Parallel flows with step function velocity and density profiles can support waves which have negative energy, in the sense that exciting them lowers the total energy of the system. A number of instabilities can occur because of the coexistence of positive and negative energy waves, or because of the damping of negative energy waves; some particular examples are discussed to show how appreciation of this role of negative energy waves allows one to predict the existence of instability before doing any detailed analysis, and to gain insight into the instability mechanism.

The effect of pair interactions between charged macromolecules on the bulk stress is calculated for the Newtonian low-shear limit. Electrostatic force laws are derived for molecular conformations corresponding to the limits of weak and strong intramolecular repulsions and used to determine the equilibrium pair distribution function and the perturbation due to the flow. Intramolecular and near-field intermolecular hydrodynamic interactions are neglected as appropriate for so-called free draining macromolecules. The resulting bulk stress contains separate contributions from the far-field hydrodynamic interactions and the electrostatic forces. The coefficient of the O(c2) term in the viscosity which equals 0.4 in the purely hydrodynamic limit is predicted to increase dramatically with decreasing ionic strength for charged macromolecules in agreement with experimental data in the literature.

Kr, Xe and SiCI4 have been investigated for convective instabilities in closed vertical cylinders with conductive walls heated from below. Critical Rayleigh numbers NiRa for the onset of various convective modes (including the onset of marginally stable and periodic flow) have been determined with a high resolution differential temperature sensing method. Flow patterns were deduced from a multiple sensor arrangement. For the three lowest modes (i = 1, 2, 3) good quantitative agreement with linear stability theory is found. Stable oscillatory modes (periodic fluctuations of the mean flow) with a period of approximately 5 s are found for a relatively narrow range of NRa. The critical Rayleigh number NoscRa for the onset of oscillatory temperature fluctuations is 1348 ± 50 for an aspect ratio (height/radius) of 6.

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.

Non-reactive binary gas mixtures (Xe + He, SiCl4 + H2) have been investigated for convective instabilities in closed vertical cylinders with conductive walls heated from below. Critical Rayleigh numbers NiRa for the onset of various convective modes (including the onset of marginally stable and periodic flow) have been determined with a high resolution differential temperature sensing method. It is found that the second component can significantly alter the hydrodynamic state of the fluid compared to the monocomponent behaviour. Considerably lower critical thermal Rayleigh numbers for steady and time dependent convective modes are observed. The Xe : He system shows stable oscillatory modes similar to those observed in monocomponent gases (periodic disturbances of the mean flow, T0 ≈ 5 s) from NRa = 713 to 780, where a new mode with T0 = 15 s sets in. The frequency of these slower temperature oscillations can be fitted by an equation of the form f2 = k’(NRa − N0Ra) where k’ and N0Ra are constants, which supports the contention that these oscillations are the result of vertical vorticity. For SiCl4 : H2 the high frequency oscillations occur only as a transient mode eventually evolving into the low frequency mode characteristic of binary gas mixtures. This low frequency state is degenerate with a stable time-independent state over a considerable range of NRα. Finite amplitude perturbations can lead to (1) transient oscillatory phenomena accompanied by reorientations of the roll cells with mean periods of 3–5 min; and (2) stable oscillatory flow at NRa 's considerably below NoscRα. The unique behaviour of these binary fluids is tentatively assigned to thermal diffusion.

The distortion by a linear flow of the electric double layer around a small particle is studied for the case of a charge cloud which is thick in comparison with the particle radius and for arbitrary flow strengths, including those which are strong enough to produce a significant distortion of the cloud. For weak flows a second-order-fluid approximation is obtained for the stress contribution for a dilute suspension of such particles. For arbitrarily strong flows integral representations of the charge density and numerical calculations of the stress contribution are given for three representative flows: simple shear, axisymmetric strain and two-dimensional straining motion.

