The stability of a fluid cylinder in a plane-parallel flow of an ideal fluid

The plane problem of a steady-state potential flow of an ideal fluid around an infinite fluid cylinder with surface tension is considered. A family of solutions is constructed. An approximate relation is found between the Weber number and the ratio of the sizes of the cross-sections of the cylinder along the normal and along the free stream velocity. (A ratio of 1112 corresponds to the exact McLeod special solution.) The problem of the stability of this flow is solved in the sense of a relaxed Lyapunov definition. For a ratio of the density of the cylinder to the density of the fluid flowing around it of less than 26.35, the flow is stable, and, for a greater value, it is unstable. The conventional Lyapunov stability is proved when the ratio of the densities is less than 11.07. (C) 2016 Elsevier Ltd. All rights reserved.