When homogeneous turbulence acts upon a non-uniform magnetic field B0(x, t), a mean electromotive force [Escr ](x, t) is in general established owing to the correlation between the velocity field and the fluctuating magnetic field that is generated. The relation between [Escr ] and B0 is linear, and it is generally believed that, when the scale of inhomogeneity of B0 is sufficiently large, it can be expressed as a series involving successively higher spatial derivatives of B0: \[ {\cal E}_i = \alpha_{il} B_{0l}+\beta_{ilm}\partial B_{0l}/\partial x_m+\ldots, \] where the tensors αil, βilm,… are determined (in principle) by the statistical properties of the turbulence and the magnetic diffusivity Λ of the fluid. These tensors are of crucial importance in turbulent dynamo theory. In this paper the question of their asymptotic form in the limit Λ → 0 is considered. By putting Λ = 0 and assuming that the field is non-random at an initial instant t = 0, the developing form of the tensors αl(t) and βm(t) is determined. The expressions involve time integrals of Lagrangian correlation functions associated with the velocity field, which are comparable in structure with the eddy diffusion tensor in the analogous turbulent diffusion problem (Taylor 1921). Some doubts are expressed concerning the convergence of the time integrals as t → ∞, and it is concluded that a satisfactory treatment of the problem will require the inclusion of weak diffusion effects (as recognized by Parker 1955).

This paper deals with the motion of a heavy particle in a turbulent flow in an open channel with a smooth bottom. For the case when the particle stays in suspension in the main body of the flow almost all the time, (a) the probability density function of the projection on a cross-sectional plane of the particle position at any instant, and (b) the mean velocity and longitudinal dispersion coefficient of particles are determined analytically by employing the Eulerian formulation and applying the Aris moment transformations. It is found that the mean particle velocity decreases and the longitudinal dispersion coefficient of particles increases with the fall velocity.

In two earlier papers (Gallagher & Mercer 1962, 1964) the results for the first four eigenvalues of the problem of the stability of plane Couette flow were given. The first twelve eigenvalues have been calculated by the same method and the results show that the manner in which the eigenvalues join to form complex pairs depends on α, the wavenumber of the disturbance. They also would appear to indicate that mode-crossing always occurs.

Attention is drawn to a principal difference between the transfer of a horizontal magnetic field by turbulence and by three-dimensional cell convection.

If the motion of the conducting medium in the cells is such that the heated material ascends at the centre while descending along the sides of the cells, then the magnetic tubes of force will be carried downwards by peripheral flows. Discrete ascending flows separated from one another by descending material carry only closed magnetic field loops. Such loops do not transfer net magnetic flux. As a result, the magnetic flux becomes blocked at the base of the convective layer.

The structure of density interfaces upon which turbulent motions have been imposed is investigated in the laboratory. Particular attention is paid to the profiles of density across such interfaces, and the temporal response of the interface to the imposed turbulence. Interfaces over a range of Péclet numbers and Richardson numbers are examined. It is found that the interface thickness h/l (non-dimensionalized with respect to the length scale l of the turbulence) is a function of the Péclet number but independent of the Richardson number. At low Péclet numbers (Pe [lsim ] 200) molecular diffusion is important in the determination of the interface structure and a diffusive core (across which all transport occurs by molecular diffusion) is formed in the centre of the interface. At higher Péclet numbers the interface structure appears to be determined by non-diffusive processes and h/l becomes approximately constant at a value of about 1·5. Some information concerning the intermittent nature of the mixing process at high Péclet number is obtained from records of salinity fluctuations measured at a fixed point. Finally, the implications of these data concerning the interpretations of the measurements of entrainment across an interface made by Turner (1968) are discussed.

We use some well-known properties of the Taylor-Goldstein equation to generate a set of stably stratified shear flows with known singular neutral-mode solutions. The novel feature of the analysis is that it includes such solutions for flows in which, proceeding upwards from a rigid boundary, the Brunt-Väisälä frequency and the flow shear do not change sign and are monotonically decreasing functions of height. Such profiles are much closer to the conditions met in work on the atmospheric boundary layer than the more frequently used inflected flow profiles.

A fluid-fluid interface that joins a solid surface forms a common line. If the common line moves along the solid, a mutual displacement process is involved and is studied here. Some simple experiments motivate the formulation of the basic assumption of the analysis. The basic assumption is a formalization of the idea that the fluid-fluid interface rolls on or unrolls off the solid. This forms an axiom for the mostly kinematical analysis that follows. The predictions are tested through a series of qualitative experiments. The role of the no-slip boundary condition at the solid surface is discussed.

Velocity measurements were made in the flow field behind a circular cylinder at Reynolds numbers from 10 to 80 and results compared with existing numerical solutions. Takami & Keller's solution for the velocity distribution in the wake shows good agreement at low Reynolds numbers and fair agreement at high Reynolds numbers. The drag coefficient of the cylinder and the size of the standing eddies behind the cylinder were also determined. They are compatible with existing experimental and numerical results. Details of the velocity distribution in the standing eddies are clarified.

The effect of surface roughness on the flow past spheres has been investigated over the Reynolds number range 5 × 104 < Re < 6 × 106. The drag coefficient has been determined as a function of the Reynolds number for five surface roughnesses. With increasing roughness parameter the critical Reynolds number decreases. At the same time the transcritical drag coefficient rises, having a maximum value of 0·4.

The vortex shedding frequency has been measured under subcritical flow conditions. It was found that the Strouhal number for each of the various roughness conditions was equal to its value for a smooth sphere. Beyond the critical Reynolds number no prevailing shedding frequency could be detected by the measurement techniques employed.

