On the theory of shear flow

Abstract

In this report are collected together some introductory notes on the theory of the three-dimensional, steady flow of an inviscid fluid. The equations of motion are discussed and transformed and expressions for the streamwise or secondary vorticity derived both for incompressible and compressible flow. A special form of the Clebsch Transformation is used to show that three linearizing approximations are possible, depending on the order of magnitude of the stagnation pressure gradient and the disturbance to the upstream flow. The equations for each approximation are developed in turn and are applied to some elementary examples of the flow through actuator discs, over slender bodies and thin airfoils--isolated and in cascade, the flow in curved channels, and about thick struts, airfoils and through cascades of large deflection.