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.

We have made computational experiments to study the stability and long-time evolution of two-dimensional wakes. We have used the VORTEX code, a finite-difference realization of two-dimensional motions in incompressible inviscid fluids. In the first experiment an initial shear-unstable triangular velocity profile evolves into a non-homogeneous, finite-area, asymmetric vortex array and like-signed regions attract and fuse (or coalesce). Enhanced transport across the profile is due to ‘capture’ and convection of small-scale vortex regions by larger opposite-signed vortex regions. In the following experiments we study the stability of an asymmetric four-vortex finite-area system corresponding to a von Kármán street of point vortices. Here the critical parameter is b/a, the initial transverse-to-longitudinal separation ratio of vortex centres. At \[ b/a = 0.281 \] the four-vortex system is stable and we observe that large-area vortex regions develop elliptical (m = 2), triangular (m = 3), etc. surface modes owing to mutual interactions. At b/a = 0 the measured growth rate is smaller than that for the corresponding von Kármán system and at b/a = 0·6 the measured growth rate is larger. At b/a = 0 one vortex undergoes fission in the high-shear field produced by two nearest-neighbour opposite-signed vortex regions. Heuristic comparisons are made with the two-dimensional tunnel experiments of Taneda and others.

The first part of the paper is an extension of the statistical theory of turbulent diffusion to the problem of turbulent diffusion from a point or line source in an inhomogeneous straining flow such as flow round a two-dimensional body. The new effects which have to be considered are the convergence and divergence of mean streamlines, the inhomogeneity of the mean and turbulent velocities, and the presence of a boundary. We assume that the upstream turbulence intensity $u^{\prime}_{\infty}/\overline{u}_{\infty} $ is weak, i.e. $u^{\prime}_{\infty}/\overline{u}_{\infty} $ [Lt ] 1, and that molecular diffusion is negligible, i.e. $(\overline{u}_{\infty}/u^{\prime}_{\infty})^2[D/(a\overline{u}_{\infty})] $ [Lt ] 1, D and a being the molecular diffusivity and the scale of the obstacle respectively. The theory predicts the mean-square dispersion of the plume about the mean streamline through the source in terms of the Lagrangian statistics of the turbulence. Making the further assumption that the scale LE of the turbulence is large enough to satisfy the condition that ($(u^{\prime}_{\infty}/\overline{u}_{\infty}) $) (a/LE) [Lt ] 1, it is shown that the turbulent dispersion can be calculated in terms of the Eulerian statistics, which can either be measured or in some cases calculated. In the second part we analyse diffusion from various sources in potential flows over two-dimensional obstacles assuming constant (or variable) eddy diffusivity, and compare the results with those of the more rigorous statistical analysis for sources one or two diameters upwind of the obstacle. However, unlike the statistical analysis, this eddy-diffusivity analysis can also be extended to calculate diffusion from sources placed some distance upwind of an obstacle, and an example is given of how this analysis may be applied to calculating concentrations on hills due to distant sources.

Turbulent entrainment across a density interface is studied in a laboratory wind–wave tank in which a stably stratified system consisting of two homogeneous fluid layers is introduced. The results indicate that the rate of change of the potential energy of the mixing layer is proportional to the rate of work done by the wind. However, only a very small fraction of the work done by the wind is used for interfacial mixing or developing a seasonal thermocline. A formula relating the entrainment rate to the density stratification and the wind-friction velocity is derived from the experimental results.

The laser-Doppler ambiguities predicted by George & Lumley have been verified experimentally for turbulent pipe flows. Experiments were performed at Reynolds numbers from 5000 to 15000 at the centre-line and near the wall. Ambiguity levels were measured from power spectral densities of FM demodulated laser signals and compared with calculations based on the theory. The turbulent spectra for these water flows after accounting for the ambiguity were equivalent to hot-film measurements at similar Reynolds numbers. The feasibility of laser-Doppler measurements very close to the wall in shear flows is demonstrated.

The propagation of an internal wave in an ocean which is stratified in both temperature and salinity is considered. It is shown how the effects of viscosity, heat conduction and solute diffusion attenuate a cross-wave from an oscillatory disturbance. Under certain conditions there is no wave solution even though the oscillatory frequency is less than the Brunt–Väisälä frequency and the fluid is stably stratified.

