Crowdy, D. G. Exact solutions for steady capillary waves on a fluid annulus. (English) Zbl 0949.76012 J. Nonlinear Sci. 9, No. 6, 615-640 (1999). Summary: We present exact solutions for steady capillary waves on an annulus of swirling irrotational fluid. The solutions have an intimate mathematical connection with the finite amplitude waves on fluid sheets identified by W. Kinnersley [J. Fluid Mech. 77, 229-241 (1976; Zbl 0359.76017)]. 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. 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. Cited in 13 Documents MSC: 76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction 76B45 Capillarity (surface tension) for incompressible inviscid fluids 76B07 Free-surface potential flows for incompressible inviscid fluids 76M40 Complex variables methods applied to problems in fluid mechanics Keywords:steady capillary waves; annulus of swirling irrotational fluid; finite amplitude waves on fluid sheets; free surface potential flows Citations:Zbl 0359.76017 PDFBibTeX XMLCite \textit{D. G. Crowdy}, J. Nonlinear Sci. 9, No. 6, 615--640 (1999; Zbl 0949.76012) Full Text: DOI