The rheology of particulate dispersions which are strongly influenced by particular types of non-hydrodynamic forces is analysed within the framework of suspension mechanics. Interactions between particles in a homogeneous shear flow without inertia are governed by viscous, electrostatic, London-van der Waals and Brownian forces. The balance among these provides the fluid with a microstructure described quantitatively at dilute concentrations by a pair distribution function and qualitatively by a characteristic interaction length. The bulk rheology follows from the microstructural variables through suitable averaging.

In dilute electrostatically stabilized suspensions of small rigid spheres for which London-van der Waals attractions and hydrodynamic interactions can be ignored, the theory predicts a Newtonian low-shear limit. The analytic expression for the viscosity contains a ϕ2-coefficient which can be quite large and agrees well with experimental data. At higher flow strengths a scale analysis of the pair conservation equation indicates a shear-and strain-thinning rheology, representing a breakdown of the fluid microstructure. Without flow the interaction length attains a maximum determined by the balance between Brownian motion and electrostatic repulsion. A weak shear merely perturbs this balance but generates stresses proportional to the fifth power of the length. With increasing shear rate this length and consequently the shear viscosity are reduced until viscous interactions completely dominate. Asymptotic solutions for an intermediate regime in which Brownian motion and hydrodynamic interactions are both negligible reveal power-law extensional and shear viscosities with non-zero normal stresses.

In the absence of molecular diffusion there exists a space-independent transformation which transforms the probability density of dynamically passive scalars undergoing chemical reaction and advection into the probability density of scalar fields undergoing advection alone. In two well-known limits the equation for the probability density of non-reacting scalars is linear and parabolic in physical space. In such cases it is shown that the equation for the probability density of reacting scalars is likewise linear and parabolic in physical space, although hyperbolic in concentration space. The general solution of such an equation is obtained and the particular case of a second-order, decaying, single-species reaction is displayed.

The axisymmetry of a body which is diffracting water waves may be exploited to give a line integral equation to be solved for the scattered wave field and forces on the body. Each term in a previously established surface integral equation is shown to be expressible as a Fourier series, which is then integrated once analytically. The resulting one-dimensional equation is shown to possess singularities, previously ignored by Black (1975). This equation, with series transformations and subtraction of singularities such that all series are quickly convergent and that it has to be solved only along a curve, reduces computational effort by some three orders of magnitude. Results obtained by this method give good agreement with previous analytical and experimental results, even if a rather coarse numerical approximation is used.

The methods described by Bluman & Cole (1974) are used to derive the infinitesimals of the general invariance group of the unsteady, two-dimensional, stream-function equation for the case where the kinematic viscosity v is equal to a constant and the case where v = 0. The infinitesimals in each case involve ten independent parameters, seven of which appear explicitly and three of which are contained implicitly in three arbitrary functions of time. The various finite groups and similarity transformations which may be derived from the infinitesimals are discussed through examples. Two of the arbitrary functions of time are non-trivial and represent invariance of the stream-function equation under a transformation to a co-ordinate system which moves in a non-uniform irrotational fashion. A general similarity form is derived for which the equations dx/dt = u(x, y, t) and dy/dt = v(x, y, t) for the particle paths may be reduced to an autonomous system. This form is general enough to suggest the hypothesis that, under certain restrictions, the entrainment processes of unsteady flows dominated by two-dimensional large-scale motions may be displayed diagrammatically on a phase-plane plot of particle trajectories.

This paper describes a detailed study of the structure of turbulence in boundary layers along mildly curved convex and concave surfaces. The surface curvature studied corresponds to δ/Rw = ± 0·01, δ being the boundary-layer thickness and Rw the radius of curvature of the wall, taken as positive for convex and negative for concave curvature. Measurements of turbulent energy balance, autocorrelations, auto- and cross-power spectra, amplitude probability distributions and conditional correlations are reported. It is observed that even mild curvature has very strong effects on the various aspects of the turbulent structure. For example, convex curvature suppresses the diffusion of turbulent energy away from the wall, reduces drastically the integral time scales and shifts the spectral distributions of turbulent energy and Reynolds shear stress towards high wavenumbers. Exactly opposite effects, though generally of a smaller magnitude, are produced by concave wall curvature. It is also found that curvature of either sign affects the v fluctuations more strongly than the u fluctuations and that curvature effects are more significant in the outer region of the boundary layer than in the region close to the wall. The data on the conditional correlations are used to study, in detail, the mechanism of turbulent transport in curved boundary layers.

