A proof is given that, in spite of certain singularities in the oblique area distributions, the supersonic area rule can be used to determine correctly the wave drag, according to linearized theory, of thin symmetrical rectangular wings at zero incidence. The proof could be extended to cover the case of swept wings with supersonic edges, for which similar singularities also exist.

An exothermal hydromagnetic discontinuity in a perfectly conducting gas is studied for the case of an arbitrarily orientated magnetic field. The evolutionary modes and the manner of variation of the physical properties for such phenomena are determined. The Hugoniot adiabatic is obtained and analysed.

The effect of combustion or heating on a slightly non-uniform flow in a tube of constant radius is explored by examining a simplified model, in which a density decrease occurs across a plane actuator-disk normal to the axis of the tube. The flow is considered to be steady, axi-symmetric, incompressible and inviscid and to originate at an injector-plate which is situated upstream of the disk. This paper analyses and discusses the effects caused by the density decrease when the velocity of flow through the injector-plate has a fractional non-uniformity ue, when there is a curvature θe, of the injector-plate, and when the density decrease has a fractional non-uniformity δ2. It is shown that the non-uniformity of the flow far downstream of the disk caused by the disturbances ue and θe is diminished by the density decrease; while that due to the disturbances δ2 is increased, unless the density decrease occurs close to the injector-plate. The distance separating the injector-plate and actuator-disk is found to be an important parameter. When this distance is small, compared to the radius of the tube, and the density decrease is severe, a small disturbance ue, θe or δ2 may set up a pressure variation at the injector-plate of many times the inlet dynamic pressure of the flow. It is conjectured that this pressure variation could affect the uniformity of velocity and composition of the flow through the injector-plate, and thus cause the disturbances ue and δ2 to grow or diminish.

A series of flat-plate laminar boundary layer experiments carried out in an arc-heated supersonic wind tunnel is described. Measurements of the static pressure distribution, the total pressure profiles through the boundary layer, and the heat-transfer rates to catalytic and non-catalytic surfaces at moderately high enthalpies are given and compared with various theoretical predictions. The observations indicate that the dissociation fraction affects the boundary-layer profiles through its influence on the local transport properties. It is confirmed that the atomic recombination at the surface is retarded by using a non-catalytic oxide coating, and hence the heat transfer to the wall is reduced.

The decay of perturbations in an infinite, thermally radiating gas of perfect electrical conductivity in the presence of magnetic field is studied. Complete solutions for the decay of initial sinusoidal perturbations in the temperature, gas velocity and pressure are determined. The sinusoidal perturbations are superposed to yield solutions for the decay of initial ‘step’ temperature profiles consisting of a constant initial temperature perturbation inside a finite planar region, with zero temperature perturbation outside. For a broad range of small and intermediate Boltzmann numbers the cooling proceeds in time from being a constant-density cooling process to being a constant-pressure cooling process. The magnetic field causes slower temperature decay with time and makes the temperature perturbations tend to attain constant-pressure cooling values. It quickens the decay of velocity and pressure perturbations and thus the transition from a constant-density to a constant-pressure cooling process is hastened. This transition is produced by the magneto-acoustic waves generated near the profile edges by the radiative cooling.

A theoretical analysis is made of the effect described in the title. It is shown that both (i) the eigenfrequencies of the inertial waves and (ii) the moment produced by the inertial wave pressure distribution are independent of the location of the off-axis cylinders. Hence, one can use Stewartson's tables computed for a centrally located cylinder to calculate the frequencies and residues for an eccentrically located cylinder.

