The theoretical work reported herein makes a departure from the many previous analyses of the solitary wave which have treated the wave as an example of irrotational fluid motion. The present analysis is of more general scope in that it covers the whole category of examples in which the wave may propagate in either direction on a horizontal stream whose primary velocity distribution U(y) is an arbitrary function (i.e. there is no restriction on the extent of the variations of U(y)). An approximate form of the wave profile is found in general to be a sech2 {(x − ct)/b}, as it is according to previous theories applicable to the wave on a uniform stream, but the relationships amongst the wave amplitude a, the length scale b, and the two propagation velocities c (positive downstream and negative upstream) depend in complicated fashion on the form of U(y).

When using a hot wire for velocity measurements close to a solid boundary, errors may be introduced if the effect of the boundary on the rate of heat loss from the wire is ignored. An experimental determination of the effect is described, in which a hot wire was mounted at various distances from a metal surface forming one wall of a two-dimensional channel. The rate of heat loss was determined electrically, and the air velocity at the wire found from the known laminar velocity profile. The application of the results to turbulent flows is discussed briefly.

An investigation has been made of the flow over spiked cone-cylinders mainly at a Mach number of 10. Five distinct types of flow were discovered. The occurrence of each is defined in terms of spike length and cone angle.

Following a discussion of the flow mechanism, a semi-empirical separation relation is derived. This can be used to predict the flow pattern for the most common type of separated flow.

This paper describes the use of a hot film flowmeter in the sea and presents experimental measurements of the ‘downstream’ component of turbulent velocity in a tidal channel. The Reynolds number of the flow is about 108 and the scale of the turbulence is so large that a ship is carried about to a considerable extent by the energy-containing eddies. Under these conditions, a velocity measuring probe attached to a ship cannot be used for reliable measurements in the energy-containing range of the spectrum. It is possible, however, to observe the intertial and dissipation ranges. Records have been made at various stages of the tide. The one-dimensional spectra are found to be proportional to $k|^{-{\frac {5}{3}}}$ for several decades in k as predicted by Kolmogoroff, and a value is given for Kolmogoroff's constant. In the dissipation range there is close agreement with both Kovasznay's theory and Heisenberg's theory. These two theories are not very different in the low wave-number end of the range and the observations do not extend to high enough wave-numbers to distinguish between them.

It is shown, with a high degree of certainty, that a general compressible laminar boundary layer can develop a singularity at a point of zero skin-friction only if the heat transfer at that point is zero.

This paper is concerned with the magnetohydrodynamic boundary layer in uniform flow past a flat plate, when a uniform magnetic field in the stream direction is applied at the plate. For both large and small values of the electrical conductivity parameter, solutions in series are derived for the velocity and magnetic fields. In each of the cases it is shown that if the strength of the applied field exceeds a certain critical value, boundary-layer separation occurs.

This paper considers the stability of a barotropic current on a beta earth. The motion is assumed to be horizontal, non-divergent and barotropic. The current is taken to be of the form U(y) = A sech2by+B. The perturbations are required to approach zero as y approaches ± ∞. We introduce the non-dimensional wave-number l and a parameter χ, which is a measure of the rotation effect. χ is inversely proportional to β.

There are only two kinds of perturbations: symmetric disturbances (those with maximum amplitude at y = 0) and antisymmetric disturbances (those with zero amplitude at y = 0). We find the neutral curve in the (χ, l2)-plane for both types of disturbances. The rates of amplification in the immediate vicinity of the neutral curves are also found. It is seen that the beta effect, which is due to the earth's rotation, tends to stabilize the current. For the symmetric disturbances we find a band of unstable wavelengths when χ > 1/2; and for large χ the estimated curve of the maximum value of the imaginary part of the phase velocity is asymptotic to the lower branch of the neutral curve. The antisymmetric disturbances are more stable than the symmetric disturbances.

A new explanation of the vortex tube is presented. The proposed model leads to an equivalent unsteady-flow analysis for the development of the flow in the vortex tube. Using this analysis, radial distributions of velocity and temperature can now be calculated at successive axial positions in the tube. Many characteristics of these calculated profiles are found to be in qualitative agreement with corresponding experimental profiles. The qualitative similarity in the development of the calculated and experimental sets profiles with axial position is considered especially significant.

A theory of vortex-tube performance based upon an idealized three-dimensional flow pattern for the vortex tube is derived. Some experiments relating the idealized vortex tube analysed to previous vortex-tube measurements are described. The performance curves obtained from the theory resemble those measured. An important additional effect predicted by the theory is that both the hot and the cold temperature differences should increase as the effective height of the inlet nozzle increases, and this result has been substantiated by experiment.

