Irrotational flow of two-dimensional jets from a channel is treated without direct use of a logarithmic hodograph plane. An analytical approach is introduced for solving the general problem of two jets issuing from a channel with three end plates. Numerical values of the contraction coefficient and the angle of jet deflexion are obtained for the special case where the two jets are located symmetrically and all the end plates are in line. Limiting cases of the resulting single-jet problem are the symmetric and asymmetric configurations solved by von Mises. Results for the asymmetric case improve upon the theoretical values reported by von Mises, and compare favourably with existing experimental data.

The paper presents a new analytical and experimental study of transonic flow around spheres. The results of the analytical study, which employs the method of orthogonal collocation for simultaneous solution of the momentum equations, the equation of continuity and the energy equation, are compared with hitherto unpublished measurements obtained on spheres of various sizes (1·02, 2·54 and 3·81 cm in diameter) in air, in dry steam and in wet steam with free-stream Mach numbers in the transonic range (0·58 < M∞ < 0·97). The relationship θ h = 91·78 + 8·59 M∞ between the attached-shock angle and the free-stream Mach number was obtained by fitting the theoretical pressure distributions to the experimental ones.

When a contaminant molecule is released in a laminar flow in a straight tube its motion differs from that of the fluid particle with which it initially coincided because of its random motion, whose intensity is measured by the molecular diffusivity κ. For T = kt/a2 ≤ 0·25, where t is the time after release and a is a length characteristic of the cross-section, the statistics of its motion can be determined in the way described by Taylor (1953), Aris (1956) and Chatwin (1970). However, in many applications, including blood flow, the values of T which are attained are much smaller, and the purpose of this paper is to present first approximations for T [Gt ] 1 to some of the statistics measuring the deviations between the motion of the molecule and that of the fluid particle with which it initially coincided. To obtain these a technique due to Saffman (1960) is used for molecules released well away from the tube wall, and an extension of the same technique is used for molecules released near the tube wall. It is shown how the results can be used to describe the initial stages of dispersion of a cloud of contaminant molecules distributed arbitrarily over the cross-section in any laminar flow, steady or unsteady. Comparisons with some exact results for steady Poiseuille flow in a circular tube confirm that the approximations are formally correct, but show that in certain cases their practical use is limited to very small values of T, because of the high coefficients of the first two terms neglected in deriving the approximation.

In the mixing of a jet with a cross-stream, it is found that in the near field, defined as the region of the flow from the jet exit to a distance of a few diameters downstream of this exit, a considerable amount of dynamical adjustment takes place. This near-field region characterizes the subsequent behaviour and development of the jet, its wake and the cross-stream in the vicinity of this mixing region. The rapid evolution of the flow gives rise to a pair of bound vortices attached to the lee side of the jet boundary, to fast development of the turbulent and mean vorticity, to a vortex-shedding system, and to the largest rates of entrainment of cross-stream flow into the jet. Furthermore, it is found that the geometrical configuration of the boundaries at the jet exit plays an important role in the mixing and development processes.

An intrinsic method is proposed for the delineation of the flow boundaries between the jet and the cross-stream. Calculations of mass, momentum and vorticity fluxes have been made. The vorticity flux gives evidence of the rapid stretching and tilting of the vorticity vector field in the near-field region.

Mahony & Smith (1972) put forward a model to explain the phenomenon of energy transfer between nearly resonant oscillations at greatly differing frequencies. However, their model of ‘spatial resonance’ is restricted to situations where the geometry of the system is very simple. The present paper shows how to derive Mahony & Smith's equations in a general manner, and compares the theoretical predictions for a situation with circular symmetry with existing experimental results (Huntley 1972). In addition, it suggests a simple method for evaluating the resonance frequencies when a liquid-filled beaker is vibrated in one of its bell modes.

In this paper we intend to predict the magnitude of the contribution to the Reynolds stress of bursting events: ‘ejections’, ‘sweeps’, ‘inward interactions’ and ‘outward interactions’. We shall do this by making use of the conditional probability distribution of the Reynolds stress − uv, which can be derived by applying the cumulant-discard method to the Gram-Charlier probability distribution of the two variables u and v. The Reynolds-stress fluctuations in openchannel flows over smooth and rough beds are measured by dual-sensor hot-film anemometers, whose signals are conditionally sampled and sorted into the four quadrants of the u, v plane by using a high-speed digital data processing system.

