Potential flow around two circular cylinders

The two-dimensional problem of potential flow around two circular cylinders is considered for given velocity at infinity, circulations around cylinders, and the radii and relative position of the cylinders. Exact analytical formulas for the complex potential and the complex conjugate velocities in terms of the Jacobi theta functions are derived. The circulations around the cylinders are uniquely determined using the Gol'dshtik's minimax principle: the circulations should be selected so that the maximum fluid velocity in the stream is minimal.