Asymptotic far field conditions for unsteady subsonic and transonic flows

Far field conditions for unsteady flow at subsonic and transonic Mach numbers are derived under the assumption that the changes that occur in the flow field are not too slow. One then can derive far field conditions from analytic expressions which approximate the behaviour of wave fronts and sound rays at large distances. In subsonic blows, one uses for this purpose equations linearized for the vicinity of a parallel flow with the free stream Mach number. This leads to the result of Bayliss, Gunzburger, and Tyrkel, but extended to nonspherical wave fronts. Some theoretical insight from a different point of view is provided by interpreting the waves fronts as characteristic surfaces. The linearization used for subsonic flows fails for free stream Mach number one, because it leads to a pilling up of waves in a plane perpendicular to the free stream direction. A linearization is again carried out but with respect to a flow field in which the term of the steady flow, which dominates at a large distance, is taken into account.