In this paper the flow behind a pair of bluff bodies placed side by side in a stream is studied using a variety of flow-visualization methods. Above a critical gap size between the bodies, vortex-shedding synchronization occurs, either in phase or in antiphase. It has previously been assumed that such synchronization forms a wake comprising two parallel vortex streets in phase and in antiphase respectively. In the present paper we find that two antiphase streets are indeed formed, although in-phase shedding leads to the development of a single large-scale wake. The vortices which are formed simultaneously at the cylinders rotate around one another downstream, each pair forming a ‘binary vortex’. The combined wake comprises a street of such vortices, which we term a binary vortex street. Below a critical gap size between the bluff bodies the flow becomes asymmetric. We observe in this regime certain harmonic modes of vortex shedding whereby the shedding frequency on one side of the wake is a multiple of that on the other. Again, a large-scale wake is formed downstream. The present observations lead to a new interpretation of hot-wire-frequency data from other studies in terms of the harmonic modes.

In Part 1 a study is made of the internal solitary wave on the pycnocline of a continuously stratified fluid. A Korteweg–de Vries (KdV) equation for the ‘interfacial’ displacement is developed following Benney's method for long nonlinear waves. Experiments were conducted in a long wave tank with the pycnocline at several different depths below the free surface, while keeping the total depth approximately constant. A step-like pool of light water, trapped behind a sliding gate, served as the initial disturbance condition. The number of solitons generated was verified to satisfy the prediction of inverse-scattering theory. The fully developed soliton was found to satisfy the KdV theory for all ratios of upper-layer thickness to total depth.

In Part 2 of this study we investigate experimentally the evolution and breaking of an internal solitary wave as it shoals on a sloping bottom connecting the deeper region where the waves were generated to a shallower shelf region. It is found through quantitative measurements that the onset of wave-breaking was governed by shear instability, which was initiated when the local gradient Richardson number became less than ¼. The internal solitary wave of depression was found to steepen at the back of the wave before breaking, in contrast with waves of elevation. Two slopes were used, with ratios 1:16 and 1:9, and the fluid was a Boussinesq fluid with weak stratification using brine solutions.

The stability of an infinitely long compound liquid column is analysed by using a one-dimensional inviscid slice model. Results obtained from this one-dimensional linear analysis are applicable to the study of compound capillary jets, which are used in the ink-jet printing technique. Stability limits and the breaking regimes of such fluid configurations are established, and, whenever possible, theoretical results are compared with experimental ones.

This paper describes an experimental study, conducted in the I.M.S.T. air–sea interaction tunnel, of waves excited on a water surface by a periodic train of vortices in the air flow above. The water surface, under some conditions, shows a rapidly developing resonant response, while in the non-resonant case waves propagate both upstream and downstream at speeds different from, but dependent upon, the vortex-convection speed.

Large-scale coherent structures in a large, single-stream plane mixing layer of air have been investigated experimentally. The unforced, initially fully turbulent mixing layer rolls up into organized structures whose average passage frequency fm at any downstream distance x from the lip depends on x. These structures are detected for the entire length of the measurement, i.e. up to x = 3 m or 5000θe. The Strouhal number Stθ (= fm θ/Ue) is observed to be a constant (≈ 0.024) at all x. θe and θ are, respectively, the exit and local momentum thicknesses of the mixing layer, and Ue is the free-stream velocity. (The entrainment velocity on the zero-speed side is found to be 0.032 Ue.) The coherent-structure properties are educed in the developing and self-preserving regions of the mixing layer using an optimized conditional-sampling method, triggered on the peaks of a local reference ũ-signal obtained from the high-speed edge of the layer. Sectional-plane contours of the properties of the structure such as coherent vorticity, Reynolds stress and production reveal that the structure formation and evolution are complete by x ≅ 500θe, beyond which the structure achieves an ‘equilibrium’ state as defined by the structure properties.

