary layer, are shown to provide considerable evidence for the existence of Kolmogorov normalized spectral shapes which are universal in the sense that they describe the high wave-number spectral behaviour of all turbulent flow fields with a similar value of the turbulence Reynolds number Rλ. The normalized spectral shapes vary with Rλ in a manner consistent with the later reformulations. The Reynolds number dependence of the normalized spectra is demonstrated for the Rλ range from about 40 to 13 000. Expressions for the Kolmogorov normalized spectral functions are presented for three values of Rλ. Also revealed in this study is the importance of considering effects on spectra caused by deviations from Taylor's approximation in high intensity turbulent flows. Lumley's (1965) model is used to correct the high frequency portion of the measured one-dimensional spectra for these effects. An analytical solution to Lumley's expression is presented and applied to the data.

A photographic technique has been used to make observations of the motion of heavy suspended particles in an open channel with a smooth bottom. The observations showed that the path of an individual heavy particle consists of an alternation between upward and downward paths traced by the particle as it travels close to the bottom. The path records appear to reveal most of the flow patterns near the wall shown up by earlier visualization observations; the measured kinematical quantities concerning the particle motion are in accord with those of earlier observations (e.g. Nychas, Hershey & Brodkey 1973). Making use of the present observations and following Offen & Kline's (1975) model of the bursting process in turbulent boundary layers, an attempt was made to explain the mechanism of particle suspension close to the wall in turbulent flows.

Dean's series for steady fully developed laminar flow through a toroidal pipe of small curvature ratio has been extended by computer to 24 terms. Analysis suggests that convergence is limited by a square-root singularity on the negative axis of the square of the Dean number. An Euler transformation and extraction of the leading and secondary singularities at infinity render the series accurate for all Dean numbers. For curvature ratios no greater than $\frac{1}{250} $, experimental measurements of the laminar friction factor agree with the theory over a wide range of Dean numbers. In particular, they confirm our conclusion that the friction in a loosely coiled pipe grows asymptotically as the one-quarter power of the Dean number based on mean flow speed. This contradicts a number of incomplete boundary-layer analyses in the literature, which predict a square-root variation.

Heat-transfer measurements have been carried out in a right circular cylinder of fluid which is heated from above and rotated steadily about its vertical axis. Convection is produced relative to solid-body rotation through the coupling of the centrifugal acceleration and density variations in the fluid. Two silicone oils having kinematic viscosities of 350 cS and 0·65 cS were used in the experiments. In the former case viscous forces are important throughout the cylinder whereas in the latter case Ekman layers form and the Coriolis acceleration controls the interior flow.

With the 350 cS oil the Nusselt number for heat transfer from the top to the bottom of the cylinder is a function of Grω and r0, where Grω is a Grashof number defined by employing the centrifugal acceleration evaluated at the outer edge of the cylinder in place of the gravitational acceleration, and r0 is the cylinder aspect ratio.

The behaviour is quite different for the 0·65 cS oil. Ekman layers form on the horizontal surfaces and heat is convected by Ekman suction. The Nusselt number is given by \[ Nu = 4.16\beta^{0.822}\epsilon^{-0.499}r_0^{0.173},\quad Ac\leqslant 0.025,\quad\sigma\beta\epsilon^{-\frac{1}{2}} > 0.7, \] where β is the thermal Rossby number, ε is the Ekman number, σ is the Prandtl number, and Ac is the ratio of gravitational to centrifugal accelerations. This is consistent with previous theories which indicate that the system should depend on the parameters σβε−½ and r0 in the limit as ε and β approach zero.

Symmetrical flow past a double wedge is studied for a high subsonic Mach number. The main features of the flow field are discussed in the physical and the hodograph plane. It is shown how a regular solution to the hodograph equation exhibits limit lines in the physical plane, which are eliminated through a ‘cut’ corresponding to the shock wave. In the case of the wedge it is assumed that the shock which is likely to be the most stable is the weakest possible.

The boundary-value problem is solved in the hodograph plane using Telenin's method, which has proved to be successful when dealing with equations of mixed type. The bounded analytic solution which is thus constructed is regular in the hodograph plane but presents three folds in the physical plane.

The computation is carried out for flow past a 4·5° half-angle wedge at a Mach number M∞ = 0·89. These figures are chosen so that the problem may be justifiably treated by potential theory, the entropy gradient behind the shock being negligible. In this case the mapping of the solution into the physical plane gives the pressure distribution along the double wedge, the sonic line and the shock wave. Of particular interest is the point where the sonic line meets the shock. This configuration is in agreement with the hypothesis of Nocilla, according to which the shock terminates in the supersonic domain. Experimental evidence cannot be obtained, however, because of the lack of resolution in this region.

In flows around three-dimensional surface obstacles in laminar or turbulent streamsthere are a number of points where the shear stress or where two or more component,s of the mean velocity are zero. In the first part of this paper we summarize and extend the kinematical theory for the flow near these points, particularly by emphasizing the topological classification of these points as nodes or saddles. We show that the zero-shear-stress points on the surface and on the obstacle must be such that the sum of the nodes ΣN and the sum of the saddles Σs satisfy \[ \Sigma_N -\Sigma_S = 0. \] If the obstacle has a hole through it, such as a passageway under a building, \[ \Sigma_N -\Sigma_S =-2. \] If the surface is a junction between two pipes, \[ \Sigma_N -\Sigma_S =-1. \] We also consider, in two-dimensional plane sections of the flow, the points where the components of the mean velocity parallel to the planes are zero, both in the flow and near surfaces cutting the sections. The latter points are half-nodes N′ or half-saddles S′. We find that \[ (\Sigma_N +{\textstyle\frac{1}{2}}\Sigma_{N^{\prime}}-(\Sigma_{S^{\prime}}+{\textstyle\frac{1}{2}}\Sigma_{S^{\prime}}) = 1-n, \] where n is the connectivity of the section of the flow considered.

In the second part new flow-visualization studies of laminar and turbulent flows around cuboids and axisymmetric humps (i.e. model hills) are reported. A new method of obtaining a high resolution of the surface shear-stress lines was used. These studies show how enumerating the nodes and saddle points acts as a check on the inferred flow pattern.

Two specific conclusions drawn from these studies are that:

1. for all the flows we observed, there are no closed surfaces of mean streamlines around the separated flows behind three-dimensional surface obstacles, which con-tradicts most of the previous suggestions for such flows (e.g. Halitsky 1968);

2. the separation streamline on the centre-line of a three-dimensional bluff obstacle does not, in general, reattach to the surface.

The equation usually used to describe the conservation of volume flux in free turbulence (such as mixing layers, jets, etc.) is discussed.