Two problems involving the unsteady motion of two-dimensional vortex sheets are considered. The first is the roll-up of an initially plane semi-infinite vortex sheet while the second is the power-law starting flow past an infinite wedge with separation at the wedge apex modelled by a growing vortex sheet. In both cases well-known similarity solutions are used to transform the time-dependent problem for the sheet motion into an integro-differential equation. Finite-difference numerical solutions to these equations are obtained which give details of the large-scale structure of the rolled-up portion of the sheet. For the semi-infinite sheet good agreement with Kaden's asymptotic spiral solution is obtained. However, for the starting-flow problem distortions in the sheet shape and strength not predicted by the leading-order asymptotic solutions were found to be significant.

Detailed measurements of turbulent concentration parameters in a round free methane jet up to 70 diameters downstream from the jet source are described. The concentration changes were obtained using a Raman spectrometer designed for the measurement of a methane vibrational transition function, and processed using a photon correlator. Mean and fluctuating concentration levels are given, together with the concentration probability density distribution.

A theory for interpreting the statistical aspects of the signal is presented and results are compared with other data from the literature on jets of uniform and non-uniform density. It is shown that the intensity of concentration fluctuations has an asymptotic value of 28·5% in the far field region of the jet. One interesting feature of the data is the deviation from Gaussian statistics along the jet centre-line.

By applying small lateral oscillations to a glass tube from which smoke was issuing, perfectly periodic coflowing jets and wake structures were produced at Reynolds numbers of order 300-1000. These structures remained coherent over long streamwise distances and appeared to be perfectly frozen when viewed under stroboscopic light which was synchronized with the disturbing oscillation. By the use of strobing laser beams, longitudinal sections of the structures were photographed and an account of the geometry of these structures is reported.

When the tube was unforced, similar structures occurred but they modulated in scale and frequency, and their orientation was random.

A classification of structures is presented and examples are demonstrated in naturally occurring situations such as smoke from a cigarette, the wake behind a three-dimensional blunt body, and the high Reynolds number flow in a plume from a chimney. It is suggested that an examination of these structures may give some insight into the large-scale motion in fully turbulent flow.

The developing flow in the entry region of a heated horizontal pipe is analysed. The asymptotic solution of the developing flow near the entrance of the heated straight pipe, distance O(a), is obtained by perturbing the solution of the developing flow in an unheated straight pipe. Two vortices result from the combination of the radial-directional and the downward motions of the fluid particles which are induced by the displacement of the boundary layer and develop along the pipe. The axial velocity has a concave profile in the inviscid core with its maximum off the centre-line near the entrance and it grows toward a uniformly distributed profile downstream. The downward stream caused by the displacement of the secondary boundary layer forces the axial velocity profile to turn anticlockwise continuously along the pipe if the flow is from left to right. The core flow induced by the axial boundary-layer displacement generates a favourable pressure gradient. Simultaneously, the secondary boundary-layer displacement affects the core flow to induce a favourable pressure gradient on the bottom of the pipe and an unfavourable pressure gradient on the top wall. The effect of the axial boundary-layer displacement is stronger than that of the secondary boundary layer near to the entrance. Downstream the growth of the boundary-layer thickness is suppressed by the inviscid secondary flow. It is expected that the displacement effect of the secondary boundary layer becomes dominant downstream from the region of O(d) when Gr is large.

The hydrodynamic forces due to the motion of a flexible foil in a large amplitude curved path in an inviscid incompressible flow are analysed. A parametric study of large amplitude oscillatory propulsion, with special emphasis on the effect of chordwise flexibility of the fin, is presented. This flexibility was found to increase the propulsive efficiency by up to 2% while causing small decreases in the overall thrust, compared with similar motion with rigid foils.

A technique has been developed to study the phenomenon of ultrasonic emulsification in which oil is dispersed as a fine suspension into water at 20 kHz. It was found that the emulsification takes place in two stages. In the first stage, oil droplets of the order of 70 μm are formed from the instability of interfacial waves. In the second stage these large droplets are successively broken into small droplets by cavitation until a stable droplet size is reached. In this paper, the criterion for the instability of the interfacial waves is developed from a linearized stability analysis of the planar oil-water interface exposed to acoustic excitation. The characteristic droplet diameter produced by the instability is related to the induced capillary wavelength at the interface.