The results are presented of turbulence measurements on an ‘infinite’ swept wing, simulated by a duct attached to a blower tunnel. The configuration is close to that used at the Netherlands NLR except that the boundary layer does not quite separate. The measurements include triple products, and a balance of the transport equation for turbulent energy is presented. The results confirm the NLR finding of a significant decrease in the magnitude of shear stress compared with an equivalent two-dimensional boundary layer: this is evidently the effect of crossflow on large eddies that have initially developed in a two-dimensional boundary layer. This unexpected effect of three-dimensionality is at least as important in prediction of real-life flows as the better-known lag between the direction of the shear stress and that of the mean-velocity gradient. Tentative suggestions for modelling the reduction in shear-stress magnitude are advanced.

Cavitation-noise measurements from an axisymmetric body with ‘controlled’ generation of cavitation are reported. The control was achieved by seeding artificial nuclei in the boundary layer by electrolysis. It was possible to alter the number density of nuclei by varying the electrolysis voltage, polarity and the geometry of the electrode. From the observed trend of cavitation-noise data it is postulated that there exists an ‘interference effect’ which influences cavitation noise. When the nucleus-number density is high and cavitation numbers are low this effect is strong. Under these conditions the properties of cavitation noise are found to differ considerably from those expected based on theories concerning noise from single-spherical-bubble cavitation.

The absolute or convective character of inviscid instabilities in parallel shear flows can be determined by examining the branch-point singularities of the dispersion relation for complex frequencies and wavenumbers. According to a criterion developed in the study of plasma instabilities, a flow is convectively unstable when the branch-point singularities are in the lower half complex-frequency plane. These concepts are applied to a family of free shear layers with varying velocity ratio $R = \Delta U/2\overline{U}$, where ΔU is the velocity difference between the two streams and $\overline{U}$ their average velocity. It is demonstrated that spatially growing waves can only be observed if the mixing layer is convectively unstable, i.e. when the velocity ratio is smaller than Rt = 1.315. When the velocity ratio is larger than Rt, the instability develops temporally. Finally, the implications of these concepts are discussed also for wakes and hot jets.

Zakharov's (1968) Hamiltonian formulation of water waves is used to prove analytically Tanaka's (1983) numerical result that superharmonic disturbances to periodic waves of permanent form exchange stability when the wave energy is an extremum as a function of wave height. Tanaka's (1985) explanation for the non-appearance of superharmonic bifurcation is also derived, and the non-existence of stability exchange when the wave speed is an extremum is explained.

The effect of fluid compressibility on the dynamic stability of a two-dimensional flow through a flexible channel is analysed. The compressibility parameter Q is defined as the ratio of a reference elastic wave speed of the wall to the local speed of sound. As the fluid speed increases, the walls become dynamically unstable at the critical fluid speed S0 and start to flutter at critical frequency ω0. The effect of three other dimensionless parameters on the critical condition is also analysed. These are the ratio γ of fluid damping to wall damping, the ratio B of wall bending resistance to elastance, and the ratio μ of wall to fluid mass. Nonlinear analysis using the Poincaré–Lindstedt method shows stiffening at supercritical speeds. Further stability analysis using the method of multiple scales shows that the amplitude growth is finite and the nonlinear fluttering state is stable. Both symmetric and antisymmetric modes of oscillation are analysed. A frictionless system is found to be a singular case in the nonlinear theory. The hydraulic approximation employed in the analysis is shown to be a particular limiting form of the corresponding Orr–Sommerfeld system.

A method is described for solving the integral equations governing Stokes flow in arbitrary two-dimensional domains. It is demonstrated that the boundary-integral method provides an accurate, efficient and easy-to-implement strategy for the solution of Stokes-flow problems. Calculations are presented for simple shear flow in a variety of geometries including cylindrical and rectangular, ridges and cavities. A full description of the flow field is presented including streamline patterns, velocity profiles and shear-stress distributions along the solid surfaces. The results are discussed with special relevance to convective transport processes in low-Reynolds-number flows.

