In a large-scale process at I.C.I. Mond Division a flocculated suspension of fine solid particles is allowed to settle through an aqueous solution towards the horizontal interface with an underlying denser solution. When the solids have settled into the lower layer they are pumped away and dumped while the clarified upper layer can be safely disposed of or recycled. The passage of the floes through the interface is the rate-determining step in the process, and the analysis of this part of it is the subject of the paper. It is hoped that the analysis may have a much wider application in that the settling process could be used as the basis of a direct laboratory method of measuring properties of floes. At present both the porosity and permeability of flocs are almost impossible to measure directly, but, using the present analysis, the settling of a single floc through two successive density interfaces would provide (in principle) values for both.

Double-diffusive convection is studied for the case where a large coupled diffusion (or cross-diffusion) effect is present. The Soret effect is a familiar example of this cross-diffusion where the flux of the solute depends not only on its own spatial gradient but also on the in situ temperature gradient. The linear stability analysis of double-diffusive convection has been extended to include the two cross-diffusion flux terms and it has been shown that, with a sufficiently large coupled diffusion effect, fingers can form even when the concentrations of both components make the fluid's density gradient statically stable. The conditions under which the diffusive instability can occur are compared with those for the formation of fingers and it is shown that these two types of double-diffusive convection cannot occur together in any particular set of linear property gradients. We then consider finite-amplitude, steady, infinitely long fingers and show that a sufficiently large cross-diffusion effect can again allow fingers to exist when the concentrations of both solutes increase with depth. It is also shown that the diffusion of properties from an initially sharp interface may set up vertical gradients that are favourable for the formation of fingers.

Measurements of mean axial velocity have been obtained in two perspex models which simulate important features of gas-turbine combustors and are compared with calculations based on the numerical solution of the three-dimensional equations that represent conservation of mass and momentum. The measurements show, for example, the effect of primary jet trajectory on the magnitude and proportion of total mass flow contained in the primary vortex. They also allow the value of the calculation method to be appraised and, in this context, it is shown that the local velocity values are subject to large errors in small regions of the flow but important parameters, such as the length of the primary vortex, are represented more than adequately for engineering purposes. Errors due to numerical approximations appear to be at least as important as those due to the two-equation turbulence model used to represent turbulent features of the flow.

The steady laminar flow driven by the meridional electromagnetic force due to an electric-current point source on a plane is considered. The previous studies of the problem (Shercliff 1970; Shilova & Shcherbinin 1971) lead to a self-similar solution of the full Navier–Stokes equations analogous to the classic Landau jet. The solution breaks down when a critical electric-current magnitude is exceeded (Sozou 1971). In the present paper the converging meridional flow is shown to be unstable to an axisymmetric azimuthal perturbation when the corresponding critical Reynolds number is exceeded. The flow solution breakdown is eliminated for the coupled converging and rotating flow. The physical process is suggested by the draining-vortex formation. The fluid-flow equations are solved by the Galerkin method, using expansions in Gegenbauer functions. The mechanism sustaining the rotation is examined; the increased angular momentum in the fluid region is maintained by the balance of viscous diffusion upstream and convection to the axis of symmetry. The experimental evidence for vortex formation is considered.

Gaseous flow in a pie-shaped cylinder of infinite length rotating about the apex is considered. The horizontal flow is induced either by the temperature distribution or by the source/sink distribution on the walls θ = constant. It is found that along the vertical walls θ = constant the E½ boundary layer is formed, where E is the Ekman number. Although the equation governing the above boundary layer is very similar to that of the Ekman layer, it is a new type of boundary layer which may be called the buoyancy layer. Along the wall on which r is constant thermal boundary layers very similar to the Stewartson layers are found to be formed. The role of these layers is to mediate the temperature jump. These layers disappear in the incompressible limit.

Two-dimensional boundary-layer flows of water down an inclined table were investigated in both the laminar and turbulent regimes. Mean, r.m.s. and skewness and velocity spectra were determined from streamwise velocity measurements. Two laser-Doppler anemometry methods were developed (for studying polymer-solution flows using this same water table) and compared with measurements obtained using hot-film anemometry. All three techniques obtained consistent results.

An analysis based on a von Mises transformation is presented which accurately predicts the mean-velocity profile and flow development in the laminar regime. High strain rates are achieved which can be varied independently of Reynolds number, and turbulent flows are easily generated by inserting a disturbance. These turbulent flows are surprisingly similar to more commonly investigated turbulent boundarylayer flows of much greater y+ extent. Turbulent water-table flows typically extend only to y+ = 100, yet mean velocity essentially follows the law of the wall, and intensity and skewness measurements are similar to those obtained in flows much less limited in y+.

Sufficient stability conditions are derived for a zonal flow on the β-plane or the sphere. Two conditions guarantee both shear stability (to perturbations with vanishing zonal average) and inertial stability (to longitude-independent perturbations). These conditions are not restricted to normal-mode disturbances, and are derived without making use of the quasi-geostrophic approximation. The main limitation of the model is to have only one layer.

On the β-plane, the conditions are: (i) that the product of the meridional gradient of potential vorticity and the difference between an arbitrary constant and the zonal velocity be everywhere non-negative; and (ii) that the absolute value of this difference be nowhere larger than the local phase speed of long gravity waves. Inertial stability is independently assured if the Cariolis parameter and the potential vorticity are everywhere of the same sign (this well-known condition can be easily violated near the equator, but the flow may nonetheless be stable).

