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Exact solutions for steady capillary waves on a fluid annulus. (English) Zbl 0949.76012

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.

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

Citations:

Zbl 0359.76017
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