Coefficients of longitudinal and lateral dispersion were measured for steady uniform laminar flow through an isotropic porous medium. A unique experimental method for measuring lateral dispersion is described. It is found that the ratio of the coefficient of longitudinal dispersion D1 to the coefficient of lateral dispersion D2 is given by $\frac {D_1}{D_2} = \lambda \Re ^n$ where λ and n are dimensionless coefficients dependent upon the pore-system geometry, and [real ] is the Reynolds number based on the seepage velocity, the average grain diameter, and the kinematic viscosity.

The conditions which determine the existence and position of cavitation in the narrow passages of hydrodynamically lubricated bearings have been assumed to be the same as those which produce cavitation bubbles, namely a lowering of pressure below that at which gas separates out of fluid. This assumption enables certain predictions to be made which in some cases are verified, but it does not provide a physical description of the interface between oil and air. Theoretical analysis of the situation seems to be beyond our present capacity, and in none of the experiments so far published has it been possible to measure both the most important relevant data, namely the minimum clearance and the oil flow through it.

A method is described here which enables this to be done. It turns out that two physically different kinds of cavitation can occur. One of these is well described by the existing theory and assumption. Surface tension plays no part in it, and in most text books on hydrodynamic lubrication is not even mentioned. The other kind, which is akin to hydrodynamic separation rather than bubble cavitation, depends essentially on surface tension. Both kinds appear clearly in published photographs taken through transparent bearings, but the experimenters do not seem to have distinguished between them.

The reason why surface tension, which is only able to supply stresses that are exceedingly small compared with the pressure variation in the fluid itself, may have a large effect on the flow can be understood by considering the flow of a viscous fluid in a tube when blown out by air pressure applied at one end. For any given length of fluid the rate of outflow depends almost entirely on the pressure applied, the surface tension force being negligible; but the amount of fluid left in the tube after the air column has reached the end depends essentially on surface tension.

Experiments have been carried out in a cylindrical magnetic shock tube on the propagation of a shock wave into a fluid containing a uniform transverse magnetic field. Cylindrical shock waves in the Mach number range from 20 to 100 have been produced which are very stable and reproducible. Theory predicts basic differences between the case where the gas is initially highly conducting (pre-ionized) and the case where a gas-ionizing shock propagates into a cold gas. Good agreement between theory and experiment has been obtained for the gas ionizing shocks.

Consideration is given to the flow of an idealized elastico-viscous liquid in a curved pipe under a pressure gradient. By using the series expansion method of Dean (1927, 1928) in powers of a/R where a is the radius of the pipe and R the radius of curvature of its ‘central line’, it is shown that the general nature of the motion is similar to that of the motion of a Newtonian viscous liquid, the liquid elements moving along the pipe in two sets of spirals separated by the central plane. However elasticity of the type considered could strongly affect the pitch of these spirals. To the approximation considered, the flow pattern of the elastico-viscous liquid depends only on the limiting (zero-shear-rate) viscosity η0 and the first moment, K0, of the distribution of relaxation times. The corresponding stress components involve also the second moment of this distribution.

It is also shown that the presence of elasticity in the liquid increases the rate of discharge of the liquid.

The effect of radiative transfer on thermal stability when a Coriolis force is also acting has been examined. Two asymptotic approximations of the radiative transfer equation have been used to study the stability problem in detail. The necessary and sufficient conditions for the validity of the principle of exchange of stabilities are also obtained.

The flow inside rectangular and other cavities in a wall has been investigated at low subsonic velocities using oil flow and surface static-pressure distributions. Evidence has been found of regular three-dimensional flows in cavities with large span-to-chord ratios which would normally be considered to have two-dimensional flow near their centre-lines. The dependence of the steadiness of the flow upon the cavity's span as well as its chord and depth has also been observed.

