XXV. The boundary layer in three dimensional flow.—Part I. Derivation of the equations for flow along a general curved surface

Abstract

The general equations of boundary layer flow along a curved surface S are set up in an appropriate system of orthogonal coordinates and the importance of the curvatures in the general case is made evident. It is shown that, for a general flow, the necessary and sufficient condition for the curvatures to disappear from the equations of flow is that the boundary layer should be along the surface of a cylinder or a plane. The form assumed by the equations when S is a surface of revolution is derived. In Part II. there will be a discussion of the flow in the vicinity of a stagnation point on a general surface.