Unsteady vortical and entropic distortions of potential flows round arbitrary obstacles

The analysis concerns the alterations produced when small amplitude disturbances, including entropy and vorticity disturbances, are imposed on steady potential flows. For the most general nonacoustic incident distortion field that can be imposed on the uniform upstream flow, it is shown that the perturbation velocity at any point of the resulting unsteady compressible and vortical flow consists of a part that is a known function of the imposed upstream distortion field and the mean flow variables and a potential part that can be found by solving a linear inhomogeneous wave equation with a dipole-type source term whose strength is a known function of the imposed upstream distortion field. The theory is applied to the unsteady flow past a corner, and a closed-form analytical solution is found.