An attempt has been made to establish the laws governing the flow in a turbulent line vortex. Up to the present time theoretical solutions for laminar flow have been used for comparison with experimental results for turbulent flow to find an ‘eddy viscosity’ term and its variation with various parameters. An approach is developed along lines similar to the methods used in turbulent boundary-layer theory and is found to be reasonably successful as far as the work has proceeded. It is predicted by theory, and confirmed by experiment, that the circulation in the vortex is proportional to the logarithm of radius under certain conditions. For the present experimental conditions, the vortices are found to be completely independent of viscosity effects when the parameter WZ/K0 exceeds 150, and above this value the experimental results may be correlated to give a universal distribution of circulation in the inner region of the vortex. Further experiments are necessary to verify and extend the results of these tests before any definite conclusions may be made regarding the circulation distribution in the outer core region of the vortex and the growth and development of the vortex.

The propagation of a one-dimensional combustion wave into a non-ionized gas at rest in the presence of an electromagnetic field is considered when ionization of the gas occurs across either the combustion wave or a preceding shock wave. The electric and magnetic fields in the undisturbed gas ahead of the waves are mutually perpendicular and orthogonal to the direction of wave propagation. It is shown that steady detonation occurs at a point which is analogous to the Chapman-Jouguet point of ordinary gasdynamic combustion theory. Numerical calculations are made of the state of the gas between and behind the waves in two particlar models, in both of which the upstream electric field is zero. The models are then equivalent to magnetogasdynamic phenomena in a perfectly conducting gas. First, the case of steady detonation is studied. Secondly, steady deflagration in a tube, closed at one end, is discussed.

Asymptotic forms, valid for high Hartmann number M, are obtained for the mean velocity for laminar magnetohydrodynamic flow in a rectangular tube. For a tube with non-conducting walls it is found that, neglecting exponentially damped terms, the mean velocity can be expressed in closed form in terms of tabulated functions. The first three terms of the expansion of the mean velocity in inverse powers of M are in extremely close agreement with a corresponding expansion obtained by Shercliff (1953) using a boundary-layer method.

For perfectly conducting walls the first five terms of an expansion in inverse powers of M are obtained.

A continuous-flow system is fed with a liquid which turns blue a specified time θ after entering. A more or less stationary pattern is thus set up, those parts of the liquid which have spent times longer than θ in the system being blue while the rest is colourless. The value of θ can be changed at will, enabling details of the flow-pattern to be deduced. The interpretation of the finer points of the colour-pattern is made difficult by the effects molecular interdiffusion of different parts of the liquid.

The investigations to the shoreward travel of a bore into water at rest is extended to beaches of non-uniform slope. It is shown that the shore singularity established in Part 1 (Ho & Meyer 1962) still furnishes an approximate solution. The shape of the beach, like the shape of the wave forming the bore, is found to influence the bore development close to shore almost only in so far as it determines the basic velocity scale of the bore.

An experimental study has been made of transition to turbulence in the free convective flows on a heated plate. Observations have been made with the plate vertical and inclined at angles up to about 50° to the vertical, both above and below the plate. A fibre anemometer was used to survey the region of intermittent turbulence. Information has thus been obtained about the range of Grashof numbers over which transition takes place. Even when the plate is vertical the region of intermittent turbulence is long. When it is inclined, this region becomes still longer in the flow below the plate as a result of the stabilizing stratification, a Richardson number effect. It is possible to have a whole flow such that it should be described as transitional, not laminar or turbulent. It was noticed that in this flow and the vertical plate one, the velocity during the laminar periods could be either of two characteristic values, one of them close to zero. The behaviour above an inclined plate could be interpreted largely as a trend towards the behaviour described in a preceding paper.

The observations on the stably stratified flow help to explain a feature of glacier winds.

