Laterally converging flow occurs between two parallel surfaces with an exit hole formed in one. The present study examines the flow at a distance from the exit as a means of investigating an accelerating radial internal flow induced by the lateral convergence and satisfying the boundary-layer approximations. The measurements range from laminar to turbulent conditions, including the intermediate stage referred to by some investigators as laminarizing or laminarescent. The acceleration parameter Kv = (ν/V2)dV/dr ranges from 2·6 × 10−8 to 2·2 × 10×4 and the local Reynolds number varies from 210 to 6·8 × 104 for the data reported; the relation between the Reynolds number and the acceleration parameter was varied by adjusting the convergence angle or the plate spacing. For the main experiment the accelerating region is 86 plate spacings in length. Comparison with numerical predictions for laminar and turbulent flow leads to identification of flow regimes in terms of popular acceleration parameters Kv, Kp = (ν/ρ u3*) dp/dr and Kτ = (ν/ρu3*) (∂τ/∂z)w. Results demonstrate that a potentially turbulent entry flow subjected to accleration due to lateral convergence shows features common to laminarization in accelerating turbulent boundary layers in other geometries. Application of the function A+(Kp) for a modified van Driest wall-region model is examined briefly for the intermediate regime.

Instantaneous measurements of the wall shear stress were made in the laterally converging duct also used for mean measurements in part 1 and were analysed by conditional sampling and by conditional averaging. The sidewalls of the duct were adjusted to provide (i) a straight duct of constant rectangular cross-section and (ii) laterally (spanwise) converging ducts resulting in streamwise acceleration of the flow. The Reynolds number varied from 7600 to 47 200 and the dimensionless acceleration parameter Kv = (ν/V2)dV/dx ranged from 0 to 3·4 × 10−6, yielding a variation of the flow regime from fully turbulent to nearly laminar. The typical burst pattern, or conditionally averaged time history of the wall shear stress, resembled the time history of the streamwise velocity component deduced at y+ = 15 by Blackwelder and Kaplan using the same general technique. For fully developed flows, inner or wall scaling of the bursting frequency was found to be less dependent upon Reynolds number than outer scaling; other characteristics examined varied with both inner and outer scaling. For converging flows measurements of bursting characteristics essentially confirmed the indicated flow regimes deduced in part 1 and showed that the measured characteristic that was most affected by acceleration was the bursting frequency. All characteristics varied with acceleration, but the variation was generally less when normalized by wall variables rather than when normalized by outer variables.

A simplified model is developed for the dynamics of pressure fields supported by deflagrations in open axisymmetric configurations. The model employs overall conservation of mass, laws of flame propagation, overall conservation of momentum and a statement of conservation of mass and momentum across a shock that precedes the flame. The model represents an improvement over an earlier model in a number of respects, notably in allowing pressures at the flame and at the shock to differ. Explicit results for time histories are obtained by an expansion method for small values of the Mach number of flame propagation. The model may be employed to estimate overpressures that may develop subsequent to ignition of flat vapour clouds.

The drag force acting on a circular cylinder fluctuating erratically in a viscous fluid is measured with a laser–cantilever force transducer. The experimental results compare very well with the theory.

Experiments were performed on concentrated suspensions of large (0·97–1·78 mm mean diameters) neutrally buoyant spherical particles sheared in a concentric-cylinder Couette-flow apparatus in which the inner cylinder rotated while the outer one was fixed. The variations of shear stress with apparent shear rate, concentration, particle diameter and wall roughness were studied, and the results are compared with related experiments of Bagnold. Generally the shear stresses measured in the present experiments were larger than those of Bagnold. The difference can be attributed to differences in the experimental arrangements; Bagnold's flexible-walled inner cylinder was fixed while the outer cylinder rotated. A strong effect of wall roughness was observed. The higher stresses generated with rough walls imply that particle ‘slip’ may have occurred in the smooth wall tests. The larger stresses might also be due to an increase in strength of the interparticle collisions caused by the roughness. No dependence of stress upon particle diameter d was observed for concentrations of about 0·3, but a strong dependence (> d2) was found at the highest concentrations with the rough walls.

Laser-Doppler measurements of velocity distribution and reattachment length are reported downstream of a single backward-facing step mounted in a two-dimensional channel. Results are presented for laminar, transitional and turbulent flow of air in a Reynolds-number range of 70 < Re < 8000. The experimental results show that the various flow regimes are characterized by typical variations of the separation length with Reynolds number. The reported laser-Doppler measurements do not only yield the expected primary zone of recirculating flow attached to the backward-facing step but also show additional regions of flow separation downstream of the step and on both sides of the channel test section. These additional separation regions have not been previously reported in the literature.

Although the high aspect ratio of the test section (1:36) ensured that the oncoming flow was fully developed and two-dimensional, the experiments showed that the flow downstream of the step only remained two-dimensional at low and high Reynolds numbers.

The present study also included numerical predictions of backward-facing step flow. The two-dimensional steady differential equations for conservation of mass and momentum were solved. Results are reported and are compared with experiments for those Reynolds numbers for which the flow maintained its two-dimensionality in the experiments. Under these circumstances, good agreement between experimental and numerical results is obtained.

Unsteady three-dimensional incompressible viscous flow fields induced by initial vorticity distributions are studied. Relevant invariants and decay laws of the moments of vorticity distributions are presented and shown to be useful in the numerical calculation of flow fields in two ways. First, the moments determine the leading terms of the far-field velocity, which can be employed as boundary conditions for the numerical calculation. Secondly, the deviations of the numerical results from the invariants and the decay laws can be used to measure the error of the numerical solution.

In this paper we derive solutions for two stagnation flows of an incompressible Newtonian fluid with infinite Prandtl number and exponentially temperature-dependent viscosity. The two stagnation flows are the impingement of a hot fluid against a cold wall and against a cold half-space of the same material. We find that the same solutions apply to both axisymmetric and two-dimensional flows. We apply these solutions to the thinning of the Earth's lithosphere by a mantle plume. The equilibrium lithospheric thickness and the rate of lithospheric thinning are obtained.

Moderate-amplitude axisymmetric oscillations of incompressible inviscid drops and bubbles are studied using a Poincaré–Lindstedt expansion technique. The corrections to the drop shape and velocity potential caused by mode coupling at second order in amplitude are predicted for two-, three- and four-lobed motions. The frequency of oscillation is found to decrease with the square of the amplitude; this result compares well with experiments and numerical calculations for drops undergoing two-lobed oscillations.

The theory of shock dynamics in two dimensions is reformulated to treat shock propagation in a non-uniform medium. The analysis yields a system of hyperbolic equations with source terms representing the generation of disturbances on the shock wave as it propagates into the fluid non-uniformities. The theory is applied to problems involving the refraction of a plane shock wave at a free plane gaseous interface. The ‘slow–fast’ interface is investigated in detail, while the ‘fast–slow’ interface is treated only briefly. Intrinsic to the theory is a relationship analogous to Snell's law of refraction at an interface. The theory predicts both regular and irregular (Mach) refraction, and a criterion is developed for the transition from one to the other. Quantitative results for several different shock strengths, angles of incidence and sound-speed ratios are presented. An analogy between shock refraction and the motion of a force field in unsteady one-dimensional gasdynamics is pointed out. Also discussed is the limiting case for a shock front to be continuous at the interface. Comparison of results is made with existing experimental data, with transition calculations based on three-shock theory, and with the simple case of normal interaction.