SOME ANALYTICAL PROPERTIES OF SOLUTIONS TO A 2-DIMENSIONAL STEADILY TRANSLATING INVISCID BUBBLE

We consider some analytical properties for a steadily translating two- dimensional bubble in an inviscid irrotational flow when surface tensi on effects are included but gravity neglected. For a general value of the Bernoulli constant, we show that a conformal mapping function from a unit circle to the exterior of the bubble has a very specific polar decomposition. The pole locations and corresponding residues are dete rmined numerically, while, in specific limits, their values are determ ined asymptotically.