The problem solved is that of the interaction between a laminar boundary layer on a semi-infinite flat plate and an oncoming shear flow of finite lateral dimensions bounded by uniform irrotational flow extending to infinity. The pressures along the plate and upstream of the same are deduced (to a linearized approximation) in the form of a Fourier integral based on the solution of a simpler periodic flow problem. It is found that while the assumption of an infinite, uniform shear flow gives asymptotically correct interaction pressure gradients on the plate near the leading edge, the pressure level even there (compared to upstream infinity) is strongly influenced by the boundedness of the external shear. At distances from the leading edge which are large compared to the lateral extent of the shear flow, the pressure gradients along the plate are shown to be vanishingly smaller than in the infinite shear case.

Propagation of a transverse electromagnetic wave along a d.c. magnetic field and interaction with a moving shock wave is investigated. The direction of propagation is normal to the shock front. Solutions to electromagnetic fields, gas velocities and Doppler shifts in frequency are found in both the ionized and un-ionized gases. A frequency is obtained at which electromagnetic reflexion from the shock front is minimized. In the ionized gas behind the shock front a fast and a slow electromagnetic wave result. By adjusting the shock velocity the frequency of the slow wave can be either raised or lowered. This frequency change, however, is not the Doppler shift and, consequently, can be made much larger than the Doppler shifts encountered at non-relativistic velocities. The slow wave attenuates much less than the ordinary fast wave, and applications to diagnostics and communications through plasmas and laser-beam frequency multiplication may be possible.

A steady-state technique of heat-transfer measurement has been developed based on the method of Seban, Emery & Levy (1959) whereby energy is dissipated by the Joule effect in a thin metal sheet on the surface of a model. For the present application, use was made of very thin but mechanically resistant films of metal of very nearly constant thickness, obtained by a simple mirror-silvering technique. The present investigation was prompted by the desire to make very local measurements of heat transfer for application in regions where large variations in convective heat flux and therefore in temperature could be expected.

Comparison between theory and experiment has been made in the simple case of a flat plate with constant heat flux for which a rigorous computation could be made based on the theory of Chapman & Rubesin (1949). The model was so conceived that the heat losses were small enough to be neglected. Therefore no corrections, which are often inaccurate, were needed for the experimental results, contrary to what is generally done when using other techniques for heat-transfer measurements. The excellent agreement between theory and experiment gives complete confidence in the method. The theoretical analysis showed that the measurements are simply related to the results that could be obtained in the case of an isothermal surface, because of the constant ratio that exists between the corresponding heat-transfer coefficients.

A thin, flexible hydrofoil has been used as a model to simulate the swimming of a two-dimensional fish in an ideal, incompressible fluid, as treated in recent theoretical papers. The apparatus is described in some detail and typical data are compared with the predictions of theory. An error analysis is given, showing that, within the expected errors and limits of validity of theory, experimental verification of theory is very good.

The boundary layers due to finite viscosity and magnetic diffusivity are studied in relation to two models of the flow of a conducting fluid past a body in an aligned magnetic field. In each case it is deduced that the growth of the boundary layer may have substantial effects, such as to raise doubts about the validity of the assumed basic flow patterns.

The steady separated flow past a circular cylinder was investigated experimentally. By artificially stabilizing the steady wake, this system was studied up to Reynolds numbers R considerably larger than any previously attained, thus providing a much clearer insight into the asymptotic character of such flows at high Reynolds numbers. Some of the experimental results were unexpected. It was found that the pressure coefficient at the rear of the cylinder remained unchanged for 25 [les ] R [les ] 177, that the circulation velocity within the wake approached a non-zero limit as the Reynolds number increased, and that the wake length increased in direct proportion to the Reynolds number.

A weak expansion wave propagating in a relaxing gas is discussed with particular reference to the ‘near-equilibrium’ and ‘near-frozen’ regions. The concept of bulk viscosity is used in conjunction with Burger's equation in the near-equilibrium region. The asymptotic equilibrium simple wave is modified by diffusive regions in the neighbourhood of the first and last rays. It is shown that in the case of a weak expansion wave, Chu's asymptotic solution of the acoustic equation describes the wave-form for a finite time interval before convection effects become noticeable. In the near-frozen region a characteristic perturbation method is used to describe the flow near the wave-front.