We shall verify that even the third-order conditional probability distribution of the Reynolds stress shows fairly good agreement with the experimental results and that the sequence of events in the bursting process, i.e. ejections, sweeps and interactions, is directly related to the turbulent energy budget in the form of turbulent diffusion. Also, we shall show that the roughness effect is marked in the area from the wall to the middle of the equilibrium region, and that sweeps appear to be more important than ejections as the roughness increases and as the distance from the wall decreases.

A laser light-scattering technique has been used to study the relative particle concentration field in a round turbulent air jet. Measurements were made in the far field of a smoke-marked turbulent jet exhausting into a secondary air stream. Radial distributions of mean particle concentration, concentration fluctuation intensity and intermittency were measured at several streamwise locations. Concentration fluctuation power spectra and the micro- and integral scales of the concentration fluctuations were measured on the jet axis. The effects of ambiguity noise and noise due to optical path attenuation on the performance of the laser light-scattering system are discussed.

Johnson's (1973) description of a solitary wave in water of slowly varying depth is extended to a channel of slowly varying breadth and depth b and d on the assumption that the scale for the variation of b and d is large compared with d5/2a3/2. It is inferred from conservation of energy that the amplitude of the wave is proportional to $b^{-\frac{2}{3}}d^{-1}$ (cf. Green's law $a\propto b^{-\frac{1}{2}}d^{-\frac{1}{4}}$ for long waves of small amplitude). Comparison with experiment (Perroud 1957) yields fairly satisfactory agreement for a linearly converging channel of constant depth. The agreement for a linearly diverging channel is not satisfactory, but the experimental data are inadequate to support any firm conclusion.

Measurements of both the velocity and the temperature field have been made in the thermal layer that grows inside a turbulent boundary layer which is subjected to a small step change in surface heat flux. Upstream of the step, the wall heat flux is zero and the velocity boundary layer is nearly self-preserving. The thermal-layer measurements are discussed in the context of a self-preserving analysis for the temperature disturbance which grows underneath a thick external turbulent boundary layer. A logarithmic mean temperature profile is established downstream of the step but the budget for the mean-square temperature fluctuations shows that, in the inner region of the thermal layer, the production and dissipation of temperature fluctuations are not quite equal at the furthest downstream measurement station. The measurements for both the mean and the fluctuating temperature field indicate that the relaxation distance for the thermal layer is quite large, of the order of 1000θ0, where θ0 is the momentum thickness of the boundary layer at the step. Statistics of the thermal-layer interface and conditionally sampled measurements with respect to this interface are presented. Measurements of the temperature intermittency factor indicate that the interface is normally distributed with respect to its mean position. Near the step, the passive heat contaminant acts as an effective marker of the organized turbulence structure that has been observed in the wall region of a boundary layer. Accordingly, conditional averages of Reynolds stresses and heat fluxes measured in the heated part of the flow are considerably larger than the conventional averages when the temperature intermittency factor is small.

Large (gigajoule) amounts of energy can in principle be stored as kinetic energy in liquid metal circulating round a torus and can be extracted at the gigawatt level by Alfvén waves propagating along an imposed axial field. A major limitation on the energy that may be so stored is the disruption of these primary Alfvén waves by secondary flows in meridional planes, associated with out-of-balance centrifugal forces ahead of and behind the waves and non-uniform magnetic pressures at the wave fronts. Vorticity, created at the wave, itself propagates in secondary Alfvén waves.

This paper gives a linearized treatment of these secondary motions and the associated perturbations of the imposed axial field and compares the resulting disruption of the primary wave mode with crude estimates made in an earlier paper. The main case treated is the discharge of the stored energy into a matched resistor by an Alfvén step wave but the secondary consequences of standing primary waves are also explored. The nature of the solutions depends on the electromagnetic characteristics of the walls normal to the imposed field. The problem is mathematically interesting because it involves the joint solving of elliptic and hyperbolic equations that are coupled by the boundary conditions at these walls.