The drag coefficient of a sphere under the blockage conditions 0·5 < ds/dt < 0·92 has been determined over the Reynolds number range 3 × 104 < Re < 2 × 106. Increasing blockage causes an increase in both the drag coefficient and the critical Reynolds number. The characteristic quantities were referred to the flow conditions in the smallest cross-section between sphere and tube. In addition the effect of the turbulence level on the flow past a sphere under various blockage conditions was studied.

The nonlinear Boltzmann equation has been solved for shock waves in a Max-wellian gas for eight upstream Mach numbers M1 ranging from 1·1 to 10. The numerical solutions were obtained by using Nordsieck's method, which was revised for use with the differential cross-section corresponding to an intermolecular force potential following an inverse fifth-power law. The accuracy of the calculations of microscopic and macroscopic properties for this collision law is comparable with that for elastic spheres published earlier (Hicks, Yen & Reilly 1972).

We have made comparisons of the detailed characteristics of the internal shock structure in a Maxwellian gas with those in a gas of elastic spheres. The purpose of this comparative study is to find the shock properties that are sensitive as well as those which are insensitive to the change in collision law and to find effective ways to study them.

The variation of thermodynamic and transport properties of interest with respect to density and to each other was found to depend only weakly on the change in collision law. The principal effect on the macroscopic shock structure due to the change in intermolecular potential is in the spatial variation of the macroscopic properties. The spatial variation of macroscopic properties may be determined accurately from the corresponding moments of the collision integral, especially in the upstream and downstream wings of the shock wave. The results for the velocity distribution function exhibit the microscopic shock characteristics influenced by a difference in intermolecular collisions, in particular the departure from equilibrium in the upstream wing of the shock and the relaxation towards equilibrium in the downstream wing. The departure of several characteristics of weak shock waves from those of the Chapman-Enskog linearized theory and the Navier-Stokes shock is also insensitive to the change in collision law. The deviation of the half-width of the function ∫fdvyduz from the Chapman-Enskog first iterate at M1 = 1·59 is in agreement with an experiment (Muntz & Harnett 1969).

The Markovian random coupling (MRC) model is a modified form of the stochastic model of the Navier-Stokes equations introduced by Kraichnan (1958, 1961). Instead of constant random coupling coefficients, white-noise time dependence is assumed for the MRC model. Like the Kraichnan model, the MRC model preserves many structural properties of the original Navier-Stokes equations and should be useful for investigating qualitative features of turbulent flows, in particular in the limit of vanishing viscosity. The closure problem is solved exactly for the MRC model by a technique which, contrary to the original Kraichnan derivation, is not based on diagrammatic expansions. A closed equation is obtained for the functional probability distribution of the velocity field which is a special case of Edwards’ (1964) Fokker-Planck equation; this equation is an exact consequence of the stochastic model whereas Edwards’ equation constitutes only the first step in a formal expansion based directly on the Navier-Stokes equations. From the functional equation an exact master equation is derived for simultaneous second-order moments which happens to be essentially a Markovianized version of the single-time quasi-normal approximation characterized by a constant triad-interaction time.

The explicit form of the MRC master equation is given for the Burgers equation and for two- and three-dimensional homogeneous isotropic turbulence.

The mixing layer bounding the exhaust plume associated with hypersonic highaltitude rockets is analysed as a laminar binary mixture of perfect gases with Lewis and Prandtl numbers of unity. A far-field approximation to the undisturbed jet core and a Newtonian pressure balance between the jet and ambient gases are used to construct the mixing-layer location. Longitudinal pressure variations are neglected and resultant errors are evaluated. Boundary conditions at the edge of the mixing layer are evaluated by streamline tracing to shock entry points. The sensitivity of properties in the mixing layer to variations in the plume angle of attack, engine nozzle efficiency and engine thrust are examined, and an approximate density and thrust scaling of mixing-layer overall properties is developed.

The results of an experimental investigation of the mean- and fluctuating-flow properties of a compressible turbulent boundary layer in a shock-wave-induced adverse pressure gradient are presented. The turbulent boundary layer developed on the wall of an axially symmetric nozzle and test section whose nominal free-stream Mach number and boundary-layer-thickness Reynolds number were 4 and 105, respectively. The adverse pressure gradient was induced by an externally generated, conical shock wave.

Mean and time-averaged fluctuating-flow data, including the experimental Reynolds shear stresses and experimental turbulent heat-transfer rates, are presented for the boundary layer and external flow, upstream, within and downstream of the pressure gradient. The turbulent mixing properties of the flow were determined experimentally with a hot-wire anemometer. The calibration of the wires and the interpretation of the data are discussed.

From the results of the investigation, it is concluded that the shock-wave/boundary-layer interaction significantly alters the shear-stress characteristics of the boundary layer.

We discuss the creation of a finite-element program suitable for solving incompressible, viscous free-surface problems in steady axisymmetric or plane flows. For convenience in extending program capability to non-Newtonian flow, non-zero Reynolds numbers, and transient flow, a Galerkin formulation of the governing equations is chosen, rather than an extremum principle. The resulting program is used to solve the Newtonian die-swell problem for creeping jets free of surface tension constraints. We conclude that a Newtonian jet expands about 13%, in substantial agreement with experiments made with both small finite Reynolds numbers and small ratios of surface tension to viscous forces. The solutions to the related ‘stick-slip’ problem and the tube inlet problem, both of which also contain stress singularities, are also given.