Exact Solutions for Steady Capillary Waves on a Fluid Annulus

Summary.

Exact solutions for steady capillary waves on an annulus of swirling irrotational fluid are presented. The solutions have an intimate mathematical connection with the finite amplitude waves on fluid sheets identified by Kinnersley [8]. This mathematical connection is made explicit by first retrieving the solutions of Kinnersley using an extension of a new approach to free surface potential flows with capillarity recently devised by the present author (Crowdy [3]). A much-simplified representation of Kinnersley's original solutions results from the reformulation. The method is then generalized to identify the exact solutions for steady capillary waves on an annulus.