The present study is to investigate the structure of space-time correlations of bursting motions, such as ejections and sweeps in an open-channel flow, by a new conditional sampling analysis of the instantaneous velocity and Reynolds-stress signals measured simultaneously by two dual-sensor hot-film probes. One probe was fixed near the edge of the buffer layer, while the other probe was moved in the streamwise, vertical and spanwise directions. The sorted instantaneous Reynolds-stress signals obtained from the fixed probe were used as a detecting information of the occurrences of ejection or sweep events. The streamwise and vertical spatial characteristics of the ejection-sweep motions, and their convection process are investigated in detail. Also, the spanwise spatial properties of the high- and low-speed streaks in the bursting motions are examined experimentally by the present conditional sampling method.

Next, a qualitative model is proposed which attempts to explain the space-time structures of the bursting phenomenon, on the basis of the above anemometry information and other visual observations.

Kaden's problem of the roll-up of an initially planar semi-infinite vortex sheet with a parabolic distribution of circulation is extended to include vortex sheets exhibiting a general power law circulation distribution, resulting in the presence of a power law, and in one case a logarithmic-like, velocity-field singularity. Both semi-infinite and infinite initially plane sheets with this property are considered and the form of their roll-up in the similarity plane, into single and double-branched spirals respectively, is obtained numerically. Estimates of the Betz constant obtained from the solutions are found to be significantly different from values predicted by the Betz approximation.

TEMTY, a code for large-eddy simulation of a passive scalar in isotropic turbulence, is developed and proved by successful simulation of experiment. The role of each term in the scalar equation and the concept of prefiltering the scalar equation is examined. The ratio of the exponents in the decay of velocity and temperature intensities is found to parametrize with the ratio Λu/Λ0, where Λu, Λ0, are the velocity and temperature Taylor microscales respectively.

A systematic low-frequency theory is developed for the propagation of one-dimensional sound waves in a variable-area duct. The mean flow in the duct is assumed to be isentropic, compressible, and one-dimensional. Two applications are made of the theory. One concerns the reflexion coefficient from a pipe-nozzle combination, in which case comparisons are also made with some experimental data. In the second application, we consider the case of a sonic throat separating subsonic and supersonic flow. In this case, if the mean Mach number distribution in addition to being unity at the throat is also stationary at the throat, there is an axial ‘boundary-layer’ region in which the impedance of the sound wave changes from a fundamentally unsteady (reflexion-free) value at the sonic throat to the quasi-steady value away from the throat.

Thermal fluctuations introduced into decaying grid turbulence at two different downstream locations are shown to be initially correlated and this correlation decays with distance from the grid. The fluctuations are introduced by placing two mandolines (Warhaft & Lumley 1978) at different distances downstream from the grid. The sum of the thermal variances produced by each mandoline operating separately, $\overline{\theta^2_1}+\overline{\theta^2_2}$, is significantly less than the total variance produced by both mandolines operating simultaneously, $\overline{(\theta_1+\theta_2)^2} = \overline{\theta^2_1} + \overline{\theta^2_2} + \overline{2\theta_1\theta_2} $, i.e. the deficit is due to the covariance term $\overline{2\overline{\theta_1\theta_2}}$. This covariance is responsible for a cross-correlation, $\rho = \overline{\theta_1\theta_2}/(\overline{\theta_1^2}\overline{\theta^2_2})^{\frac{1}{2}}$, as great as 0·6. The decay of $\overline{\theta_1\theta_2} $ and ρ is studied for various initial input thermal scale sizes and for various input locations. It is shown that the covariance follows a power-law decay, the exponent varying from - 5·5 if the thermal fluctuations are introduced close to the grid where the turbulence dissipation rate is large and the flow is inhomogeneous to - 4 if they are introduced further downstream (x/M ≥ 10, where x is the distance from the grid and M is the grid mesh length) in the region where the approximately isotropic turbulence is beginning to develop. The decay rate of $\overline{\theta_1\theta_2} $ and ρ was insensitive to the intensity of the thermal fluctuations. In all these experiments the cross-correlation between velocity and temperature fluctuations was very small (∼ − 0·05) and temperature was a passive additive. The results, which appear to be the first quantitative measurements of the rate of destruction of scalar covariance and hence of the mixing rate between two scalars, are shown to provide good confirmation of recent predictions of the decay of ρ by the second-order closure techniques of Lumley (1978 a, b).