The reflection and transmission of a gravity wave propagating through a jet-type background flow is studied. Only the linear, non-dissipative case is treated, and the hydrostatic approximation used in a stratified non-rotating medium. The behaviour of the gravity wave in the presence of two or one critical levels is investigated. In the first case, i.e. two critical levels, it is found that for high values of the Richardson number the wave is highly attenuated. For sufficiently low values of the Richardson number overreflection and overtransmission occur. It is demonstrated that a wave generated below the jet and propagating upward takes energy from the mean flow at the upper critical level for all values of the Richardson number. The single critical level has been studied as a limiting case of two merging critical levels. In this approach it is found that the wave is not transmitted and no overreflection can occur.

The linear stability of a two-dimensional buoyant plume is analysed by taking into account the transverse velocity component and the streamwise variations of the basic flow and of the disturbance waves. The solutions indicate the dependence of the spatial amplification rate and wavenumber on the disturbance flow quantity under consideration as well as on the streamwise and transverse coordinates. The use of the flow quantity relative to the basic flow leads to close agreement with the neutral curve according to quasi-parallel-stability theory, the usual method for treating nearly parallel flows. However, the amplification rate within an unstable region shows substantial deviation from that predicted by the quasi-parallel theory. The validity of this non-parallel theory is supported by the existing experimental data.

The ‘stability’ of flows in symmetric curved-walled channels is investigated by essentially combining Fraenkel's ‘small’ wall-curvature theory with the multiple-scaling (or WKB) method. The basic flow is characterized by the steady-state stream function Ω, which varies ‘slowly’ in the streamwise direction. An asymptotic scheme is posed for Ω in such a way that at lowest order Ω represents a class of Jeffery–Hamel solutions. An infinitesimal disturbance is superimposed on the basic flow through a time-dependent stream function Φ, and the resulting linearized disturbance equation suggests that fixed-frequency disturbances with ‘slowly’ varying wavenumber are appropriate. The asymptotic scheme for Φ yields the Orr–Sommerfeld equation at lowest order. Two classes of channels are considered. In the first class the curvature is constant in sign, and under certain conditions they reduce to symmetric divergent straight-walled channels. In the second class of channels the curvature varies in sign, and these may be more suitable for experimentation. A spatially dependent growth rate of the disturbance relative to the basic flow is defined; this forms the basis of the ‘stability’ analysis. Critical Reynolds numbers are deduced, below which the disturbance decays as it travels downstream, and above which the disturbance grows for a limited range in the streamwise direction. For the first class of channels the ‘stability’ analysis is carried out locally, and the dependence of the critical Reynolds numbers on curvature and higher-order terms is investigated. For the second class of channels the ‘stability’ analysis is carried out at various positions downstream, and an overall minimum critical Reynolds number is predicted for a range of channels and flows.

Stably stratified viscous fluid in a container with vertical walls is initially at rest with tilted density surfaces, following a rotation of the container from its orientation when being filled. The initial state so generated is not in equilibrium, and the resultant motion will decay under the action of viscosity and of the diffusion of the salt producing the stratification. The timescales for the succession of stages by which equilibrium is attained are identified, and are found to depend on the strengths of the two diffusive processes, separately and interactively.

The effect of varying the initial concentration distribution is investigated for a sudden contaminant release in a uniform straight channel. Taking the optimal choice to be that which maximizes the variance of the contaminant cloud far downstream, it is found that, unless the topography is very unusual, the largest variance can be generated by splitting the contaminant into two parts, placing the larger part at the bank where the channel bed slopes most gently, and the remainder near to where the channel is deepest. This procedure significantly reduces peak concentrations far downstream when compared with making the entire release at any single point across the flow. Even at distances as large as six times the e-folding distance for cross-sectional mixing, the splitting of the discharge is shown to reduce the peak concentrations by a third.