The three-dimensional incompressible magnetohydrodynamic (MHD) equations for rectangular geometry and periodic boundary conditions are solved numerically using the spectral method of Orszag & Patterson (1972). The calculations are restricted to a magnetic Prandtl number of one and to Gaussian random initial conditions with zero mean magnetic and momentum fields. We permit non-mirror-symmetric (helical) flows. In all cases, there is a continuous transfer of energy from the momentum field to the magnetic field. A proposed mechanism for this transfer involves the cascading of energy from the large scales of the momentum field to the small scales, thence a redistribution of energy between the momentum and magnetic fields by Alfvén waves, and, finally, an inverse cascade of energy from the small scales of the magnetic field to the large scales. This inverse cascade is found when magnetic helicity (〈a. b〉, where b = curl a is the magnetic induction) is present in the flow.

The problem of decaying isotropic turbulence has been studied using a Wiener-Hermite expansion with a renormalized time-dependent base. The theory is largely deductive and uses no modelling approximations. It has been found that many properties of large Reynolds number turbulence can be calculated (at least for moderate time) using the moving-base expansion alone. Such properties found are the spectrum shape in the dissipation range, the Kolmogorov constant, and the energy cascade in the inertial subrange. Furthermore, by using a renormalization scheme, it is possible to extend the calculation to larger times and to initial conditions significantly different from the equilibrium form. If the initial spectrum is the Kolmogorov spectrum perturbed with a spike or dip in the inertial subrange, the process proceeds to eliminate the perturbation and relax to the preferred spectrum shape. The turbulence decays with the proper dissipation rate and several other properties are found to agree with measured data. The theory is also used to calculate the energy transfer and the flatness factor of turbulence.

It is shown that the approximation of a thin thermal boundary layer gives an accurate description of the growth of spherical vapour bubbles in a superheated liquid except for very small superheats. If the further approximations of a linear variation of vapour pressure with temperature and of constant physical properties are made, then scaled variables can be introduced which describe the growth under any conditions. This scaled description is not valid during the early, surface-tension dominated, portion of the growth. The rate of bubble growth for large superheats is somewhat overestimated in the intermediate stage in which both inertial and thermal effects play a role. This overestimate does not lead to a serious error in the radius-time behaviour for ranges of practical interest. The asymptotic, or thermally controlled, stage of growth is accurately described by the scaled formulation.

Measurements of the velocity characteristics of near-wake flows were obtained with a direction-sensitive laser-Doppler anemometer. The wakes were formed downstream of central disks of diameters 8·9, 12·5 and 14·2 mm which were located on the centreline of a 20·0 mm jet. Detailed measurements were obtained with initial annular-jet velocities of from 9·4 to 39·5 m/s and include values of the axial and radial components of the mean velocity, the three normal stresses and the shear stress. Probability density distributions and energy spectra were also measured.

The results show, for example, that the curvature of the annular jet increases with disk diameter and that the ratios of the maximum positive and negative centre-line velocities to the exit velocity increase with decreasing disk diameter and are essentially independent of the initial velocity. The turbulent field is substantially anisotropic with a minimum turbulence intensity of around 30% in the recirculation region; the locations of zero shear stress and zero mean velocity gradient are not coincident. The measured spectra reveal predominant frequencies in a small region of the outer-shear layer and in the vicinity of the jet exit; these discrete frequencies did not propagate downstream nor into the recirculation region.

A study is made of the steady radial-axial flow generated in a non-Newtonian fluid confined between two infinite parallel planes by torsional oscillations of one of the planes. Canonical equations of motion appropriate for the small amplitude motion of a simple fluid are used. It is shown that under certain circumstances the direction of the radial-axial flow is opposite to that in a Newtonian fluid.