Cairns (1979) has recently shown how the concept of negative wave energy used in plasma physics can be exploited to obtain insights into the linear and nonlinear instability of certain parallel flows. We here analyse the linear stability and nonlinear three-wave resonance in a three-layer flow with step-wise velocity and density profiles. The results are in complete agreement with Cairns’ qualitative predictions. In particular, the existence is confirmed of an ‘explosive’ instability in which all three waves of a resonant triad grow simultaneously while total wave energy is conserved. Such nonlinear instabilities, previously undetected in fluid flows, may well be important in the ocean and atmosphere.

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 studies the effect of alternating or rotating magnetic fields on containers of conducting fluid. The magnetic Reynolds number is assumed small. The frequency of alternation or rotation is rapid so the magnetic field is confined to a thin layer on the surface of the container. A boundary-layer analysis is used to find the rate of vorticity generation due to the Lorentz force. When the container is an infinitely long cylinder of uniform cross-section, alternating fields normal to the generators or fields rotating about an axis parallel to the generators generate vorticity at a constant rate. For containers of any other shape the rate of vorticity generation includes both constant and oscillatory terms. A perturbation analysis is used to study the flow induced in a slightly distorted circular cylinder by a rotating field. Complex flows develop in the viscous-magnetic boundary layer which may be unstable.

Surface streamline patterns on a spheroid have been examined at several angles of attack. Most of the tests were performed at low Reynolds numbers in a hydraulic flume using coloured dye to make the surface flow visible. A limited number of experiments was also carried out in a wind tunnel, using wool tufts, to study the influence of Reynolds number and turbulent separation. The study has verified some of the important qualitative features of three-dimensional separation criteria proposed earlier by Maskell, Wang and others. The observed locations of laminar separation lines on a spheroid at various incidences have been compared with the numerical solutions of Wang and show qualitative agreement. The quantitative differences are attributed largely to the significant viscous-inviscid flow interaction which is present, especially at large incidences.

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.

Using the principles of continuum mechanics, a theory is developed for describing quantitatively the sedimentation of small particles in vessels having walls that are inclined to the vertical. The theory assumes that the flow is laminar and that the particle Reynolds number is small, but c0, the concentration in the suspension, and the vessel geometry are left arbitrary. The settling rate S is shown to depend upon two dimensionless groups, in addition to the vessel geometry: a sedimentation Reynolds number R, typically O(1)-O(10); and Λ, the ratio of a sedimentation Grashof number to R, which is typically very large. By means of an asymptotic analysis it is then concluded that, as Λ → ∞ and for a given geometry, S can be predicted from the well-known Ponder-Nakamura-Kuroda formula which was obtained using only kinematic arguments. The present theory also gives an expression for the thickness of the clear-fluid slit that forms underneath the downward-facing segment of the vessel walls, as well as for the velocity profile both in this slit and in the adjoining suspension.

The sedimentation rate and thickness of the clear-fluid slit were also measured in a vessel consisting of two parallel plates under the following set of conditions: c0 ≤ 0·1, R ∼ O(1), O(10)5 ≤ Λ ≤ O(107) and 0° ≤ α ≤ 50°, where α is the angle of inclination. Excellent agreement was obtained with the theoretical predictions. This suggests that the deviations from the Ponder-Nakamura-Kuroda formula reported in the literature are probably due to a flow instability which causes the particles to resuspend and thereby reduces the efficiency of the process.

A constitutive equation appropriate for flow of cohesionless granular materials at high deformation rates and low stress levels is proposed. It consists of an extension and a reinterpretation of the theory of Goodman & Cowin (1972), and accounts for the non-Newtonian nature of the flow as evidenced by Bagnold's (1954) experiments. The theory is applied to analyses of gravity flows in inclined chutes and vertical channels. Experiments were set up in an attempt to generate two-dimensional shear flows corresponding to these analyses. Velocity profiles measured by a technique which makes use of fibre optic probes agree qualitatively with the theoretical predictions, but direct comparison is inappropriate because of unavoidable side-wall friction effects in the experiments. The existing measure of agreement suggests that the most prominent effects have been included in the proposed constitutive relations. Tests in the inclined chute revealed the possible existence of surge waves and granular jumps analogous to hydraulic jumps.

