Using a ‘clean’ jet facility the relationship between the jet flow and its radiation field was studied experimentally in the Mach-number range 0.05 < Mj < 0.20 and a Reynolds-number range 6 × 104 < ReD < 2.3 × 105. The various acoustic source parameters such as strength, frequency and Mach number were varied systematically, and the far-field pressure measured simultaneously. On the basis of these measurements the nature of the sources in the initial shear layer could be characterized. The principal results, equally valid for unexcited and excited jets, are as follows: the acoustic sources are not convected but are located within a confined volume fixed with respect to the nozzle even though they are being generated by moving disturbances in the jet; they are associated with the nonlinear saturation of the unstable wave amplitudes of the shear layer occurring at the vortex-pairing locations; the radiation intensity varies nonlinearly with the source strength and is highly directional, exponential in character.

The present paper is devoted to the experimental study of the noise generated by an airfoil profile placed in a uniform laminar flow. The far-field acoustic spectrum is shown to be composed of a broadband contribution around frequency fs and a discrete contribution at equidistant frequencies fn, which follow power laws of the forms fs ∼ U1.5 and fn ∼ U0.85. Both contributions can be accounted for by a simple model derived from the original suggestions of Tam (1974) and Fink (1975). It is essentially assumed that the diffraction of the Tollmien-Schlichting instabilities by the trailing edge generates acoustic waves which propagate in the far field and also trigger an aeroacoustic feedback loop, whose length is equal to the distance between the trailing edge and the maximum velocity point of the airfoil.

Measurements of space–time correlations of longitudinal and normal velocity fluctuations and of temperature fluctuations support the existence of counter-rotating spanwise structures appearing alternately on opposite sides of the jet centreline in the self-preserving region of the flow. The frequency of these structures closely satisfies self-preservation. The asymmetric arrangement of the structures is first observed downstream of the position where the jet mixing layers nominally merge but upstream of the onset of self-preservation. Closer to the jet exit, the space–time correlations indicate the existence of spanwise structures that are symmetrical about the centreline.

The transport equation for the destruction of temperature fluctuations in a turbulent shear flow is briefly discussed from the point of view of the experimenter's ability to measure the important terms. The transport equation for only one component of the destruction, the mean-square streamwise temperature derivative, is considered in detail in the case of a steady two-dimensional turbulent shear flow. Measurements of most of the terms in this equation have been made in the self-preserving region of a turbulent plane jet. They indicate that the advection and diffusion terms are negligible compared with the production and dissipation terms. The measured terms are discussed in the context of local isotropy. Mean-square values of second-order derivatives satisfy local isotropy more closely than those of first-order derivatives.

A coloured-smoke-visualization technique has been developed for the investigation of complex three-dimensional fluid flows. In particular, a coloured-smoke wire technique is used for the study of secondary flows in straight turbine cascades. Based on a large number of photographs and direct flow observation, the evolution of horseshoe and passage vortices through a high-turning turbine-blade passage is described.

Calculations of the refraction of water waves obliquely incident on a beach indicate that in certain circumstances finite-amplitude waves are refracted to turn in a sense opposite to the refraction of linear waves. This is termed ‘anomalous refraction’. It is demonstrated that similar solutions exist for a wide class of weakly nonlinear dispersive waves. When anomalous refraction solutions exist there are two ‘conjugate’ solutions satisfying the slowly varying wave equations. Properties of the conjugate solutions are given here. Discussion of the possibility of jumps in wave properties between conjugate solutions and their relevance to refraction is in another paper (Peregrine 1983), which shows that the anomalous-refraction solution is not normally relevant on a beach.

Laser-Doppler velocity measurements were obtained in water between finite rotating disks, with and without throughflow, in four cases: ω1 = ω2 = 0; ω2/ω1 = −1; ω2/ω1 = 0; ω2/ω1 = 1. The equilibrium flows are unique, and at mid-radius they show a high degree of independence from boundary conditions in r. With one disk rotating and the other stationary, this mid-radius ‘limiting flow’ is recognized as the Batchelor profile of infinite-disk theory. Other profiles, predicted by this theory to coexist with the Batchelor profile, were neither observed experimentally nor were they calculated numerically by the finite-disk solutions, obtained here via a Galerkin, B-spline formulation. Agreement on velocity between numerical results and experimental data is good at large values of the ratio RQ/Re, where RQ = Q/2πνs is the throughflow Reynolds number and Re = R22ω/ν is the rotational Reynolds number.

