A method is developed for determining any thin steady two-dimensional potential flow with free and/or rigid boundaries in the presence of gravity. The flow is divided into a number of parts and in each part the flow and its free boundaries are represented as asymptotic series in powers of the slenderness ratio of the stream. There are three basic flows, having two, one and no free boundaries and called jet flow, wall flow and channel flow, respectively. First the three expansions for these flows are found, extending results of Keller & Weitz (1952). They are called outer expansions to distinguish them from the inner expansions which apply near the ends of the stream or at the junction of two different types of flow. The inner and outer expansions must be matched at a junction to find how the emerging flow is related to the entering flow. This process can be continued to build up any complex flow involving thin streams. The method is illustrated in the case of a wall flow that leaves the wall to become a jet, which includes the case of a waterfall treated by Clarke (1965) in a similar way. In part 2 (to be published) other inner expansions are found and matched to outer expansions, providing the ingredients for the construction of the solutions of many flow problems.

The behaviour of a conserved scalar field in the final period of an axisymmetric turbulent wake is investigated theoretically. Explicit formulae are derived for the behaviour, during and just prior to the scalar field final period, of quantities such as mean concentration, concentration correlations and velocity–scalar or vorticity–scalar cross-correlations. In particular, if τ is the time measured from a virtual origin it is shown that scalar intensity, which decays as τ−5/2, is more persistent asymptotically than turbulence intensity, which displays a τ−7/2 decay. By deriving the scalar field structure as perturbed by the Reynolds stresses acting on mean scalar gradients in the final period it is shown, e.g., that the mean field perturbation dies out at least as rapidly as τ−4, whereas the mean field itself decays as τ−1. Numerical results are presented to display the spatial structure of typical scalar correlations and velocity–scalar cross-correlations, which are compared where possible with non-asymptotic measurements in the wake of a heated sphere.

The Phillips (1960) convected wave equation is employed in this paper to study aerodynamic noise emission processes in subsonic and supersonic shear layers. The wave equation in three spatial dimensions is first reduced to an ordinary differential equation by Fourier transformation, then solved via the WKBJ method. Three typical solutions are required for discussions in this paper. The current results are different from the classical conclusions. The effects of refraction, convection, Mach-number dependence and temperature dependence of turbulent noise emission are analysed in the light of solutions to the Phillips equation. Owing to the inherent restrictions of the WKBJ transformation, the results of the present paper should be applied to wave radiation from shear layers whose thickness is no less than approximately one quarter of a wavelength. Such a condition is satisfied for turbulent round jets with an exit velocity greater than 0·6 times the ambient speed of sound.

A two-dimensional oil slick is examined as it spreads on water under the influence of gravitational and viscous forces. An exact analytical and numerical description of the flow is obtained in a certain rational asymptotic limit. The central result is an expression for the size of the slick as a function of time. This expression contains no free parameters to be empirically determined, and is in substantial agreement with experiment.

This paper deals with nonlinear streaming effects associated with oscillatory motion in a viscous fluid. A previous theory by Holtsmark et al. (1954) for the streaming near a circular cylinder in an incompressible fluid of infinite extent is reconsidered and used to obtain new numerical results, which are compared with earlier observations. The regime of validity of this theory is considered. The condition to be satisfied by the Reynolds number is found to be less stringent than was previously supposed.

The more recent theory by Wang (1968) based on the outer–inner expansion technique is discussed and corrected with the Stokes drift.

The case of an incompressible fluid enclosed between two coaxial cylinders, one of which is oscillating, is considered in detail. New theoretical and experimental results are given for various values of the parameters involved (Reynolds number, amplitude and cylinder radii).

Numerical methods are used to investigate the separated flow over a finite flat plate when the flow at large distances is given by the stream function ψ∞ = −xy and the plate is situated on the x axis from -1 to 1. The range of nominal Reynolds number is 10–800. Reduced-mesh calculations are used for fine resolution of the flow field in the immediate vicinity of the separation point. Streamlines, equi-vorticity lines, and shear stress and pressure gradient at the plate surface illustrate the overall structure of the flow. In each case the streamwise pressure gradient is less than that for undisturbed potential flow and the position of separation is consequently downstream of that predicted by classical boundary-layer theory. The boundary-layer structure in the vicinity of the separation point shows a direct transition between the regular upstream behaviour and Dean's (1950) solution right at separation with no sign whatever of intermediate singular behaviour of the type predicted by Goldstein (1948). The implications of these results for the structure of high Reynolds number, steady, laminar flow are discussed.

Some of the statistical characteristics of the breakdown coefficient, defined as the ratio of averages over different spatial regions of positive variables characterizing the fine structure and internal intermittency in high Reynolds number turbulence, have been investigated using experimental data for the streamwise velocity derivative ∂u/∂t measured in an atmospheric boundary layer. The assumptions and predictions of the hypothesis of scale similarity developed by Novikov and by Gurvich & Yaglom do not adequately describe or predict the statistical characteristics of the breakdown coefficient qr,l of the square of the streamwise velocity derivative. Systematic variations in the measured probability densities and consistent variations in the measured moments show that the assumption that the probability density of the breakdown coefficient is a function only of the scale ratio is not satisfied. The small positive correlation between adjoint values of qr,l and measurements of higher moments indicate that the assumption that the probability densities for adjoint values of qr,l are statistically independent is also not satisfied. The moments of qr,l do not have the simple power-law character that is a consequence of scale similarity.

As the scale ratio l/r changes, the probability density of qr,l evolves from a sharply peaked, highly negatively skewed density for large values of the scale ratio to a very symmetrical distribution when the scale ratio is equal to two, and then to a highly positively skewed density as the scale ratio approaches one. There is a considerable effect of heterogeneity on the values of the higher moments, and a small but measurable effect on the mean value. The moments are roughly symmetrical functions of the displacement of the shorter segment from the centre of the larger one, with a minimum value when the shorter segment is centrally located within the larger one.

A unique stagnation condition is derived as a guide for analysing systems of combined or branched flows through the use of the free-streamline theory and the Schwarz–Christoffel transformation. Moreover, the physical significance of such a condition is illustrated through its application to the analysis of the penetration and deflexion of jets normal to a bounded stream.

The proper corrections for non-parallel flow to the eigenvalues for small disturbances on a nearly parallel shear flow have been determined through a perturbation about the parallel flow solutions. The resulting shifts in the neutral stability curves have been calculated for the Blasius boundary layer, for the two-dimensional jet, and for the two-dimensional flat-plate wake.

A finite-difference method recently developed to study three-dimensional viscous flow is applied here to the supersonic boundary layer on a sharp cone at moderate angles of incidence (α/θ [les ] 2, angle of attack α, cone half-angle θ). The present analysis differs from previous investigations of this region in that (i) boundary-layer similarity is not assumed, (ii) the system of governing equations incorporates lateral diffusion and centrifugal force effects, and (iii) an improved numerical scheme for three-dimensional viscous flows of the type considered here is used. Solutions are shown to be non-similar at the separation streamline with local shear-layer formation. Detailed flow structure, including surface heat transfer, boundary-layer profiles and thickness, and the formation of swirling pairwise symmetric vortices, associated with cross-flow separation, are obtained. Good agreement is obtained between the present theoretical results and the existing experimental data.