The amplitude of the ultrasonic transducer and the theoretical amplitude of vibration necessary for the instability of the interfacial waves were found to be in agreement. In addition, the sizes of the large droplets present in the suspension systems at short irradiation times agree closely with the predicted droplet diameters.

A theoretical model is presented for the liquid-liquid emulsification phenomenon based on the deformation and breakup of an oil droplet exposed to a cavitation shock wave generated by an acoustic field. The model predicts a relationship between the Ohnesorge number and the critical Weber number ratio for long acoustic irradiation times. At short irradiation times, the mean particle size and variance decrease with increasing time of acoustic irradiation. The results show remarkable agreement when compared with results obtained from the studies on liquid droplets exposed to shock impact from a gas stream. The mechanism for acoustic emulsification is that large oil droplets originally formed from the instability oil-water interface are disintegrated into smaller ones by the cavitation until a critical size, characteristic of the particular oil-water system, is reached.

The Faxén relations for a rigid particle in an arbitrary Stokes flow are generalized to give expressions for the stresslet (and higher stress moments) exerted by the particle on the fluid, and also to viscous drops immersed in a viscous fluid.

The classical power laws describing the similarity solutions for turbulent jets, wakes and shearing layers are found to determine a fixed turbulent Reynolds number for each flow. The power laws are then derived from the principle of marginal instability without the usual assumptions.

Several models are developed for the high-wavenumber portion of the spectral transfer function of scalar quantities advected by high-Reynolds-number, locally isotropic turbulent flow. These models are applicable for arbitrary Prandtl or Schmidt number, v/D, and the resultant scalar spectra are compared with several experiments having different v/D. The ‘bump’ in the temperature spectrum of air observed over land is shown to be due to a tendency toward a viscous-convective range and the presence of this bump is consistent with experiments for large v/D. The wavenumbers defining the transition between the inertial-convective range and viscous-convective range for asymptotically large v/D (denoted k* and k1* for the three- and one-dimensional spectra) are determined by comparison of the models with experiments. A measurement of the transitional wavenumber k1* [denoted (k1*)s] is found to depend on v/D and on any filter cut-off. On the basis of the k* values it is shown that measurements of β1 from temperature spectra in moderate Reynolds number turbulence in air (v/D = 0·72) maybe over-estimates and that the inertial-diffusive range of temperature fluctuations in mercury (v/D ≃ 0·02) is of very limited extent.

The structure and development of turbulent plane jets in still air and moving streams are described. The nature of the small-scale turbulence cannot be accurately ascertained because of the difficulties inherent in the measurement of dissipation in highly turbulent flows. Although correlation measurements in a jet in still air indicate a large-scale structure which can best be described as ‘local flapping’, measurements in a jet in a moving stream do not reveal a similar structure. The development of the turbulence structure in a jet in a moving parallel stream is described and the properties of turbulent jets and wakes are shown to be reasonably well predicted by the use of a variable-eddy-viscosity formula together with the formal self-preserving properties of the equations of motion.

The paper describes correlation measurements in both broad and narrow frequency bands of the longitudinal velocity fluctuations in fully developed pipe flow at four positions for a reference probe whilst a second probe was traversed radially from deep in the sublayer to a position near the axis with both longitudinal and transverse separations zero (Δx = Δz = 0). Such measurements require that both the Covariant (Co) and Quadrature (Quad) correlations be determined for each of the 15 frequencies used to constrain the wave component λx.

The new data demonstrate that low frequency, large scale turbulence fluctuations extend over the majority of the radial region and that these components are highly correlated. By using a similarity variable kxy, along with a normalized wall distance y/y REF, both correlation functions, i.e. the Co and the Quad components, are shown to collapse. The physical significance of this is discussed.

The broad-band data do not collapse because of the large range of wave sizes. However, the present experiment does show that strong radial correlations exist even when one probe is at y+ = 1. This conflicts with the earlier data of Favre, but agrees with the more recent work of Comte-Bellot. There is a significant amount of turbulent energy in frequencies less than 16 Hz (ω+ = 0·008) for turbulent flows of about 105 Reynolds number.

The spectral function ωΦ(ω) is also presented for a range of y+ values. Using this form for the power spectral density, along with the stochastic wave modelling and similarity arguments of this paper, it is shown how a consistent explanation for the behaviour of these spectra is obtained. In addition some preliminary results from cross-spectral analyses are presented and suggestions made as to their physical significance.