Stream-function Co-ordinates in Rotational Flow and an Analysis of the Flow in a Shock Layer: I. Two-dimensional flow

For the analysis of two-dimensional rotational flow of inviscidfluids a new set of co-ordinates are proposed. The co-ordinatesare composed of a pair of functions, the stream function anda function to be constant on each trajectory perpendicular tothe stream-lines in the flow field. The theory is then appliedto the analysis of the flow in a shock layer around a blunt-nosedbody in a hypersonic stream. The problem treated in this paperis the inverse problem to be solved with a prescribed shockshape. Some numerical computations are carried out for a parabolicshape of shock, by making use of an electronic computer.