Consider the flow of an incompressible fluid between two infinite concentric circular cylinders. The outer cylinder is at rest whilst the angular velocity of the inner cylinder has a steady part and also a harmonically oscillating component. We examine the situation where, for a suitable choice of parameters, two types of vortex instability can occur simultaneously; first a short-wavelength mode which is essentially trapped in a thin ‘Stokes’ layer near the inner cylinder and, secondly, a long-wavelength mode which fills the whole region between the cylinders. We investigate the problem in which two short-wavelength vortices and one long-wavelength vortex coexist and are such that each pair interacts to drive the third. Additionally, the short-wavelength disturbances are nonlinear in their own right. Coupled amplitude equations for the three modes are derived and their solution discussed.

This form of interaction may also take place in a boundary layer. Such a situation is more complex than that under consideration here as it would be necessary to take into account the growth of the boundary layer. However, this simplified problem gives an insight into the behaviour of the more difficult situation.

Henry & Roux have recently conducted extensive numerical studies on the interaction of Soret separation with convection in cylindrical geometry. Many of their solutions exhibit parallel flow away from endwalls. We show that their parallel flow results can be matched by closed-form solutions. We find that solutions are non-unique in some parameter regions. Disappearance of one branch of solutions correlates with a sudden transition of Henry & Roux's results from a separated to a well-mixed flow.

Laminar flow through slots is investigated using a flow-visualization technique and the numerical solution of the Navier-Stokes equations for steady flow. In the flow situation studied here, the fluid enters an upper channel blocked at the rear end and leaves through a lower channel blocked at the front end. The two channels are interconnected by one, two and three slots. The flow-visualization technique effectively brings out the various features of the flow through slot(s). The ratio of the slot width to the channel height w/h is varied between 0.5 to 4.0 and the Reynolds number Re, based on the velocity at the entry to the channel and the height of the channel, is varied between 300 and 2000. Both w/h and Re influence the flow in general and the extent of the regions of recirculating flow in particular. The Reynolds number at which the vortex shedding begins depends on w/h. Computations are carried out using the computer code 2/E/FIX of Pun & Spalding (1977). The computed flow patterns closely resemble the observed patterns at various Reynolds numbers investigated except around the Reynolds number where the vortex shedding begins.

We use the method of Phythian & Curtis (1978) to obtain a self-consistent calculation, in lowest order of perturbation theory, for the α-coefficient and effective diffusivity of a magnetic field in a plasma with Gaussian turbulence.

Laboratory measurements on the instability of axisymmetric capillary surfaces pinned to the corners of annular grooves of rectangular section rotating at constant angular velocity Ω have been conducted. In stable configurations the fluid contact lines remain pinned to the corners of the groove with contact angles θ1,2 relative to the inner and outer vertical walls. Using water as the test fluid in narrow grooves of nearly constant width, the critical frequency Ωc for instability generally decreases with increasing overfill volume ΔV and mean groove radius. Numerical integration of the describing equation gives the shape of the rotating meniscus as a function of five independent parameters. In the range of contact angles θ1, 2 < π, a comparison of experimental results with numerically computed meniscus profiles suggests three mechanisms for contact line movement based on the effective static advancing (θA) and receding (θR) contact angles for liquid pinned to a sharp corner. Measurements of critical frequencies over a wide range of overfill volumes in six different grooves are in favourable agreement with composite regime diagrams for the critical static meniscus configuration. An interesting feature of this system is the existence of a range of overfill volumes inaccessible to experiments conducted by fixing the overfill volume on a stationary disk and subsequently elevating the disk rotation until contact line movement is observed. Numerical studies showing the effects of Bond number, groove curvature and contact angle hysteresis are presented.

Density gradients modify the flow and hence the shear dispersion of one miscible fluid in another. A solution procedure is given for calculating the effects of weak buoyancy for vertical laminar parallel shear flows. A particular extrapolation to large buoyancy gives an exactly solvable nonlinear diffusion equation. For the particular case of vertical plane Poiseuille flow explicit formulae are derived for the flow, for the nonlinear shear dispersion coefficient and for the onset of instability. The exactly solvable model gives reasonably accurate results for the buoyancy-modified shear dispersion over a range from half to one-and-a-half times the non-buoyant value.