Discontinuous fluid motion past circular and elliptic cylinders

Abstract 1. The problem of discontinuous fluid motion past a curved barrier has become one of the classical problems of mechanics. For plane barriers the Schwartz-Christoffel transformation offers a direct method of solution; in the case of curved barriers no direct method of solution has been found. “A quicker start . . . can be made . . . by the simpler process of writing down a likely expression . . . and then investigating the streaming motion implied and the shape of the boundary.” In the present paper the procedure is essentially in pursuance of Greenhill’s advice, with the important modification that an attempt is made to solve problems that have a bearing on practical applications. Although many types of barriers have been suggested by various writers, very little in the way of actual numerical calculation has been done. Apparently, the only case worked out in detail is that by Brillouin, and this case is somewhat artificial and of little use. Such barriers as the circular and elliptic cylinders—important for the aerodynamics of struts—have not been attempted at all, while application to a barrier like a modern aeroplane wing seems very remote indeed.