The hydromagnetic flow of a thermally stratified fluid confined between two rotating parallel plates is studied. The flow is assumed to be linear, steady and axially symmetric. The flow is driven both mechanically and thermally and general thermal boundary conditions are applied. Attention is focused upon the mechanism controlling the interior fluid (diffusion, Ekman pumping or hydro-magnetic forces) and upon the conditions under which laminated flow (∂v/∂z ≠ 0) may occur. It is found that the occurrence of laminated flow is very sensitive to the thermal boundary conditions and is suppressed by hydromagnetic effects. For mixed boundary conditions, hydromagnetic forces control the interior and laminated flow is suppressed if α [ges ] O(1), where α2 represents the ratio of hydro-magnetic to Coriolis forces. For a constant heat flux, this occurs for a much weaker magnetic field: if α [ges ] O(E¼). For a restricted range of the parameters, a new boundary layer, called the thermomagnetic layer, in which Coriolis, thermal and hydromagnetic forces balance may occur.

Exact solutions in closed form have been found using the singularity method for various quadratic flows of an unbounded incompressible viscous fluid at low Reynolds numbers past a prolate spheroid with an arbitrary orientation with respect to the fluid. The quadratic flows considered here include unidirectional paraboloidal flows, with either an elliptic or a hyperbolic velocity distribution, and stagnation-like quadratic flows as typical representations. The motion of a force-free spheroidal particle in a paraboloidal flow has been determined. It is shown that the spheroid rotates about three principal axes with angular velocities governed by a set of Jeffery orbital equations with the rate of shear evaluated at the centre of the spheroid. These angular velocities depend on the minor-to-major axis ratio of the spheroid and its instantaneous orientation, but are independent of its actual size. The spheroid also translates at a variable speed, depending on its orientation relative to the surrounding fluid, along a straight path parallel to the main flow direction without any side drift or migration. This ‘jerk’ motion obeys a trajectory equation which is size dependent.

A novel technique for injecting buoyancy (heat) into a liquid is described and demonstrated. When buoyancy was injected for a short time a laminar vortex ring formed. Its vertical displacement was found to be only approximately proportional to the square root of time (measured from an apparent initial time). Approximate geometrical similarity was also observed although the Reynolds number decreased from 28 to about 14.

This paper investigates the three-dimensional laminar boundary layer over a blunt body (a prolate spheroid) at low incidence and with reversed flow. Results reflecting the general characteristics of such a problem are presented. More significant are the features relating to the circumferential flow reversal. Some of these features confirm our early hypotheses concerning the existence of a reversed region ahead of separation and the role of the zero-cfθ line in the general context of separation in three dimensions. Other features are unexpected, including the distribution of cfμ and the shape of the separation line. Here cfθ and cfμ denote, respectively, the circumferential and meridional components of the skin friction.

The problem of the pattern of motion realized in a convectively unstable system with spherical symmetry can be considered without reference to the physical details of the system. Since the solution of the linear problem is degenerate because of the spherical homogeneity, the nonlinear terms must be taken into account in order to remove the degeneracy. The solvability condition leads to the selection of patterns distinguished by their symmetries among spherical harmonics of even order. It is shown that the corresponding convective motions set in as subcritical finite amplitude instabilities.

The secondary and tertiary motions which were observed by Elder (1965) during his experimental study of natural convection in a vertical cavity have been obtained in a numerical solution of the Boussinesq equations. Aspect ratios up to 20, Rayleigh numbers up to 3000000, a Prandtl number of 1000, and up to almost 11000 effective mesh points were used.

The paper is the second part of a study of the failure of the insulation of a layer of dielectric fluid of arbitrary volume, occupying a hole in a solid dielectric sheet, when stressed by an applied electric field. In part 1 symmetric and asymmetric equilibria were found for the two-dimensional problem, using an approximation given by Taylor (1968) for the electric field, which is valid for large holes. In this paper axisymmetric equilibria are given for a circular hole, under the same conditions. In addition the points of bifurcation of asymmetric solutions have been found, and provide sufficient information to give the stability characteristics. It is found that when the volume-excess fraction δ exceeds a value of approximately −0·3 instability occurs in an asymmetric form reported earlier for large holes by Michael, O'Neill & Zuercher (1971) in the case δ = 0. For δ < −0·3 the nature of the instability changes to an axisymmetric form of failure associated with a maximum of the loading parameter.