Quartz fibre anemometers have been used (as described in subsequent papers) to survey the velocity field of turbulent free convective air flows. This paper discusses the reasons for the choice of this instrument and provides the background information for its use in this way. Some practical points concerning fibre anemometers are mentioned. The rest of the paper is a theoretical study of the response of a fibre to a turbulent flow. An approximate representation of the force on the fibre due to the velocity field and the equation for a bending beam, representing the response to this force, form the basis of a consideration of the mean and fluctuating displacement of the fibre. Emphasis is placed on the behaviour when the spectrum of the turbulence is largely in frequencies low enough for the fibre to respond effectively instantaneously (as this corresponds to the practical situation). Incomplete correlation of the turbulence along the length of the fibre is taken into account. Brief mention is made to the theory of the higher-frequency (resonant) response in the context of an experimental check on the applicability of the low-frequency theory.

When a bore travels shoreward into water at rest on a beach, then according to the first-order non-linear long-wave theory, the bore accelerates and decreases in height, until it collapses at the shore. The investigation here reported concerns the question, what happens next? It is formulated as a singular characteristic boundary-value problem with somewhat unusual mathematical properties. Its asymptotic solution predicts a rather thin sheet of run-up and back-wash with some unexpected features.

An investigation has been made of the structure of the motion above a heated plate inclined at a small angle (about 10°) to the horizontal. The turbulence is considered in terms of the similarities to and differences from the motion above an exactly horizontal surface. One effect of inclination is, of course, that there is also a mean motion.

Accurate data on the mean temperature field and the intensity of the temperature fluctuations have been obtained with platinum resistance thermometers, the signals being processed electronically. More approximate information on the velocity field has been obtained with quartz fibre anemometers. These results have been supplemented qualitatively by simultaneous observations of the temperature and velocity fluctuations and also by smoke experiments.

The principal features of the flow inferred from these observations are as follows. The heat transfer and the mean temperature field are not much altered by the inclination, though small, not very systematic, variations may result from the complexities of the velocity field. This supports the view that the mean temperature field is largely governed by the large-scale motions. The temperature fluctuations show a systematic variation with distance from the lower edge and resemble those above a horizontal plate when this distance is large. The largescale motions of the turbulence start close to the lower edge, but the smaller eddies do not attain full intensity until the air has moved some distance up the plate. The mean velocity receives a sizable contribution from a ‘through-flow’ between the side-walls. Superimposed on this are developments that show that the momentum transfer processes are complex and certainly not capable of representation by any simple theory such as an eddy viscosity. On the lower part of the plate there is surprisingly large acceleration, but further up the mixing action of the small eddies has a decelerating effect.

A conductivity tensor is calculated for a partially ionized gas subject to electric fields which are harmonic in space and time, and to a uniform magnetic field. The collisions between charged particles and neutral molecules are included in the theory in an approximate way by means of a simplified form of Boltzmann's equation, as proposed by Bhatnagar, Gross and Krook. A simplified expression for the longitudinal component of the tensor is derived. Some applications of the results are mentioned, and will be described in detail in further papers.

This paper discusses the general idea that in systems where a flexible solid is coupled with a flowing fluid three different types of instability are possible. These were originally designated by Brooke Benjamin (1960) as ‘class A’, ‘class B’ and ‘Kelvin-Helmholtz’ instability, and their collective significance has been clarified recently by Landahl (1962). Class A and class B disturbances are essentially oscillations involving conservative energy-exchanges between the fluid and solid, but their stability is determined by the net effect of irreversible processes, which include dissipation and energy-transfer to the solid by non-conservative hydrodynamic forces. Dissipation in the solid tends to stabilize class B distrbances but to destabilize class A ones. Class C instability (i.e. the ‘Kelvin-Helmholtz’ type) occurs when conservative hydrodynamic forces cause a unidirectional transfer of energy to the solid.

In § 2 this idea is examined fundamentally by way of the Lagrangian method of generalized co-ordinates, and in § 3 the example of inviscid-fluid flow past a flexible plane boundary is considered. The treatment of this example amplifies the work of Landahl, in particular by including the effect of non-conservative forces of the kind investigated by Miles in his series of papers on water-wave generation by wind.