In order to gain insight into the macroscopic behaviour of gas interacting with electric and magnetic fields, while its degree of ionization is changing, the one-dimensional unsteady flow of gas with temperature-dependent conductivity is investigated. A simple continuum model is used for the gas. It is assumed to be compressible and to obey polytropic gas laws and its conductivity is supposed to change discontinuously at a critical temperature. Particular attention is devoted to the various types of transition boundaries which can occur as the conductivity changes, and it is shown that complete flow patterns can be constructed with these as elements. A wide variety of transitions are possible and some of these have remarkable properties. For example, it is shown that discontinuous deionising fronts can exist and are expansive in nature. This contrasts sharply with the situation in conventional gas dynamics and magneto-gasdynamics where only compressive discontinuities can exist.

An approximate analysis is developed for the propagation of water waves past long obstacles by considering separately the effects of diffraction at each end. The motion is two-dimensional, and linearized potential flow is assumed. Reflexion and transmission coefficients are obtained for the long obstacle, and it is shown that for suitably chosen values of the obstacle length there is complete transmission due to interference between the two ends. A comparison is made with experiments for the case of a rectangular obstacle.

The structure of a self-preserving turbulent plane jet exhausting into a slow-moving parallel airstream is studied. The investigation includes results of turbulence measurements and the structure is compared with that of a self-preserving plane wake. The results show that self-preservation is established at a distance of about thirty jet widths downstream of the jet nozzle and that, in the self-preserving region of the jet, the distributions of the turbulent intensities and shear stress across the jet are very similar to those found in the plane wake. The distribution of the intermittency factor, however, is found to be more like that found in an axi-symmetric jet than in a plane wake. The turbulent energy balance also shows important differences to that of the wake flow. The unsteady irrotational flow outside the turbulent shear layer is investigated and it is found that the experimental results agree with the predictions of the theories of Phillips (1955) and Stewart (1956). Some comments are also made on the eddy structure and the applicability of the simple theories of turbulence.

A solution is presented of the asymptotic flow due to a point source of momentum in a uniformly rotating unbounded environment. Under the condition that the relative swirl velocity of the jet is small compared with the ambient swirl velocity, the equations of motion reduce to a set of linear equations. These equations are expressed in terms of similarity variables and a single ordinary differential equation is derived in terms of the similarity stream function. The profiles of the flow are calculated numerically.

The jet is shown to have a narrow viscous core whose thickness increases with distance z from the virtual source of momentum as ($(vz|\Omega)^{\frac {1}{3}}$, where v is the kinematic viscosity and Ω the ambient angular velocity.

This is largely an experimental study of the interaction of buoyancy and shear forces in the free convective flow of a liquid in a rectangular cavity across which there is a uniform temperature difference, ΔT, produced by maintaining the two vertical walls at two different temperatures. The height of the cavity, H, is made larger than the width of the cavity, L, and the cavity is sufficiently long in the third dimension for the mean flow to be nearly everywhere two-dimensional. The flow is specified by three dimensionless parameters: σ, the Prandtl number; h = H|L, the aspect ratio; A = γgΔTL3|κν, the Rayleigh number. The experiments are generally restricted to h = 1–60, σ ÷ 103 and A < 108.

For A < 103 the temperature field closely satisfies Laplace's equation but a weak stable unicellular circulation is generated. The flow is vertical throughout the slot except for regions within a distance of order L from the ends.

For 103 < A < 105, large temperature gradients grow near the walls, and in an interior region a uniform vertical temperature gradient is established. The flow is similar to that near an isolated, heated, vertical plate except that the vertical growth of the wall layers is inhibited in the central part of the slot by the presence of the other layer which prevents entrainment of fluid.

Near A = 105 the interior region of the flow generates a steady secondary flow. A regular cellular pattern becomes superimposed on the basic flow to produce a ‘cats-eye’ pattern of streamlines. Near A = 106 when the secondary cell amplitude is large, a further steady cellular motion is generated in the weak shear regions between each cell.

