A modification is made to the traditional Lagrangian approach to the derivation of the mean EMF of turbulent fluids which allows for finite conductivities. Consideration is confined to the case of homogeneous, isotropic but generally mirrornon-invariant and compressible turbulence. The eddy magnetic diffusivity and the coefficient α of the alpha-effect are expressed in terms of statistical moments of displacements of adjacent particles which undergo convective transport and microscopic diffusion in a turbulent flow. These expressions, being valid for arbitrary conductivities, reproduce known results in the cases of both very large and very small magnetic Reynolds numbers. Difficulties and advantages of the use of the results obtained for evaluations of the mean EMF are discussed.

Premixed turbulent flame propagation is analysed under the assumptions of stationarity and transverse homogeneity by expansions for small values of the ratio of the turbulence intensity to the laminar burning velocity. For large Zel'dovich numbers, the effects of diffusive—thermal phenomena within the flame, gas expansion, buoyancy and Lewis and Prandtl numbers different from unity are taken into account under the constraint that turbulence scales are large compared with the laminar flame thickness. A general formulation is given, involving solutions through Fourier decompositions. Parametric results for turbulent burning velocities are obtained, and the evolution of components of turbulent kinetic energies through the flame is calculated. It is shown how buoyancy counteracts the tendency for gas expansion to increase transverse components of the turbulent kinetic energy, pressure fluctuations and vorticity generation across the wrinkled flame. Strong readjustments in components of the turbulent kinetic energy are shown to occur in the downstream hydrodynamic zone. It is established that, with the effects of the hydrodynamic zones fully taken into account, the flame can induce anisotropy in initially isotropic turbulence such that the final velocity fluctuations exhibit higher intensities in the longitudinal mode than in transverse modes, while the enhanced vorticity fluctuations are entirely transverse.

General solutions for the linearized three-dimensional unsteady motion of a relaxing gas, including the effects of direct heat addition, are obtained using a Green's function technique. The possibility of direct heat addition into each separate mode of energy storage must be catered for, and the solutions have some bearing on the question of the heating of a gas by radiation.

Examples are given of initial-value and heat-source solutions in an unbounded domain and the boundary-value problem is exemplified by a study of the motion created by a spherical piston.

The phenomenon of steady cellular convection in a rotating fluid in which the stratification is statically unstable is well known. If the temperature field also varies in the horizontal direction a thermal wind is generated which can diminish the amplitude of the cells, or if inertial effects are strong enough, confine them to a narrow vertical band. On the other hand, in an enclosed container resonance can occur which increases the amplitude of the cells beyond the scope of a linear theory.

Effects of product dissociation and preferential diffusion on the structure, propagation and diffusional-thermal instability of the classical one-dimensional laminar flame have been studied by using activation energy asymptotics. Analytical expressions as functions of dissociation and diffusion parameters have been obtained for such bulk flame parameters as the flame temprature reduction and the propagation rate eigenvalue, and for the dispersion relation governing flame stability. Results on flame propagation show that while under most situations the flame speed is reduced due to product dissociation, it can attain values in excess of the non-dissociative limit for highly mobile product species which can preferentially back diffuse to the upstream portion of the reaction zone where they recombine and release the associated recombination heat. Results on flame stability show that it is promoted in the presence of product dissociation which has a moderating influence on the flame temperature fluctuations, and for highly-mobile product species because of the enhanced burning rate and curvature-induced concentration modification.

The effects of a reduction in momentum flux on the downstream flow characteristics of a steady, two-dimensional flow are investigated. In particular, quantities such as the changes in mean depth, mean fluid velocity, mean kinetic and potential energies and the length of the induced downstream wave are examined. This is done with the use of a fourth-order perturbation expansion in wave slope. The results are compared with the conflicting results that had been obtained previously by different authors. Agreement is found with the second-order theory of Benjamin (1970), but the work of Doctors & Dagan (1980) is found to be in error and is corrected.

The effect of small-amplitude, time-periodic, free-stream disturbances on an otherwise steady axisymmetric boundary layer on a circular cylinder is considered. Numerical solutions to the problem are presented, and an asymptotic solution to the flow, valid far downstream along the axis of the cylinder is detailed. Particular emphasis is placed on the unsteady eigensolutions that occur far downstream, which turn out to be very different from the analogous planar eigensolutions. These axisymmetric eigensolutions are computed numerically and also are described by asymptotic analyses valid for low and high frequencies of oscillation.

Steady flows of an incompressible, inviscid, and non-diffusive fluid of variable density in a gravitational field are first considered. By a transformation it is shown conclusively that there are infinitely many flows with the same flow pattern, provided the density gradients of these flows at any section (e.g. far upstream) differ only by a multiplicative constant. These flows have identical local internal Froude numbers at all corresponding points of the flows and, hence, identical local Richardson numbers. They are therefore dynamically similar. Every time a solution for one stratification is obtained, one has in fact obtained the solutions for infinitely many stratifications.

The creation of vorticity in steady stratified flows is then examined, and it is shown that this creation can be divided into two parts, one part being entirely due to the inertial effect and the other originating from the gravity effect of density variation.

Finally, compressibility is considered and the results on similarity of stratified flows and on vorticity and circulation are extended to apply to steady flows of gases stratified in entropy.

A uniform magnetic field is switched on at time t = 0 outside a body of conducting fluid. It is assumed that the field strength increases in time in proportion to 1 -e−αt, where α is a constant of the circuit generating the field. Under the assumption of small magnetic Reynolds number and small magnetic Prandtl number the equations governing the diffusion of the field into the fluid are derived and a simple expression is given for the initial vorticity distribution produced in the fluid. The situation in which an initially uniform field is switched off is also considered. It is shown that, for sufficiently symmetrically shaped bodies of fluid, the vorticity generated by the switching-on of the field is the same as that generated by the switching-off. The particular case of an infinitely long circular cylinder of conducting fluid is considered in detail and an explicit expression is derived for the vorticity distribution.