If the meridional gradient of potential vorticity has everywhere the same sign, then conditions (i) and (ii) can be shown to be consequences of the conservation of a total pseudo-energy E0 and pseudomomentum P0, defined so that their lowest-order contribution is quadratic in the deviation from the fundamental state (even in the case that the perturbation is longitude-independent). Thus, if there exists a value of α such that the integral of E0 − αP0 is positive-definite, then the flow is stable. In this case, the stability conditions are valid for small, rather than infinitesimal, perturbations.

The parameters of stable flows, as guaranteed by these conditions, are investigated for the family of Gaussian jets centred at the equator; both the cases of an unbounded ocean and a semi-infinite ocean, poleward from a zonal wall, are considered. Easterlies with the width of a Kelvin wave and westerlies with that width or wider may be unstable, even though the gradient of potential vorticity is positive for any strength of the jet.

When a liquid evaporates under vacuum, its free surface is potentially unstable to local variations in evaporative flux, surface depressions being produced by the recoil force of the departing vapour and sustained convection in the liquid being driven by the shearing action of the vapour on the distorted liquid surface. For a binary mixture, local variations in evaporative flux may be produced by fluctuations in both surface concentration and temperature. With the aid of linear hydrodynamic-stability theory, this paper examines the extents to which key mass-transfer properties affect the interfacial stability of the system. The mass-transfer aspects that distinguish this problem from its heat-transfer analogue centre on the dependence of relative volatility on temperature and composition as well as the importance of the bulk-flow term in Fick's law. Results indicate that the stability criteria for interfacial convection are extremely sensitive to the difference in volatility between the two components, that the destabilizing effects of surface concentration and temperature on evaporative flux are additive in determining stability limits, and that for certain operating pressures spontaneous convection can only be induced by adverse concentration gradients. Attention is limited to low-surface-tension mixtures for which there are no concentration effects on surface tension (Marangoni instability).

Measurements of the surface-height profile and the vertical distributions of velocity and total head were made behind a two-dimensional fully submerged hydrofoil moving horizontally at constant speed and angle of attack. These measurements were used to resolve the drag on the foil into two parts: one associated with the turbulent breaking region that is sometimes present on the forward face of the first wave, and the other associated with the remaining non-breaking wavetrain. It was found that at ‘incipient breaking’ the first wave existed in either a breaking or a non-breaking state depending on the starting procedures. It was possible to induce steady breaking when the wave slope was 17° or higher. The wake survey measurements showed that the drag associated with breaking reached more than three times the maximum drag that could theoretically be obtained with non-breaking waves. The drag associated with breaking was found to be proportional to the downslope component of the weight of the breaking region.

Time-dependent convection motions in the form of rolls in a thin vertical fluid layer (Hele-Shaw cell) heated from below are investigated numerically. Perpendicular to the convection-roll axis the fluid is bounded by parallel adiabatic rigid sidewalls. Stress-free top, bottom and end boundaries are assumed. The horizontal extension of the convection rolls is described by the wavenumber α. Solutions for the time-dependent behaviour of the convective motion are presented for a range of wavenumbers between α = ½π and 2π. The onset of the oscillation is shifted to higher Rayleigh numbers with increasing wavenumber. The oscillatory Hele-Shaw convection is caused by an instability of the thermal boundary layer, as is evident from the plotted temperature field and streamlines. From the variation of the Nusselt number with time it is found that the oscillatory motion starts with a sinusoidal time dependence and passes into a periodic state with several frequencies as the Rayleigh number is increased. Quantitative and qualitative agreement with previous experimental and numerical results is found.

The dynamics of a viscous particle surrounded by an elastic shell of arbitrary thickness freely suspended in a general linear flow field is investigated. Assuming the unstressed shell to be spherical, an analysis is presented for the case in which the flow-induced deformation leads to small departures from sphericity. The general time-dependent evolution of shape is derived and various special cases (purely elastic sphere, rigid and gaseous interior, elastic membranes) are discussed in detail. It is found that for steady-state flows the equilibrium deformations are absolutely stable and depend only upon the shell thickness, although the rates at which they are attained show the effect of the inside viscosity, too.

In liquid columns (Prandtl number 8·9) with free cylindrical surface heated from above, strong thermocapillary convection (TC) has been observed. Stationary thermocapillary convection exists in the form of a single axially symmetric roll bound to the free surface. For aspect ratios l/a < 1 the radial extension of the roll equals the zone length. The stream velocities and the temperature distribution were measured.

The influence of buoyant forces due to horizontal temperature gradients in the experiments was also studied. Buoyant forces become obvious for a contaminated free surface and in bulk regions far from the cylinder surface.

The thermocapillary convection shows a transition to time-dependent oscillatory motion when a critical Marangoni number Mac is exceeded. A unique Mac = 7 × 103 has been found for zones with lengths l < 3·5 mm. The oscillatory state of thermocapillary convection has experimentally been proved to be a distortion of the laminar state in form of a wave travelling in the azimuthal direction. A unique non-dimensional wavenumber ≈ 2·2 (near Mac) of the distortion has been found. The non-dimensional frequency of the temperature oscillations is independent of zone size if the aspect ratio is held constant. However, the non-dimensional frequency of temperature oscillations increases linearly with the aspect ratio of the zone. This result is interpreted as a dependence of the phase velocity of the running disturbance on the aspect ratio.