The stability of a viscous liquid curtain falling down steadily under the influence of gravity is investigated. Both spatially and temporally changing disturbances are considered in the linear analysis. Only the spatially growing sinuous disturbances whose group velocity points toward upstream are unstable. The group velocity is in the upstream direction only when the Weber number of the curtain flow exceeds ½. The predicted critical Weber number agrees completely with that found experimentally by Brown (1961). The viscosity is shown to have the dual roles of increasing the amplification rate as well as the damping rate of the disturbances.

A method for the numerical solution of steadily progressing periodic waves on irrotational flow over a horizontal bed is presented. No analytical approximations are made. A finite Fourier series, similar to Dean's stream function series, is used to give a set of nonlinear equations which can be solved using Newton's method. Application to laboratory and field situations is emphasized throughout. When compared with known results for wave speed, results from the method agree closely. Results for fluid velocities are compared with experiment and agreement found to be good, unlike results from analytical theories for high waves.

The problem of shoaling waves can conveniently be studied using the present method because of its validity for all wavelengths except the solitary wave limit, using the conventional first-order approximation that on a sloping bottom the waves at any depth act as if the bed were horizontal. Wave period, energy flux and mass flux are conserved. Comparisons with experimental results show good agreement.

There has been much recent interest in the stabilization of water boundary layers by wall heating. Calculations based upon linear stability theory have predicted transition Reynolds numbers as high as 200 million for a zero pressure gradient boundary layer over a heated wall. The experiment described in this paper was intended to investigate these predictions. The test boundary layer develops on the inside surface of a cylindrical tube which is 0·1 m in diameter and 6·1 m in length. The displacement thickness is small relative to the tube radius under all conditions of interest. The tube is heated by electrical heaters on the outside wall. The location of transition is determined by flush-mounted hot-film probes, or by flow visualization at the tube exit.

A transition Reynolds number of 15 million has been obtained without heat, which shows that free-stream turbulence and other perturbations are well controlled. A transition Reynolds number of 47 million has been obtained with an 8 °C wall overheat. However, as temperature is further increased there are no additional increases in transition Reynolds number, which is in contradiction to the theory. Several possible reasons for the discrepancy between theory and experiment have been investigated.

A cylindrical duct absorbing energy from incident surface waves is considered. The asymptotic properties of the scattering and radiation potentials are determined, to yield the hydrodynamic quantities on which the energy absorption characteristics of the duct can be shown to depend. It is shown that it is possible to tune the resonant response of the duct to absorb the maximum theoretical energy at a given frequency. Curves are presented showing the variation of energy absorption and the amplitude of the duct response with frequency for various depths of submergence and various tuning frequencies.

It has been shown (Evans 1976) that the power absorbed by a general, axisymmetric body depends solely upon the added-mass and damping coefficients. These coefficients are fundamental properties of the body, representing the component of the force on the body proportional to the acceleration and velocity of the body respectively in the radiation problem, where the body is forced to oscillate in the absence of incoming waves.

In the present paper these coefficients are determined by solution of the radiation problem, for a mouth-upward cylindrical duct situated on the sea bed and fitted with a piston undergoing forced oscillations. The added-mass and damping coefficients are then used to study the power absorption properties of the duct when the power take-off is modelled by a linear-spring–dashpot system attached to the piston. Curves of the added mass, damping coefficients and absorption length (a measure of the power absorbed) as functions of wavenumber are presented, for different duct diameters and different depths of submergence.

It is now generally agreed that an external disturbance field, such as an incident acoustic wave, can effectively couple to instabilities of a flow past a trailing edge. One purpose of the present paper is to show that there are situations where a similar coupling can occur at a leading edge. The process is analysed and the effects of experimentally controllable parameters are assessed. It is important to account for such phenomena when evaluating the effect of external disturbances on transition.

The paper describes a method to calculate homogeneous anisotropic turbulent fields associated with a constant mean velocity gradient. The equations governing the Fourier transform of the triple velocity correlations are closed by using an extended eddy-damped quasi-normal approximation. An angular parametrization of the second-order spectral tensor is introduced in order to integrate analytically all the directional terms over a spherical shell. Numerical solutions of the model are presented for typical homogeneous anisotropic flows.

