The inviscid spatial growth of spiral modes of circular, slowly diverging jets is analysed. A multiple-scales expansion is used to develop a linear stability study for non-axisymmetric disturbances of arbitrary helicity. The numerical evaluation is restricted to axisymmetric modes and to the first two helical modes. It is shown that in the case of comparatively high values of the Strouhal number the modes exhibit a very rapid growth and reach their maximal amplification after a short distance, the axisymmetric instabilities being excited more strongly than their spiral counterparts. Contrary to this, the modes grow comparatively slowly in the case of smaller values of the Strouhal number and exhibit their maximal amplification further downstream. In the latter case the first spiral mode is more unstable than the axisymmetric one. A comparison with experiments seems to support these results.

The 106th Euromech Colloquium on instability and convection driven by body forces in fluid layers was held in Grenoble from 11 to 14 September 1978 with the first two authors acting as chairmen. There were sixty-five participants coming from fifteen different countries and having widely different backgrounds. Fifty-seven papers were presented during the four full days of the meeting and are discussed in this report with the purpose of giving an up-to-date view of current research in convection.

This paper presents a theoretical and experimental investigation into a novel class of water-wave motions in narrow open channels. The distinctive condition on these motions is that the lines of contact between the free surface and the sides of the channel are fixed, which condition bears crucially on the hydrodynamic effects of surface tension. Most of the account concerns travelling waves in channels of rectangular cross-section that are exactly brimful, but the relevance of this prototype to other, more usual situations is explained with reference to the phenomenon of contact-angle hysteresis.

In § 2 a linearized theory is developed which poses an eigenvalue problem of unusual kind. Unlike the familiar and much simpler problem corresponding to mobile lines of contact at which the free surface remains horizontal, the new problem has no explicit solution and the edge conditions are not automatically compatible with the kinematic conditions at the solid boundaries. Treatment by functional analytic methods is necessary to verify that solutions exist having physically appropriate properties, but this approach gives a final bonus in securing comparatively easy estimates for some of these properties. A variational characterization of the eigenvalues is used to settle questions of existence and the ordering of possible wave modes, and finally to establish approximate formulae relating wavelength to frequency.

In § 3 experiments are reported which were performed with clean water filling three channels made of Perspex. Over continuous ranges of frequency, delimited so that only the fundamental progressive-wave mode was generated, wavelengths were measured by an electronic technique. The measurements agree well with the theoretical predictions, diverging markedly from behaviour to be expected in the absence of edge constraints.

Appendix A outlines a supplementary theoretical argument proving that the first eigenvalue of the problem treated in § 2 is always simple. Appendix B reviews three generalizations of the theory.

The flow of grid-generated turbulence past a circular cylinder is investigated using hot-wire anemometry over a Reynolds number range from 4·25 × 103 to 2·74 × 104 and a range of intensities from 0·025 to 0·062. Measurements of the mean velocity distribution, and r.m.s. intensities and spectral energy densities of the turbulent velocity fluctuations are presented for various radial and circumferential positions relative to the cylinder, and for ratios of the cylinder radius a to the scale of the incident turbulence Lx ranging from 0·05 to 1·42. The influence of upstream conditions on the flow in the cylinder wake and its associated induced velocity fluctuations is discussed.

For all measurements, detailed comparison is made with the theoretical predictions of Hunt (1973). We conclude the following.

1. The amplification and reduction of the three components of turbulence (which occur in different senses for the different components) can be explained qualitatively in terms of the distortion by the mean flow of the turbulent vorticity and the ‘blocking’ or ‘source’ effect caused by turbulence impinging on the cylinder surface. The relative importance of the first effect over the second increases as a/Lx increases or the distance from the cylinder surface increases.

2. Over certain ranges of the variables involved, the measurements are in quantitative agreement with the predictions of the asymptotic theory when a/Lx [Lt ] 1, a/Lx [Gt ] 1 or |k| a [Gt ] 1 (where k is the wavenumber).

3. The incident turbulence affects the gross properties of the flow in the cylinder wake, but the associated velocity fluctuations are probably statistically independent of those in the incident flow.

4. The dissipation of turbulent energy is greater in the straining flow near the cylinder than in the approach flow. Some estimates for this effect are proposed.

A statistical model based on the proposition that the turbulence of a fully developed two-dimensional incompressible mixing layer is in a state of quasi-equilibrium is developed. In this model the large structures observed by Brown & Roshko (1974) which will be assumed to persist into the fully developed turbulent region are represented by a superposition of the normal wave modes of the flow with arbitrary random amplitudes. The turbulence at a point in the flow is assumed to be dominated by the fluctuations associated with these large structures. These structures grow and amalgamate as they are convected in the flow direction. Because of the lack of intrinsic length and time scales the turbulence in question can, therefore, be regarded as created or initiated at an upstream point, the virtual origin of the mixing layer, by turbulence with a white noise spectrum and are subsequently convected downstream. The model is used to predict the second-order turbulence statistics of the flow including single point turbulent Reynolds stress distribution, intensity of turbulent velocity components, root-mean-square turbulent pressure fluctuations, power spectra and two-point space-time correlation functions. Numerical results based on the proposed model compare favourably with available experimental measurements. Predictions of physical quantities not yet measured by experiments, e.g. the root-mean-square pressure distribution across the mixing layer, are also made. This permits the present model to be further tested experimentally.

Free-flight and wind-tunnel measurements by previous investigators of the flat-plate autorotation phenomenon have been analysed. The variation of the autorotation characteristics with changes in the Reynolds number and the aspect ratio, thickness ratio and moment of inertia of the flat plate have been correlated. The interpretation of the role of the Reynolds number made in a previous investigation is shown to be incorrect. The tip-speed ratio, for the ranges of the dimensionless parameters investigated, is shown to be a function of only the plate aspect ratio, thickness ratio, and also the moment of inertia if the latter is sufficiently small. The lift and drag coefficients, and therefore the free-flight glide angle, are shown to be functions of the tip-speed ratio, the aspect ratio and the Reynolds numbers based on the chord and plate thickness.

The generation of internal waves by resonantly interacting surface waves is examined in the framework of spectral scattering theory in the random-phase approximation. Coupling coefficients are derived from Euler's equation of motion for arbitrary stratification. The spectral energy transfer is discussed for deep-water surface waves and a simple three-layer model of the stability frequency. Analytical and numerical evaluation of the transfer integral leads to a parametrization in terms of the basic model parameters. These are the depth, thickness and stability frequency of the thermocline and the scale parameters and bandwidth of the surface wave spectrum. Strong dependence on some of these parameters, in particular the surface wave energy and the ratio of surface and internal wave frequencies, indicates a large spatial and temporal variability of the transfer rate. The transfer to the internal wave field in the oceanic main thermocline is found to be negligible compared with the effect of other processes. High frequency waves in the seasonal thermocline may be generated very efficiently.

The flow past a cylinder bounded by parallel planes in a rotating frame is treated in terms of a nonlinear Stewartson layer. It is shown that separation is strongly dependent on the ratio of the Rossby number to the square root of the Ekman number, covering the whole range from fully attached flow to the classical non-rotating separated flow past a cylinder. The results are in agreement with published experimental observations.