The analysis given shows that axisymmetric displacements of ‘sausage’ mode type, that is, symmetric about a centre-plane, are associated with small changes in the static pressure in the dielectric layer. Such modes have not previously been examined in this context, and in an appendix to this paper Michael & O'Neill give an analysis of them when δ = 0, valid for all hole sizes, by extending the small perturbation analysis of Michael, O'Neill & Zuercher. These modes however do not provide the most unstable displacements for any configuration, and do not therefore affect the stability from a physical point of view.

In a conventional hydrostatic thrust bearing, the lubricant is supplied from the centre and flows radially outwards. It has been found that the load capacity of such a bearing decreases with increasing angular speed of the rotor. The bearing fails when a critical rotor speed is reached at which the load capacity becomes zero. In this paper a modified feeding system is suggested in which the lubricant is supplied from a ring-shaped groove situated between the exits at the centre and the edge of the bearing. Analysis shows that, by reversing the flow direction near the centre, the load capacity of a bearing of proper geometry can be made to decrease at a much slower rate than that of a conventional bearing as the rotor speed increases. The non-central feeding system might be considered for use in high-speed thrust bearings.

The characteristic function defining the eigenvalues of the Orr-Sommerfeld equation is discussed and it is shown how the expected analytic properties of this function can be exploited to generate series expansions defining eigenvalues within the circle of convergence. This technique is applied to the modes arising in the Blasius flat-plate boundary layer (treated as a parallel flow), for which the complex wavenumber α can be expanded as a convergent power series in the complex frequency parameter β in various regions of the β plane. Such power series are effectively equivalent to Fourier expansions and the properties of the latter are used to find the coefficients.

A square-root singularity in the relationship between α and β is found and it is shown how α can, nevertheless, be expressed in terms of β as the sum of one regular series and the square root of a second regular series. The loci of the real and imaginary parts of α have been computed from these series and show the behaviour in the neighbourhood of the branch point.

The series description provides a particularly simple and rapid method of evalauting eigenvalues and their derivatives within any given region.

When a mutually perpendicular horizontal magnetic field and electric current are imposed upon an electrolytic liquid in a tank covered by a lighter nonconducting fluid, the interface can become unstable. In the experiment described in this paper the tank floor is stepped so that only part of the interface becomes unstable. The result is a distinctive arch-like configuration of the electrolyte, which finally disintegrates to break the current path, but which will continue to repeat itself.

This paper deals with two main problems concerning flow in curved alluvial channels. First, the large-scale bottom geometry that develops through the interaction of flow and sediment motion is determined. Second, experiments in an annular flume indicate that the bed is unstable and that this particular instability leads to the formation of a certain number of scour holes. This is explained by a linear stability analysis.

The inviscid transonic flow past a thin wing having swept leading edges, with smooth lift and thickness distributions, is shown to possess an outer nonlinear structure determined principally by a line source and a line doublet. Three domains (the thickness-dominated, the intermediate, and the lift-dominated), representing different degrees of lift control of the outer flow, are identified; a transonic equivalence rule valid in all three domains is established. Except in one domain, departure from the Whitcomb-Oswatitsch area rule is significant; the equivalent body corresponding to the source effect has an increased cross-sectional area depending nonlinearly on the lift. This nonlinear lift contribution results from the second-order corrections to the inner (Jones) solution, but produces effects of first-order importance in the outer flow. Of interest is an afterbody effect dependent on the vortex drag, which is not accounted for by the classical transonic small-disturbance theory.

The structure of turbulence of fully-developed flow through three concentric annuli with small radius ratios was investigated experimentally for a Reynolds number range Re = 2 × 104−2 × 105. Turbulence intensities were measured in three directions, and turbulent shear stresses in the radial and azimuthal direction, in annuli of radius ratios α = 0·02, 0·04 and 0·1, respectively. The results showed that the structure of turbulence for these asymmetric flows is not the same as that for symmetrical flows (tubes and parallel plates). The main difference between symmetrical and asymmetric flows is that, for the latter, the diffusion of turbulent energy plays an important role. This is the reason not only for the non-coincidence of the positions of zero shear stress and maximum velocity, but also for the failure of most turbulence models in calculating asymmetric flows.