In an effort to resolve some controversies regarding the turbulent mixing-layer structure, the near field of a large (18 cm diameter) air jet has been investigated for the jet exit speed of 30 m s−1. The smoke-laden axisymmetric mixing layer has been illuminated by a thin sheet of laser light in an azimuthal plane passing through the jet axis. High-speed visualization films of the mixing layer in the region of its self-preservation (of which a few picture sequences depicting space-time evolutions of the structure of the layer are presented) reveal that most of the time the mixing layer is in a state of disorganization, consisting of relatively smaller scale, random and diffuse turbulent motions; only occasionally are organized distinct large-scale coherent structures formed. The survival distances of the large-scale structures are found to be comparable to their average sizes. The survival time of these structures is about one ‘turnover’ time, each being roughly about five times the local characteristic time scale of the mixing layer. It is seen that tearing is as dominant a mode of large-scale interaction as pairing is; large-scale structures are continually sheared and typically fragmented due to a segment on the high-speed side being torn and swept away from the slower-moving outer portion. Evolution of the large structures occur not primarily through complete pairing as widely believed but quite frequently through ‘fractional pairing’ between segments which have been torn from different upstream large-scale coherent structures or through ‘partial pairing’ when one structure captures only a part of another. The movies show that along with entrainment of non-vortical ambient fluid, radially outward ejection of vortical fluid into the ambient is an important aspect of jet mixing. From aligned displays of ciné film frame sequences, space-time trajectories of identifiable vortical fluid elements have been traced. The convection velocity variation across the shear layer and even the overall structure convection velocity measured from these trajectories agree with those determined from the wave-number-celerity spectra, obtained from double-Fourier transformation of longitudinal velocity space-time correlation measurements with hot-wires.

The visualization films do not bear out the two-street vortex ring model recently propounded by Lau. Based on our observations, we propose that tearing, ‘slippage’ and fractional and partial pairings are responsible for the observed radial variation of structure passage frequency, and the causes of the different coherent structures educed by Bruun on the high- and low-speed sides of the mixing layer and for Yule's failure in educing a coherent structure on the low-speed side of the layer.

The Rayleigh theory of oscillation of liquid drops is extended to include the effects of viscosity and a uniform external electric field. The resonant frequencies of the modes of the drop are shown to be shifted by the electric field. The magnitude and sign of the frequency shift depends on the dielectric constant of the drop. The condition for instability of drops in large electric fields is given and found to differ from that given by previous workers. This difference is attributed to the assumption by previous workers that the drops, under the influence of an electric field, distort into ellipsoids of revolution about the field direction. The dynamical equations are derived and the solution for small oscillations is given in an oscillating field and in an amplitude-modulated optical field.

A reasonably uniform mean temperature gradient has been superimposed upon a nearly homogeneous turbulent shear flow in a wind tunnel. The overheat is small enough to have negligible effect on the turbulence. Away from the wind-tunnel entrance, the transverse statistical homogeneity is good and the temperature fluctuations and their integral scales grow monotonically like the corresponding velocity fluctuations (Harris, Graham & Corrsin 1977). Measurements of several moments, one- and two-point correlation functions, spectra, integral scales, microscales, probability densities, and joint probability densities of the turbulent velocities, temperature fluctuations, and temperature-velocity products are reported. The heat-transport characteristics are much like those of momentum transport, with the turbulent Prandtl number nearly 1. The temperature fluctuation is better correlated with the streamwise than the transverse velocity component, and the cross-component D12 of the turbulent diffusivity tensor has sign opposite to and about twice the magnitude of the diagonal component D22. Some resemblance of directional properties (relative magnitudes of correlation functions, integral scales, microscales) of the temperature with those of the streamwise velocity is also observed. Comparisons of the present data with measurements in the inner part of a heated boundary layer and a fully turbulent pipe flow (x2/d = 0·25) show comparable magnitudes of temperature-velocity correlation coefficients, turbulent Prandtl numbers and ratios of turbulent diffusivities, and show similar shapes of two-point correlation functions.

Previous measurements in nearly homogeneous sheared turbulence with a uniform mean temperature gradient are here supplemented with data on the fine structure of the velocity and temperature fluctuation fields. The statistics of signal derivatives and of band-passed signals show that neither field is locally isotropic in the spectral range covered, possibly because of the insufficiently large turbulent Reynolds and Péclet numbers. Observed skewnesses of both velocity and temperature derivatives are explained qualitatively with the use of a kind of ‘mixing-length’ model. The flatness factors of the derivatives and of band-passed, high-frequency signals indicate appreciable departures from normality, consistent with the spatially ‘spotty’ fine structure. The temperature flatnesses are a bit larger than those of the streamwise velocity. The homogeneous shear flow data are compatible with measurements in turbulent boundary layers at comparable RΛ and PΛθ.