Infinite-disk flows appear to possess multiple solutions at E−1 = 275 (Holodniok, Kubicek & Hlavacek 1977), where E = ν/s2ω is the Ekman number. One of these solutions exhibits characteristics of Couette flow and is stable in the circular domain 0 < r/s < 50. The other two solutions, both Poiseuille-type flows, are unstable at all positions. The stable solution shows strong resemblance to experimental profiles obtained between finite disks. Stability of finite-disk flows is investigated in two cases: (i) one disk rotating and the other stationary, and (ii) counter-rotating disks. Photographs indicate presence of two instability types. Theoretical calculations are in fair agreement with experimental evidence on instability of type I.

Simplified proofs are given of the eight basic conservation laws for two-dimensional irrotational flow of a perfect fluid. The corresponding relations for rotational flow are also discussed.

Boundary absorption causes a depletion of contaminant. Since the boundary tends to be the region of lowest velocity and of strongest shear, the remaining contaminant experiences on average an increased advection velocity, a reduced rate of shear dispersion, and a tendency to develop skewness towards the rear. Here it is shown how all these effects can be incorporated into a delay-diffusion description of the longitudinal dispersion process (Smith 1981). It is the accurate reproduction of the skewness that permits a delay-diffusion equation to become applicable at an earlier stage than the more conventional diffusion-equation models for longitudinal dispersion, and before there has been an undue loss of contaminant through the boundary.

Through an extension of the concept of scale invariance we construct two invariance transformations of the equations of gasdynamics: the first is a true Bäcklund transformation, and as such we expect that it should play an important role in the search for new cases of integrability; the other one affects the shape of the entropy profile, implying that the mathematical problems of isentropic and non-isentropic flow are, at least in some cases, equivalent.

That property enables us to deduce the general solution in closed form, assuming a power-law entropy profile of the form P/ργ ≈ 1/M3γ−1, where M is the Lagrangian mass coordinate.

The linearized equations for the final stage of decay of turbulence in a stably stratified fluid are solved by three-dimensional Fourier transformation. For large Prandtl number, slowly decaying almost-horizontal modes of motion are identified. It is argued that these modes explain the experimental observation that patches of turbulence eventually settle out into a set of approximately horizontal striations. The most persistent vertical wavelength for a given geometry is determined and compared with quantitative observations from a set of experiments.

Two-dimensional solitary and periodic waves in water of finite depth are considered. The waves propagate under the combined influence of gravity and surface tension. The flow, the surface profile and the phase velocity are functions of the amplitude of the wave and the parameters l = λ/H and τ = T/ρgH2. Here λ is the wavelength, H the depth, T the surface tension, ρ the density and g the acceleration due to gravity. For $\dot{\tau} >\frac{1}{3}$, large values of l and small values of the amplitude, the profile of the wave satisfies the Korteweg–de Vries equation approximately. However, for τ close to $\frac{1}{3}$ this equation becomes invalid. In the present paper a new equation valid for τ close to 1/3 is obtained. Moreover, a numerical scheme based on an integrodifferential-equation formulation is derived to solve the problem in the fully nonlinear case. Accurate solutions for periodic and solitary waves are presented. The numerical results show that the Korteweg–de Vries equation does not provide an accurate description of periodic gravity-capillary waves for $\tau < \frac{1}{3}$. In addition, it is shown that elevation solitary waves cannot be obtained as the continuous limit of periodic waves as the wavelength tends to infinity. Graphs of the results are included.

Viscous incompressible flow around a circular disk set normal to undisturbed flow is theoretically studied at small values of the Reynolds number. The critical Reynolds number at which a standing vortex first appears behind the disk is zero, and the flow separates from the edge of the disk. Several other features of the flow are obtained from the present analysis.

