Velocity measurements in a 51 mm diameter turbulent jet are presented. The measurement programme is conducted in two parts. The first part is devoted to the validation of laser velocimeter (LV) data. This consists of comparative measurements with the LV and a hot-wire anemometer. The second part consists of a survey of the jet flow field at Mach 0·28, 0·90, and 1·37 under ambient temperature conditions. Radial and centre-line distributions of the axial and radial, mean and fluctuating velocities are obtained. The distributions indicate a decrease in the spreading rate of the mixing layer with increasing Mach number and a corresponding lengthening of the potential core. The results further indicate that these two parameters vary with the square of the jet Mach number. Radial distributions collapse when plotted in terms of ση*, where σ = 10.7/(1 - 0.273 MJ2) and η* = (r − r0·5)/x. This is true for distributions in planes located as far downstream as two potential core lengths. The collapsed data of mean velocity can be approximated by a Görtler error function profile: \[ U/U_J = 0.5[1-{\rm erf}(\sigma\eta^{*})]. \] Centre-line distributions at various Mach numbers also collapse if plotted in terms of x/xc, xc being the potential core length. A general equation for the collapsed data of mean velocity is given by: U/UJ = 1 - exp{1.35/(1 - x/xc)}, for the range of Mach numbers 0·3-1·4, where xc = 4.2 + 1.1 MJ2.

An externally applied d.c. electric field is known to produce instability in a plane layer of dielectric liquid heated from above. The stationary linear instability of a unipolar charge injection equilibrium for which carrier mobility depends linearly on temperature is investigated. It is found that the sign of the temperature gradient in relation to the emitting electrode determines whether or not such instability can occur, and that two types of instability can be distinguished: (i) a space charge modified Bénard mode; and (ii) a thermally modified space charge mode. It is shown that the critical voltage is highly dependent upon the absolute value of mobility and its variation across the layer.

From a series of experiments using simplified mechanical models we suggest certain minor modifications to the Weis-Fogh (1973)–Lighthill (1973) explanation of the so-called ‘clap and fling’ mechanism for the generation of large lift coefficients by insects in hovering flight. Of particular importance is the production and motion of a leading edge, separation vortex that accounts for virtually all of the circulation generated during the initial phase of the ‘fling’ process. The magnitude of this circulation is substantially larger than that calculated using inviscid theory. During the motion that subsequently separates the wings, the vorticity over each of them is convected and combined to become a tip vortex of uniform circulation spanning the space between them. This combined vortex moves downwards as a part of a ring, of large impulse, that is then continuously fed from quasi-steady separation bubbles that move with the wings as they continue to open at a large angle of attack. Such effects are able to account for the large lift forces generated by the insect.

In nematic homeotropic films (director n perpendicular to the horizontal limiting plates) heated from below, the distortion of the director which is coupled to the ordinary heat convection mechanism responsible for the Rayleigh–Bénard instability exerts a strongly stabilizing influence. Owing to the difference in time scales, an oscillatory instability results whose characteristics are investigated experimentally here. An inverted bifurcation with an associated hysteresis is also obtained and this was studied in some detail. A vertical magnetic field H is also used to align the sample. The decrease of the orientational time constant when H increases leads to marked changes in the overstable regime, which are well described by a simple analysis.

The variations in refractive index in stratified liquid flows have been a major impediment to the use of laser-Doppler anemometry in these situations. This paper describes a method whereby these refractive-index variations can be drastically reduced while retaining the dynamically important density differences. The method uses two solutes to produce the density differences and it is shown that double-diffusive convection (of the salt-finger type) can be avoided by using a suitable pair of solutes. A theoretical model of the lateral wander of a single laser beam propagating through a turbulent medium is developed and this explains the success of the method.

Flows of incompressible inviscid heavy fluids with free or rigid boundary surfaces are considered. For slender streams of fluid, the flow and the free boundaries are represented by a number of different asymptotic expansions in powers of the slenderness ratio. There are three kinds of outer expansions representing respectively jets, which have two free boundaries, wall flows, which have one free and one rigid boundary, and channel flows, which have two rigid boundaries. The flow at the junction of two or more outer flows is represented by an inner expansion. Previously we constructed the three outer expansions and the inner expansion at the junction of a wall flow and a jet (Keller & Geer 1973). Now we construct the inner expansions at the junctions of a channel flow and a jet, a channel flow and a wall flow, and a jet and the two wall flows into which it splits upon hitting a wall. We also match each inner expansion to the adjacent outer expansions. These seven expansions can be combined to solve many problems involving flows of slender streams.

The three-dimensional evolution of packets of gravity waves is studied using a nonlinear Schrödinger equation (the Davey–Stewartson equation). It is shown that permanent wave groups of the elliptic en and dn functions and their common limiting solitary sech forms exist and propagate along directions making an angle less than ψc = tan−1(1/√2) = 35° with the underlying wave field, whilst, along directions making an angle greater than ψc, there exist permanent wave groups of elliptic sn and negative solitary tanh form. Furthermore, exact general solutions are given showing wave groups travelling along the two characteristic directions at ψc or − ψc. These latter solutions tend to form regions of large wave slope and are used to discuss the waves produced by a ship, in particular the nonlinear evolution of the leading edge of the pattern.

Laboratory and numerical experiments have been conducted to study the secular spin-up of both a homogeneous and a thermally stratified rotating fluid in a right cylinder. In these experiments, the angular velocity of the container increases linearly in time from some initial rotation rate at t = 0. A simple quasi-geostrophic model is developed to describe the adjustment of the fluid over the characteristic spin-up time scale to the constant angular acceleration of the basin. Good agreement is found between the observed interior temperature and azimuthal velocity fields and the theory in both the homogeneous and stratified secular experiments. This result is in contrast to the much faster adjustment observed in stratified instantaneous spin-up experiments reported earlier. The main difference between these experimental cases is the inability of secular forcing to excite energetic inertial–gravity-wave transients during the initial phases of secular spin-up. Thus, the asymptotic theory which has filtered out these initial higher-frequency transients is accurate even though the inertial period is not much smaller than the characteristic spin-up time scale.

The unsteady flow past a circular disk is studied with hot-wire and microphone probes positioned in planes normal to the axis of symmetry at 3 and 9 disk diameters down-stream. Both the fluctuating velocity and pressure signals are shown to be continuously dominated by large-scale coherent motions enveloping the wake flow as a whole. This suggests narrowband two-point space correlations as an experimental tool for describing spatial coherence and phase characteristics of the basically random signals. The specific symmetry imposed by the axisymmetric boundary conditions of the disk enables a decomposition of the large-scale flow phenomena into relatively simple elementary structures or modes. The resulting azimuthal constituents are quantified in terms of their respective magnitudes and individual power spectra.

The capability of the approach to uncover characteristic features of turbulence as far as its large-scale domain is concerned is demonstrated by a comparison of the present results with certain remarkably different features found in earlier jet flow investigations: the m = 1 and m = 2 modes are found to clearly dominate in wakes whereas the m = 0 and m = 1 modes were dominant in jets in a relevant range of Strouhal numbers. These large-scale coherent structures are more than just an interesting flow phenomenon; they must have a tremendou back-reaction on rigid flow boundaries (particularly if these allow a vibrational response) and may give rise to specific feedback mechanisms.

The analysing technique proposed for studying large-scale flow phenomena injets and wakes removes part of the randomness in the turbulent signals without artificially exciting or forcing them in one way or another. No conditional sampling of the naturally occurring fluctuations is required, either. The method may be applicable to other than strictly axisymmetric flow configurations, too.