The unsteady laminar flow from a point source of momentum is considered. Dimensional considerations lead to a formulation of the problem which is self-similar in time. Three limiting cases are examined. In the limit t → ∞ the solution corresponds to the classic steady solution first discovered by Landau (1944). The limit t → 0 was examined recently by Sozou & Pickering (1977) and was shown to correspond to the flow from an unsteady dipole of linearly increasing strength. More recently Sozou (1979) determined an analytic solution for the creeping flow limit Re → 0. In the present work, unsteady particle trajectories for each of these cases are examined by reducing the particle path equations to an autonomous system with the Reynolds number as a parameter. Transition of the jet is examined as a bifurcation of this system. In the case of the creeping-flow solution, the particle-path pattern exhibits a structure which is not easily discerned in any of the other variables which govern the flow. For sufficiently small Reynolds number the particle paths converge to a single stable node which lies on the axis of the jet. At a Reynolds number of 6·7806 the pattern bifurcates to a saddle lying on the axis of the jet plus two stable nodes lying symmetrically to either side of the axis. At a Reynolds number of 10·09089 the pattern bifurcates a second time to form a saddle and two stable foci.

From the results of a flow visualization experiment, certain physical characteristics of a turbulent spot are suggested by the authors. The spot was artificially initiated at a point by a small intermittent wall jet. The authors also carried out experiments behind vibrating trip wires and observed the ‘signatures’ or ‘footprints’ of the A-shaped vortices seen by other workers. The fact that these ‘signatures’ are also observed in a turbulent spot leads one to suspect that these spots consist essentially of an array of A-shaped vortices. The formation of the spot is subsequently described in terms of three-dimensional disturbances of the cross-stream vortex filaments.

The basic structure of the turbulent spot proposed here is similar to the suggested structure of fully developed turbulent boundary layers first put forward by Theodorsen (1955) and more recently by Bandyopadhyay & Head (1979).

Free and forced oscillations in a basin that is connected through a narrow canal to either the open sea or a second basin are considered on the assumption that the spatial variation of the free-surface displacement is negligible. The free-surface displacement in the canal is allowed to be finite, subject only to the restriction (in addition to that implicit in the approximation of spatial uniformity) that the canal does not run dry. The resulting model yields a Hamiltonian pair of phase-plane equations for the free oscillations, which are integrated in terms of elliptic functions on the additional assumption that the kinetic energy of the motion in the basin(s) is negligible compared with that in the canal or otherwise through an expansion in an amplitude parameter. The corresponding model for forced oscillations that are limited by radiation damping yields a generalization of Duffing's equation for an oscillator with a soft spring, the solution of which is obtained as an expansion in the amplitude of the fundamental term in a Fourier expansion. Equivalent circuits are developed for the various models.

Liquid-sodium-cooled breeder reactors may soon be operating at magnetic Reynolds numbers RM where magnetic fields can be self-excited by a dynamo mechanism (as first suggested by Bevir 1973). Such flows have kinetic Reynolds numbers RV of the order of 107 and are therefore highly turbulent.

This leads us to investigate the behaviour of MHD turbulence with high RV and low magnetic Prandtl numbers. We use the eddy-damped quasi-normal Markovian closure applied to the MHD equations. For simplicity we restrict ourselves to homogeneous and isotropic turbulence, but we do include helicity.

We obtain a critical magnetic Reynolds number RMc of the order of a few tens (non-helical case) above which magnetic energy is present. RMc is practically independent of RV (in the range 40 to 106). RMc can be considerably decreased by the presence of helicity: when the overall size of the flow L is much larger than the integral scale l0, RMc can drop below unity as suggested by an α-effect argument. When L ≈ l0 the drop can still be substantial (factor of 6) when helicity is a maximum. We examine how the turbulence is modified when RM crosses RMc: presence of magnetic energy, decreased kinetic energy, steepening of kinetic-energy spectrum, etc.

We make no attempt to obtain quantitative estimates for a breeder reactor, but discuss some of the possible consequences of exceeding RMc, such as decreased turbulent heat transport. More precise information may be obtained from numerical simulations and experiments (including some in the subcritical regime).