A new analytic solution is presented for predicting evaporation rates from plane liquid surfaces into a neutral turbulent boundary layer. Conditions of passive dispersion are assumed. Molecular diffusivity is incorporated into the boundary conditions. Both smooth and rough surfaces are considered. A comparison with a wide variety of experimental data is made; this tends to reveal inadequacies and inconsistencies in the data, rather than test the theory. The effects of a roughness change at the boundary of the liquid surface and of high vapour pressures can be included for practical purposes by simple formulae. A criterion is derived for the validity of the neglect of buoyancy effects.

The Taylor–Goldstein problem for stability of stratified shear flows of inviscid Boussinesq fluids is treated. Perturbation of a known neutral curve is used to obtain the stability characteristics in the neighbourhood of the curve. In the cases that are studied Howard's technique for perturbing neutral modes breaks down. This is related to the vanishing of a coefficient in the expansion of the dispersion relation near the neutral curve. In that case instability may occur on either side of the neutral curve. Examples are used to illustrate how unexpected behaviour arises, such as instability on both sides of a neutral curve.

The well-known analogy between the Euler equations for steady flow of an inviscid incompressible fluid and the equations of magnetostatic equilibrium in a perfectly conducting fluid is exploited in a discussion of the existence and structure of solutions to both problems that have arbitrarily prescribed topology. A method of magnetic relaxation which conserves the magnetic-field topology is used to demonstrate the existence of magnetostatic equilibria in a domain [Dscr ] that are topologically accessible from a given field B0(x) and hence the existence of analogous steady Euler flows. The magnetostatic equilibria generally contain tangential discontinuities (i.e. current sheets) distributed in some way in the domain, even although the initial field B0(x) may be infinitely differentiable, and particular attention is paid to the manner in which these current sheets can arise. The corresponding Euler flow contains vortex sheets which must be located on streamsurfaces in regions where such surfaces exist. The magnetostatic equilibria are in general stable, and the analogous Euler flows are (probably) in general unstable.

The structure of these unstable Euler flows (regarded as fixed points in the function space in which solutions of the unsteady Euler equations evolve) may have some bearing on the problem of the spatial structure of turbulent flow. It is shown that the Euler flow contains blobs of maximal helicity (positive or negative) which may be interpreted as ‘coherent structures’, separated by regular surfaces on which vortex sheets, the site of strong viscous dissipation, may be located.

Temperature measurements taken in association with the velocity measurements described by Gargett, Osborn & Nasmyth (1984) are examined. With careful noise removal the temperature dissipation spectrum is fully resolved and χ, the dissipation rate of temperature-fluctuation variance, is determined directly. With directly measured values of χ and ε, the turbulent-kinetic-energy dissipation rate per unit mass, the observed temperature spectra are non-dimensionalized by Oboukov–Corrsin–Batchelor scaling. Shapes and levels of the resulting non-dimensional spectra are then examined as functions of the degree of isotropy (measured) in the underlying velocity field. Two limiting cases are identified: Class A, associated with isotropic velocity fields; and Class B, associated with velocity fields which are anisotropic (owing to buoyancy forces repressing vertical relative to horizontal dimensions of energy-containing ‘eddies’). The present observations suggest that the Corrsin–Oboukov–Batchelor theory does not provide a universal description of the spectrum of temperature fluctuations in water. Class A scalar spectra have neither $k^{-\frac{5}{3}}$ nor k−1 subranges: a Batchelor-spectrum fit to the high-wavenumber roll-off region yields a value of 12 for the ‘universal’ constant q. In striking contrast, the buoyancy-affected Class B spectra exhibit a clear $k^{-\frac{5}{3}}$ subrange, an approach to a k−1 subrange, and a value of q ∼ 4 which is in rough agreement with most previous estimates. Previous oceanic and atmospheric measurements are re-examined in the light of the present results. It is suggested that these previous results are also affected by vertical scale limitation. Reasons underlying the discrepancies between theories and observations are discussed: these may be different in the two classes presented.