The small amplitude stability analysis for the onset of double-diffusive convection when the density gradient is gravitationally stable is extended to include a third diffusing component. Special attention is given to systems with κ1 [Gt ] κ2, κ3 and Pr [Gt ] κ/κ1, where κi is the molecular diffusivity of the ith component and Pr is the Prandtl number based on the largest of the Ki. It is found that the boundary for the onset of overstability is approximated by two straight lines in a Rayleigh number plane. Small concentrations of a third property with a smaller diffusivity can have a significant effect upon the nature of diffusive instabilities, the magnitude of this effect being proportional to κ1/Ki. Oscillatory and direct ‘salt-finger’ modes are found to be simultaneously unstable under a wide range of conditions when the density gradients due to the components with the greatest and smallest diffusivities are of the same sign.

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.

Interferometric data were obtained in the UTIAS 10 × 18 cm hypervelocity shock tube of oblique shock-wave reflexions in nitrogen at initial temperatures and pressures of about 300 K and 15 torr. The shock-Mach-number range covered was 2 ≤ Ms ≤ 8 over a series of wedge angles 2° ≤ θw ≤ 60°. Dual-wavelength laser interferograms were obtained by using a 23 cm diameter field of view Mach-Zehnder interferometer. In addition to our numerous results the available data for nitrogen, air and oxygen obtained over the last three decades were also utilized. It is shown analytically and experimentally that in non-stationary flows seven domains exist in the (Ms, θw) plane where regular reflexion (RR), single-Mach reflexion (SMR), complex-Mach reflexion (CMR) and double-Mach reflexion (DMR) can occur. In addition, the transition boundaries between these regions were established. The experimental results from many sources substantiate the present analysis, and areas of disagreement which existed in the literature are now clarified and resolved. It is shown that real-gas effects have a significant influence on the size of the regions and their boundaries. The comprehensive, accurate and sensitive isopycnic data will form a base for comparing existing and future numerical analyses of such complex flows.

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.

Details of flow visualization, aerodynamic forces and pitching moment, static pressure and skin friction measurements have been carried out on a symmetrical aerofoil at fixed angle of incidence in longitudinal oscillations parallel to the uniform airstream of a wind-tunnel.

This investigation shows weak unsteady effects at incidences below that of static stall. For higher incidences, strong unsteady effects appear and depend on the frequency and amplitude of the oscillations. The measurements indicate an overshoot of the instantaneous lift and drag which is explained by a strong vortex shedding process occurring during the dynamic stall encountered by the aerofoil in decelerated motion, as observed for profiles oscillating in pitch through stall. When the aerofoil is going forward in accelerated motion dynamic reattachment may be observed at very high incidence over a short part of the period of oscillation.

Dynamic stall and dynamic reattachment contribute to a favourable effect of unsteadiness on the mean lift coefficient, which increases as compared to the steady state one, and which is expressed through an empirical formula involving incidence, frequency and amplitude of oscillations. At given incidence, optimization of this feature is achieved by matching the frequency and the amplitude of oscillation, respectively with the frequency linked with the highest peak of energy in the wake, and with the distance between two consecutive vortices in the mean wake when modelled as a von Kármán's vortex street.

It is shown that a symmetrical vortex pair consisting of equal and opposite vortices approaching a plane wall at right angles must approach the wall monotonically in the absence of viscous effects. An approximate calculation is carried out for uniform vortices in which the vortices are assumed to be deformed into ellipses whose axis ratio is determined by the local rate of strain according to the results of Moore & Saffman (1971).

The weakly reactive state leading to the ignition of a steady laminar boundary-layer flow of a combustible mixture over a hot, isothermal, non-permeable, non-catalytic flat plate is studied both numerically and using matched asymptotic analysis in the realistic limit of large activation energy. It is shown that the flow consists of a locally similar diffusive-reactive region next to the plate and a non-similar diffusive-convective region outside it; that the analytic solution obtained reproduces the lower half of the S-shaped ignition-extinction response curve such that ignition is expected to occur when a suitably defined Damköhler number, which increases with the streamwise distance, reaches unity; and that at the point of ignition the heat transfer from the wall vanishes identically. An explicit expression for the minimum distance for ignition to occur is also derived.