The steady two-dimensional seepage flow by gravitational convection, of a fluid of density ρ1 surrounded by a fluid of density ρ0(≠ρ1) at rest, leads to a potential problem from which the shape of the interface can be determined. When the two fluids are slightly miscible the interface is replaced by a mixing layer, and it is shown that the first-order Prandtl equations for the flow in the layer possess an exact similarity solution. The profile across the layer is of the same form as the profile of the laminar incompressible half-jet with one fluid at rest, and a formula is obtained for the scale of mixing-layer thickness as a function of distance downstream. Three examples are discussed.

(a) Flow of fluid of density ρ1 from a horizontal line source. When (ρ1 > ρ0) a stagnation point exists above the source, and the fluid ultimately descends in a vertical column of width proportional to the source strength. At the stagnation point, the mixing-layer thickness is finite and is proportional to the square root of the radius of curvature of the interface. At a sufficiently great distance downstream, the thickness increases as the square root of the distance, as in the straight laminar half-jet. These results have been tested experimentally in a Hele-Shaw cell.

(b) Symmetrical flow of an ascending column of fluid (ρ1 < ρ0) about an obstacle in the form of a finite horizontal strip. The column reforms after passing the obstacle, and the mixing-layer thickness returns to the value corresponding to an unobstructed vertical half-jet. The flow has been produced experimentally.

(c) Flow in a lens of fresh water overlying salt water, with inflow due to precipitation, as in a two-dimensional Ghyben-Herzberg lens. Here the potential flow solution is calculated approximately by means of Dupuit-Forchheimer theory. In the steady-state solution the thickness of the mixing layer between fresh and saline water is found to be finite and, as in (a), proportional to the square root of the radius of curvature of the lens.

This report is an extension of an earlier note in which a simple method of estimating the distribution of vibrational temperature along a hypersonic nozzle was described. Results were presented for hyperbolic, axisymmetric nozzles with reservoir conditions 1000[les ]p0[les ] 4000 p.s.i.a., 1000[les ] T0 [les ] 3000°K. The problem was subsequently programmed for the Ferranti Mercury computer at the University of London computing centre, and the results of these computations are given here. The vibrational temperatures are compared with those of the previous simple method. The distributions of pressure and temperature through the nozzle are also given and a simple method of estimating the vibrational temperature is described.

A general theory of unsteady cavitating flow past hydrofoils and other obstacles is given for the case of cavities of finite length L. If the circulation Γ, the cavity volume V and L are known as functions of time, the theory yields explicit formulae for the velocity over the wetted surface and for the cavitation number σ. The theory is based on the approximation that the cavity is bounded by stream-lines, and so is valid only for slow rates of change of L, V and Γ. The possibility of allowing for the presence of a vortex sheet behind the cavity is discussed. The theory is extended to the case of a cascade of hydrofoils behind which extend growing cavities.

Two examples of the theory are discussed, namely the unsteady flow past a symmetrical wedge, and the unsteady flow past a flat plate hydrofoil cavitating from the leading edge.

It is shown in general how a two-dimensional flow can be justified as a physical approximation, notwithstanding the logarithmic singularity in pressure that occurs at infinity when the cavity expands or contracts at a varying rate. The argument presented, which affords a more natural interpretation than alternatives previously suggested, refers to the approximate equivalence-to a determinable degree of accuracy-between the hypothetical plane flow and the inner region of some real three-dimensional flow with small spanwise variations. The main ideas are illustrated by the example of a long ellipsoidal body which changes in volume while also undergoing shape perturbations.

The classical laminar boundary layer on a parabolic cylinder is calculated using the Blasius series, with modifications to improve convergence, and supplemented by an asymptotic expansion valid far downstream from the nose. The flow due to displacement thickness is thereby found with sufficient accuracy to permit evaluation of its second-order effect upon the boundary layer near the stagnation point. The skin friction and heat transfer are found to be reduced there by both displacement and curvature.