If an aerofoil of chord c has a parabolic nose with radius of curvature r, and is placed at angle-of-attack α to a stream, the laminar boundary layer on its upper surface remains unseparated for α<0.8l8. In the present paper we consider some smooth local modifications to the leading edge. Symmetric modifications of the nature of local sharpening of the nose can improve this result to at least α<0.897. Further improvements are possible for unsymmetrical (e.g. drooped) noses, and an example of a ‘drooped’ nose with α<0.912 is shown.

The paper is concerned with formation of singularities in a density stratified fluid subject to a monochromatic point source of frequency σ. The frequency of the source is assumed to be such that the steady-oscillation equation is hyperbolic in the neighbourhood of the source and degenerates at a critical level. We obtain asymptotic formulae demonstrating how the solution diverges as t → ∞ on the characteristic surface emanating from the source. It is shown that, at points of the surface that belong to the critical level, the solution behaves as t⅔ exp {i(σt + π/2)} as t → ∞, whereas its large time behaviour at the other points of the surface is given by t½ exp {i(σt + π/2 ± π/4)}.