Atmospheric dissociation will be appreciable in the neighbourhood of projectiles travelling at speeds greater than 2 km/sec. This introductory paper on possible effects of dissociation on the airflow, and hence on the drag, stability and aerodynamic heating of such projectiles, is intended mainly as a source of ideas for later, more comprehensive investigations.

This paper is a discussion of recent experiments in shock-wave refraction which have clarified a special type of shock outflow process appearing to have relevance to other shock interactions, and notably to shock reflection from an oblique wall. For certain incident shock strengths and angles of incidence α, the air/methane refraction problem simulates closely the situation in the trouble-some range of the reflection problem, in which α lies between the value αe at which the theoretical solutions terminate and the value α0 that marks the onset of Mach reflection, and in which the flow deflections cannot be reconciled with theoretically permissible reflected shock strengths. In the analogous refraction cases, the reflected shock is observed to increase in strength along its length to a maximum value at the intersection point, and to be followed by a subsonic rarefaction zone which also increases in severity near the intersection. In fact, this zone appers to coalesce into a subsonic discontinuity, just at the intersection point—a feature which would contradict one of the basic assumptions of the regular reflection and refraction theories. Other refraction experiments suggest that a similar process is relevant to the Mach reflection configuration, and may account for the discrepancies in the three-shock theory for weak incident shocks.

The problem is to determine the downwind concentration of non-buoyant smoke emitted from a continuous elevated pointsource in a turbulent airstream. The velocity and eddy diffusivity coefficients are represented by related powers of the height above ground, and are independent of the position of the source. Exact solutions are obtained for the zero and second moments of the concentration distribution along lines lying in the cross-wind direction at ground level. In special cases, these moments may also be determined along lines at general height. In one such case the concentration is determined exactly (rather than just the two moments) and it is found that the cross-wind distribution always has a Gaussian form. If it is assumed that in all cases the cross-wind profile is Gaussian, a formulation for the concentration can be given purely in terms of the known zero and second moments. When the source is moving with constant velocity across the wind, the first moment as well as the zero and second moments is exactly determined, and under a similar assumption a formula for the concentration is found.

Certain two-dimensional, laminar bounday layers are considered whose streamlines are closed. The speed at the solid boundary is supposed uniform, the bounday outline being stationary, and the speed in the boundary layer is supposed to differ only slightly from that of the boundary. A formal solution is then obtained for the motion in the boundary layer. The analysis confirms that a closed boundary layer may exist and yields a condition needed to determine the inviscid motion. The condition is extracted in a simplified but approximate form and two examples of its use are given. A further class of closed boundary layers, namely those for which the pressure is uniform, is also considered. For this class the condition needed to determine the inviscid motion may be derived in a form both simple and exact.

Consider a fluid of constant viscosity μ. If the fluid is incompressible, we suppose it to move in a conservative field in which the force per unit mass is - ∇Ω. If the fluid is compressible, we suppose the field of force to be absent. Both cases are included if we write V = ερΩ, where ε = 1 for an incompressible fluid, and ε = 0 for a compressible fluid. The equation of continuity

If, in a given solution of the boundary layer equations, the position of the wall is varied, then additional solutions of the boundary layer equations may be deduced. The theorem considers the nature of such solution, for the general case of time-dependent three-dimensional compressible flow.

Applications of the theorem arise in several different fields, and it is shown that useful quantitative results can often be obtained with the minimum of calculation. In this paper, chief attention is focused on the case of a rotating circular cylinder, and explicit formulae are developed for the skin friction, valid for sufficiently low rotational speeds. The important results which the theorem gives for slip flow have been noted by previous extenions to these previous treatments are made. Other applications of the theorem are briefly mentioned.