On Irrotational Flows Equivalent to the Boundary Layer and Wake, the Fifth David Taylor Lecture

One of the simplest and most useful results of boundary-layer theory is that the flow exterior to the boundary layer, which will be assumed to be irrotational, is pushed outwards by an amount called the displacement thickness. This suggested, early in the development of boundary-layer theory, that the accuracy of a boundary-layer calculation for a body could be improved by adding the boundary-layer thickness to the body dimensions and using the predicted pressure distribution on the so-thickened body in a recalculation of the boundary layer. The irrotational field about the thickened body, including the displacement thickness of the wake, is itself of great interest, and numerous attempts have been made in this manner to calculate the effect of the boundary layer and wake on the outer irrotational flow. The concept of the thickened body gives an approximate model which is usually justified by its consistency with the approximations of thin boundary-layer theory. The basis of this model and suggested ways of refining it are reviewed. Such a development would be useful for several current problems of ship hydrodynamics, among them the determination of Betz sources in a method of calculating viscous drag by an analysis of wake survey data, and the investigation of the effect of the boundary layer and wake on wavemaking resistance.