A systematic procedure is presented for the determination of uniformly valid successive approximations to the axisymmetric incompressible potential flow about elongated bodies of revolution meeting certain shape requirements. The presence of external disturbances moving with respect to the body under study is admitted. The accuracy of the procedure and its extension beyond the scope of the present study—e.g. to problems in plane flow - are discussed.

The starting-point for this paper is the suggestion (Batchelor 1956b) that the wake behind a bluff body in a uniform stream may consist principally of two eddies rotating in opposite directions. The fluid is assumed to be incompressible and in two-dimensional steady motion at a very high Reynolds number. Along the boundary between the eddies, a viscous layer must form. This layer is unusual in that merely the vorticity, and not the velocity itself, varies appreciably across it. It will be shown that such layers can be treated theoretically much more simply than the general case, because it is possible to linearize the equation of motion. They may, of course, exist in flows other than that past a bluff body.

A discussion is also given of the flow near the rear stagnation point, where this boundary layer meets the body. It had been suggested that a large number of small eddies would have to exist there, but this seems not to be so.

Function-theoretic techniques are used for determining the supersonic flow past a wing of infinite length having a straight leading edge. The problem is reduced to a set of dual integral equations which are solved by function - theoretic methods. This approach is shown to be useful for treating more general - type leading edges yielding closed - form solutions which heretofore have been unobtainable. The general solutions obtained here are shown to be in complete agreement with previous solutions for the flow at large distances downstream on the aerofoil. For a wing of infinite span, the solution reduces to the well - known perturbation potential for a distribution of sources in a horizontal plane.