The pressure distribution which results from the disturbance of initially plane, parallel, and constant-pressure inviscid supersonic flow in which there is a strong entropy variation near a surface is investigated. The disturbance considered may arise from a small deflection of the surface or may be the result of a simple wave impinging on the entropy layer. This linear problem has been treated previously by a somewhat different technique for transonic entropy layers by Howarth (1948), Tsien & Finston (1949), and Lighthill (1950, 1953). The results obtained in this investigation are useful principally in that they permit the general behaviour of such pressure distributions to be deduced without resort to the more general method of characteristics for rotational flows.

Experiments have given evidence of strong sensitivity of the stagnation-point heat transfer on cylinders to small changes in the intensity of free-stream turbulence. A similar effect on local heat-transfer rates to flat plates has been measured, but only when a favourable pressure gradient is present. In this work it is theorized that vorticity amplification by stretching is a possible, and perhaps the dominant, underlying mechanism responsible for this sensitivity. A mathematical model is presented for a steady, basically plane stagnation flow into which is steadily transported disturbed unidirectional vorticity having the only orientation susceptible to stretching. The resulting velocity and temperature fields in the stagnation-point boundary layer are analysed assuming the fluid to be incompressible and to have constant properties. By means of iterative procedures and electronic analogue computation an approximate solution to the full Navier-Stokes equations is achieved which indicates that amplification by stretching of vorticity of sufficiently large scale can occur. Such vorticity, present in the oncoming flow with a small intensity, can appear near the boundary layer with an amplified intensity and induce substantial three-dimensional effects therein. It is found that the thermal boundary layer is much more sensitive to the induced effects than the velocity boundary layer. Computations indicate that a certain amount of distributed vorticity in the oncoming flow causes the shear stress at the wall to increase by 5%, while the heat transfer there is augmented by 26% in a fluid with a Prandtl number of 0.74. Preliminary computations reveal that the sensitivity of the thermal boundary layer increases with Prandtl number.

An analytic model of free-surface flow over an erodible bed is developed and used to investigate the stability of the fluid-bed interface and the characteristics of the bed features. The model is based on the potential flow over a two-dimensional, moving, wavy bed with a sinusoidal profile of varying amplitude, and a sediment transport relation in which the transport rate is proportional to a power of the fluid velocity at the level of the bed. By assuming that the dominant wavelength is that for which the rate of amplitude growth is the greatest, expressions are obtained for the wavelength and velocity of the bed features. In addition, conditions for the occurrence of the different configurations, dunes, flat bed, and antidunes, are found from the model. The predicted wavelengths of antidunes and ranges of wavelengths of dunes, and the predicted conditions for change of bed configuration are found to be in good agreement with experimental data. Finally, brief consideration is given to the factors involved in determining the maximum heights of the bed features and surface waves.

This paper is a contribution to the study of statistically homogeneous, dynamically passive vector fields convected by a turbulent fluid and subject to a molecular diffusivity λ that is small compared with the kinematic viscosity v. Two types are considered: the first, denoted by F, has the property that the total flux across a material surface moving with the fluid is conserved if λ = 0 (e.g. magnetic field); and the second, denoted by G, is the gradient of a conserved scalar quantity θ (e.g. temperature gradient). Attention is focused on small-scale variations with length-scale less than $(v^3|\epsilon)^{\frac {1}{4}}$. A theory of Batchelor's in terms of Eulerian correlations for the distribution of θ for the case when λ [Lt ] v is extended and applied to the vector fields, thereby giving equations for the covariance tensors of F and G appropriate for separations less than $(v^3|\epsilon)^{\frac {1}{4}}$. According to these equations, the effect of convection on small-scale components of the fields is to amplify and also to distort by reducing the scale; the ratio of these two effects is measured by a parameter σ. It is shown that if $\sigma \textless {\frac{5}{2}$, the small-scale structure is stable against perturbations however small λ/v may be, the amplification being eventually balanced by the dissipation which is increased by the reduction of scale. In the case of the quantity G, σ = 1. The value of σ for the case of F is not known, but reasons are given for believing that it is less than one, and it is concluded that the behaviour of $\overline{\bf F^2}$ and $\overline{\bf G^2}$ in a field of homogeneous turbulence is qualitatively the same. In particular, $\overline{\bf F^2}$ does not grow indefinitely with time as predicted by previous arguments. The correlation functions for small separations and the corresponding spectrum functions for a statistically steady state are obtained. The relation between this analysis and that for random vector fields in a uniform straining motion of infinite extent is considered in detail, for Pearson has shown that, if the strain is an irrotational distortion, then $\overline{\bf F^2} \rightarrow \infty$ with time. It is shown that this divergence is due to the amplification of components with very small wave-numbers or, equivalently, of very large scale, and it is therefore not considered relevant to a study of homogeneous turbulence.

The particular case of the magnetic field in a good conductor is considered. If the Lorentz forces are unimportant, it is estimated that the magnetic energy of a weak seed field will be in general amplified by the turbulence by a factor lying somewhere between the Reynolds and magnetic Reynolds numbers of the turbulence before ohmic dissipation as increased by the reduction of scale limits the growth, and it is suggested further that the magnetic field will eventually decay to zero in the absence of external electromotive forces.

In an appendix, the theory is applied tentatively to the turbulent vorticity (which satisfies the same equation as F if λ = v) and an expression for the energy spectrum function for very large wave-numbers is deduced. This is compared with an expression given by Townsend, and is found to have a similar qualitative behaviour but gives values about one-half as large.

The structure of a shock wave in a partially ionized gas, which may be in thermal non-equilibrium ahead of the shock wave, is investigated. A method is developed to solve this problem by separating it into two parts. First, the structure of the shock wave associated with the massive particles, ions and atoms, is assumed to be of the Mott-Smith form. Then the behaviour of the electrons as they pass though this shock is analysed. Using this method, calculations are carried out for shock waves at several Mach numbers and several values of the electron-ion temperature ratio ahead of the shock. An essential feature of the shock profiles is found to be the existence of a broad zone of elevated electron temperature ahead of the electron compression region, caused by the high thermal conductivity in the electron gas.

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.

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.