Asymptotic behaviour and level-curve structure in plane subsonic potential flows

The problem of constructing asymptotic forms at infinity and the problem of determining the structure of the isoclines and isobars are considered for uniform plane subsonic potential flow, horizontal at infinity, around a large class of bodies. It is shown that these problems are intimately related. In fact, the construction of a solution in the neighbourhood of the point at infinity (PAI) reduces to (i) selecting a “correct” transformation of the physical plane (PP) onto an auxiliary plane (AP), under which the PAI of the PP goes into the origin of the AP and the gas dynamic equations at the origin of the AP reduce to a Cauchy-Riemann system; (ii) finding the number of isoclines that pass through the PAI and determining the inclinations of these isoclines. With this approach, the construction of asymptotic laws and the investigation of the level curve structure in the neighbourhood of the PAI have much in common with the analogous problem in the neighbourhood of an arbitrary point of the flow at a finite distance from the body. Asymptotic forms are constructed for two cases: lift-creating flow and symmetric flow around a body. The constant factors occurring in the asymptotic formulae are expressed in terms of the physical or geometrical parameters of the problems under consideration.