On the streamline topology of inviscid flow with multiple points in a homogenous stream

Abstract

Special streamlines in the flow with circulation around a cylinder cross themselves, maybe even three times. The simple crossing happens orthogonally, while the threefold one shows up π/3 angles among the branches. There are no discontinuous changes as the pattern develops with growing circulation. These observations yield a general statement. Here we show that if a z = F (x, y) is a solution of the Δz = 0 Laplace equation and a z = const curve intersects itself (once or several times), then the branches running to that crossing point shall form equal angles.