This paper is a continuation of the experimental study (Elder 1965), of free convection in a vertical slot, to unsteady and turbulent motion. The flow is specified by three dimensionless parameters: σ, the Prandtl number; h = H|L, the aspect ratio and $A = \gamma g \Delta TL^3|kv$, the Rayleigh number. The present experiments are generally for σ = 7 (water), h = 10–30 and A > 106.

For A above about 8 × 108S|h3, travelling, wave-like motions grow up the hot wall of the slot and also down the cold wall. These waves grow most readily mid-way between the two ends. At higher values of the Rayleigh number when the wave amplitude is finite, the phase of successive wave fronts becomes increasingly random till near A = 1·0 × 1010|h3 an intense entrainment and mixing process commences between the wall region and the interior. The middle portion of the interior is then turbulent, the extent of the region growing further toward the ends as A increases.

Measurements of the mean temperature and the probability distribution of temperature fluctuations of the turbulent flow are reported. Except within the thin wall layers and distant form the ends, the interior has a mean temperature, uniform to within 0·1%, superimposed on which is a nearly Gaussian fluctuation-field of variance of order 0·01ΔT. A comparison is made with recent theories of turbulent convection; moderate agreement is found with the similarity ideas of Priestley (1959). The wall layer is seen as a marginally unstable sublayer.

In a horizontal layer of fluid, thermal expansion or the presence of dissolved salt may cause a density gradient opposite to the direction of gravity. In such cases, when the buoyancy forces are sufficient to overcome the dissipative effects, the static state becomes unstable and convective motions arise. If the layer is infinitely large in horizontal extent, the non-linear convection problem is highly degenerate, admitting many different steady-state solutions. A general necessary criterion for stability of such non-linear steady solutions is developed here for the case in which a homogeneous vertical magnetic field acts on the fluid. The criterion is demonstrated for two rigid bounding surfaces which are perfect thermal and electrical conductors, but it is applicable to more general kinds of boundary conditions.

The static state of a horizontal layer of fluid heated from below may become unstable. If the layer is infinitely large in horizontal extent, the Boussinesq equations admit many different steady solutions. A systematic method is presented here which yields the finite-amplitude steady solutions by means of successive approximations. It turns out that not every solution of the linear problem is an approximation to the non-linear problem, yet there are still an infinite number of finite amplitude solutions. A similar procedure has been applied to the stability problem for these steady finite amplitude solutions with the result that three-dimensional solutions are unstable but there is a class of two-dimensional flows which are stable. The problem has been treated for both rigid and free boundaries.

The phenomena which occur in a fluid contained in a rotating system are strongly influenced by the density gradients in that fluid and by certain features of the geometry. In this paper, we study several specific phenomena which involve stratification and/or irregular surface topography and some phenomena which arise because of an equatorial geometry. Although several of these studies are motivated by particular geophysical questions, we do not treat comprehensively any geophysical phenomenon. Nevertheless, the inferences we draw from these studies do much to clarify the roles of the mechanisms underlying various geophysical phenomena and these inferences should be of value when comprehensive geophysical investigations are attempted.

A luminescent region was observed near the axis of a cylindrical duct confining a supersonic swirling air flow at ambient temperature. The luminescence was identified as a glow discharge induced by a strong internal electric field, which was produced by condensed water droplets impinging on the duct wall.

Preston's method of measuring skin friction in the turbulent boundary layer makes use of a circular Pitot tube resting on the wall. On the assumption of a velocity distribution in the wall region common to boundary layer and pipe flows the calibration curve for the Pitot tube can be obtained in fully developed pipe flow. Earlier experiments suggested that Preston's original calibration was in error, and a revised calibration curve has been obtained and is presented here.

From experiments in strong favourable and adverse pressure gradients, limits are assigned to the pressure-gradient conditions within which the calibration can be used with prescribed accuracy. It is shown that in sufficiently strong favourable gradients the ‘inner-law’ velocity distribution breaks down completely, and it is suggested that this breakdown is associated with reversion to laminar flow.

As an incidental result, values have been obtained for the constants occurring in the logarithmic expression for the inner-law velocity distribution.