An aspect of the laminar far wake behind a symmetrical two-dimensional body placed in a uniform shear flow is described theoretically by means of the Oseen type of successive approximation, in which the shear is regarded as a small perturbation on a uniform stream. The expression for the stream function is determined up to the third approximation both in and outside the wake region, and the region in which the results of the perturbation analysis are valid is also determined. The stream function is found to contain four constants which cannot be determined from the boundary conditions for the far wake. The analysis also shows that the spreading of the wake is greater towards the side of smaller velocity than the side of larger velocity, the asymmetrical feature of the velocity defect becoming more evident as the distance from the obstacle is increased: the point which shows the maximum velocity defect shifts to the low-velocity side.

Experiments using a wind tunnel and a flow visualization technique in a towing tank were conducted to investigate the mechanism of vortex shedding from bevelled trailing edges. These reveal an important difference between the wake structures generated by heaving and steady motion. The suppression of vortex-excited vibration by means of bevelled trailing edges is attributed to the intermittency and rapid decay of the vortex trail resulting from an asymmetric circulation distribution in the vortex formation region.

An experimental investigation has been carried out to determine the behaviour of three-dimensional disturbances in laminar natural convection flow adjacent to a flat vertical surface with uniform heat flux input. A controlled two-dimensional disturbance, with a superimposed transverse variation, was introduced into the boundary region by a vibrating ribbon. The downstream propagation and amplification of these disturbances were studied in detail. Of principal interest was their nonlinear interaction with the base flow and any secondary mean flows that might arise therefrom. Measurements of the transverse mean velocity component indicate a double longitudinal vortex system. These results also show a distortion of the longitudinal base velocity profile which rapidly increases downstream. An alternate spanwise steepening and flattening of the profile is found to result. These mean flow modifications are found to be in good general agreement with existing theoretical and experimental studies of such flows. Our results are also compared with those obtained for forced flow. Several very important differences and similarities are indicated.

The fully viscous hydrodynamic stability equations for a round laminar vertical jet have been numerically solved using the proper boundary-layer base-flow velocity profile and for both symmetric and asymmetric disturbances. The symmetric mode is found to be unconditionally stable. The first asymmetric mode is found to be unstable and characteristics are compared with previous calculations. The computed critical Reynolds number for this mode is 9·4, which agrees with the calculations of Burridge (1968). Disturbance amplitude-ratio contours are also calculated and related to the convection of disturbances in the flow.

The effect of thermal buoyancy on jet stability is assessed by solving the fully viscous equations, coupled through buoyancy, and using a buoyancy-perturbed jet flow. A Prandtl number σ of 6·7 is used, and positive thermal buoyancy is found to have a destabilizing effect. Stability characteristics for the limiting case of buoyancy, a purely thermal point-source plume, are determined for a Prandtl number of 2.

Finally, an experiment was performed using water jets in water (σ ≈ 4·52–5·89) and a new method of jet production is described. The effect of varying amounts of thermal buoyancy on the laminar length of a jet undergoing naturally occurring transition was determined experimentally. These experiments confirm the calculated destabilizing effect of buoyancy. An empirical correlation is presented for the laminar length of a jet. Also, the effect of both symmetric and asymmetric artificially induced disturbances was determined experimentally. The disturbance amplitude ratio at which transition to turbulence takes place is found to be much less than for buoyant flows adjacent to a wall. The effects of frequency and amplitude of the artificial disturbances were experimentally determined and the trends are found to be consistent with the results of small disturbance theory.

The principal new result is that positive thermal buoyancy destabilizes jet flow, and consequently calls into question earlier experimental studies wherein jet flows were observed by density differences. Another new result is the calculation. of amplitude-ratio contours for a non-buoyant jet and the quantitative description of jet stability in terms of these contours along paths of constant physical frequency. A comparison of the non-buoyant theory with experimental jets containing varying amounts of thermal buoyancy indicates that transition did not occur at a well-defined value of the amplitude ratio. Perhaps experiments with truly non-buoyant jets and/or more detailed buoyant calculations could explain this remaining question.

The experimental work of Franklin, Price & Williams (1973) shows that for moderately large driving amplitudes there are features of spatial resonance that are not predicted by the model representation of Mahony & Smith (1972). We here derive an alternative model, which remains valid for moderately large driving amplitudes, and we are able to obtain a theoretical description of both hysteresis and nonlinear detuning of the low frequency wave response. An experiment in which surface waves were generated by a sinusoidal pressure field at the free surface (and which corresponds almost exactly to the theoretical problem) was conducted in order to test these predictions.