Shapes of two-dimensional bubbles deformed by circulation

In this paper we study how the shape of a two-dimensional bubble is affected by circulation in an inviscid ambient how The shape of the bubble is determined by an equation which describes the balance of pressure forces and surface tension. Analysis of this equation shows that the bubble is circular for most values of circulation with the exception of an infinite series of discrete values where bifurcation occurs and the bubble's boundary develops ripples. It turns out that fully nonlinear deformations of the bubble as well as the associated circulatory flow around the bubble can be described explicitly in terms of rational functions. AMS classification scheme numbers: 6B10, 76B45, 47H15, 30C20.