An almost rigid rotation of a viscous fluid is produced by dividing the containing cylinder into two sections and rotating them at slightly different speeds. The fluid velocity can be separated into two parts, a swirl about the axis and a streaming motion in the axial planes. When the difference in the speeds of rotation of the two sections is small, the equations of motion can be linearized. The solution is found for large Reynolds numbers and provides an illustration of the way in which the conditions of geostrophic flow (no velocity variation in the axial direction and an inability to insist on undistrubed flow at infinity) are approached as the Reynolds number tends to infinity.

The free-molecule limit of several free-flow problems is studied on the basis of the collisionless Boltzmann equation. It is shown that the density in the free expansion of a gas cloud obeys, under certain conditions, a diffusion equation with a coefficient directly proportional to the time, and the resulting flow field is described in terms of a thick ‘diffusion front’ travelling asympotically at a definite velocity and growing linearly with time. It is also show that in any free-molecule free expansion the stresses and heat flux can be expressed in terms of viscosity and conductivity coefficients, which however increase linearly with time but are such that the Stokesian relation is always valid and the Prandtl number has the value 5/6.

The flow field due to sources and jets is also discussed, and it is found that the jet has a width inversely proportional to the Mach number if the Mach number is sufficiently high. Finally, a procedure is indicated for taking approximate account of collisions among the molecules.

The paper deals with the initial motion of a two-dimensional bubble starting from rest in the form of a cylinder with its axis horizontal. The theory is based on the assumptions of irrotational motion in the liquid round the bubble, constant pressure within the bubble, and small displacements from the cylindrical form. This theory predicts that the bubble should rise with the acceleration of gravity, over a distance of at least the initial bubble radius, and that a tongue of liquid should be projected up from the base of the bubble into its interior. These predictions are confirmed by experiments which also show how the vorticity necessary for steady motion in the spherical-cap form is generated by the detachment of two small bubbles from the back of the main bubble.

Coexistent processes of heat, mass and momentum transfer operative within a combustible turbulent boundary layer have been experimentally investigated. The boundary layer was established on a porous cylinder mounted in a low-speed wind tunnel with its long axis in the flow direction. Methane was transpired into the boundary layer and ignited. Results indicate that the dimensionless transfer numbers corresponding to the three transfer processes can be correlated by the formula 0.038Re−0.2 to within ± 30% of measured values so that a rough numerical analogy exists among all three processes. The effect of mass injection on the skin friction coefficient is reasonably well accounted for by available theory. No effect of mass injection was found on the values of heat and mass transfer parameters. Finally, there was a lack of evidence indicating any sort of reaction-generated turbulence or that the experimentally demonstrated disturbance of the viscous layer by mass injection substantially affected the transport phenomena.

This paper gives a direct derivation of some results obtained by Longuet-Higgins & Stewart (1960, 1961) on the amplitude variation of waves propagating on a non-uniform stream. The derivation raises a number of subtle points in the use of the equations of conservation of mass, momentum and energy. These points are of general interest and are discussed in detail with other applications, since they do not seem to have been pointed out previously.

The instability of an annular coating of liquid on a wire or on the inside of a small tube subject to capillary forces at its free surface is discussed. It was found that for given values of s/a, the ratio of the two radii of the annulus, and S ≡ρTa/μ2, the reciprocal of the square of the Ohnesorge number, there is a disturbance of a certain wavelength (2πa/λ)*, which grows more rapidly than disturbances of any other wavelength. One would therefore expect the liquid to break up into a regular pattern of drops with spacing given by this wavelength. The dependence of (2πa/λ)* on s/a and S has been calculated and is presented graphically. Experimental observations on drop formation on wires and in tubes which agree with the calculations are given.

It is shown that the draining of liquid from a vertical tank produces a small but positive damping of free-surface oscillations. This conclusion is consistent with the experimental observations of Brooks.

The problem considered is that of the two-dimensional motion of the fluid in a cylinder of finite radius after the outer portion of the fluid is given an initial uniform velocity. The primary purpose of the investigation is the study of the changes in the energy distribution in the fluid as the initial motion decays. The appropriate flow equations are developed and then approximated by finite-difference equations. Numerical solutions of these equations are presented, and the energy-transfer processes are discussed in some detail. During the early stages of the flow, it is found that the spatial distribution of energy depends strongly on the Prandtl number. During the later stages, however, there is a net outward flow of energy for the case of a liquid and a net inward flow for a gas.

This paper describes the results of examining the influence of radiative heat transfer on turbulent natural convection above fires in an atmosphere of constant potential temperature, under both the ‘opaque’ and ‘transparent’ approximations. It turns out that on the basis of the over-all approximations introduced in this investigation, the former case reduces to that of no radiative transfer. For the latter case, the initial fire size, the energy release rate (initial temperature difference) and the absorption coefficient have been regarded as independent parameters. The solution curves presented cover a range over which these parameters are expected to vary in practice.