Linear instability analysis is applied to the slowly diverging mean profile of a turbulent axisymmetric jet and used to predict the transverse structure and axial evolution of large-scale wavelike modes with azimuthal wavenumber m = 1. Comparisons are made with measurements of filtered velocity fluctuations, and of pressure fluctuations, taken in a jet with coherent forcing at the exit plane, at Strouhal numbers St = fD/U0 around 0.5,f = ω/2π being the frequency, D the nozzle diameter and U0 the mean centreline exit velocity. The transverse structure at each axial station is well predicted by linear theory, as is the phase speed and its variation with axial distance. The downstream evolution of amplitude is much less well predicted, presumably because of cumulative nonlinear effects in the experiments, though the inclusion of mean-flow divergence itself constitutes a significant improvement over the theory for parallel flow, and in somecases permits calculation of the wave evolution well into the decay phase without any reference to viscous effects on the disturbance.

In this short note we use the results of numerical solutions of the unsteady Navier–Stokes equations to study the occurrence of separation in unsteady flow. The structure of a flow cycle depends strongly on the Strouhal number, whose value can be classified as small, intermediate or large. In each of these regions different effects are calculated, and we give guidelines for the boundaries of these regions. In particular, we show that the small-Strouhal-number region, in which quasi-steady flow is observed, is very small and decreases rapidly as the peak Reynolds number increases.

Using the semiLagrangian approach of John (1953), both Longuet-Higgins (1982) and New (1983) have proposed simple analytical models of the underside or loop of a plunging breaking wave. Although New's ellipse model appears to be remarkably accurate both in profile and free-surface particle dynamics for a limited region of the loop, both of the loop models are shown to be deficient because neither correctly accounts for the rest of the wave. On the other hand, Longuet-Higgins (1983) gives a semiLagrangian representation of the Dirichlet hyperbola, previously shown to be relevant to the jet of fluid ejected from the top of a breaking wave (see Longuet-Higgins 1980). We show that both this jet flow and the ellipse model of New describing the loop are, for large time, complementary solutions of the same free surface equation. This in turn suggests solutions which combine both the jet and the loop, to give a much more complete model of the entire overturning region not too far from the wave crest, and which has approximately correct free-surface particle velocities and accelerations.

Variations in wave amplitude and steepness across current jets have been described for broad smooth-sided jets. Here, narrow jets are modelled by a top-hat pattern; an approximate solution is found for linear waves, based on conservation of wave action and vertical averaging. The results join remarkably well to those for a broad cosine-shaped jet (cf. McKee 1975). For jet widths less than about a third of a wavelength, there is little change in amplitude; the enhancement predicted by a WKB analysis is suppressed owing to interference with reflections from the far side of the jet. For directional spectra not too different from cos2 θ, some suppression occurs near the middle of jets of all scales, owing to exclusion of the glancing wave components by reflection from the near side; this suppression can be significant for jets more than a wavelength wide. For monochromatic waves, maximum amplitudes occur some distance outside the jet owing to interference; the net reflection appears to have a positive phase shift along the near caustic of about ¼ cycle.

This paper generalizes the linear stability analysis of Pearson for Marangoni instability to the case where surface tension depends on both temperature and solute concentration. The results are expressed in terms of a thermal Marangoni number BT and a solutal Marangoni number BS. It is found when BS > 0 the onset of instability has the form of stationary convection, while when BS < 0 there are circumstances in which the onset of instability is in the form of oscillatory convection.

In a wind tunnel designed for flow-acoustic measurements, the wall-pressure fluctuations beneath a turbulent boundary layer have been investigated. The measurements were carried out with variously sized pressure transducers (19 [les ] d+ [les ] 333) and with an array of four small transducers (separation distance Δx+ = 75). It is shown that the dimensionless diameter d+ = 19 of the transducers is sufficient to resolve the essential structures of the turbulent pressure fluctuations. The power spectrum Φ(ω+) measured with the smallest transducer d+ = 19 partly exhibits power-law decay $\Phi \sim \omega^{\frac{7}{3}}$, which has been theoretically predicted for locally isotropic turbulence. By visual analysis and signal averaging in the time domain, pressure structures with high amplitudes could be detected which have the shape of short wavetrains or pulses. Their characteristic frequency and longitudinal wavelength have the mean values ω+ = 0.52 and λ+ = 145 respectively, and their mean convection velocity amounts to uc/u∞ = 0.53. It was calculated from the measured probability density that these characteristic structures play an important role, although the probability of their occurrence is low. The sources of these wall-pressure structures can be located in the buffer layer of the boundary layer.