The equation for a traveling wave on the boundary of a two‐dimensional droplet of an ideal fluid is derived by using the conformal variables technique for free surface waves. The free surface is subject only to the force of surface tension and the fluid flow is assumed to be potential. We use the canonical Hamiltonian variables discovered and map the lower complex plane to the interior of a fluid droplet conformally. The equations in this form have been originally discovered for infinitely deep water and later adapted to a bounded fluid domain.The new class of solutions satisfies a pseudodifferential equation similar to the Babenko equation for the Stokes wave. We illustrate with numerical solutions of the time‐dependent equations and observe the linear limit of traveling waves in this geometry.
 Award ID(s):
 1716822
 NSFPAR ID:
 10107097
 Date Published:
 Journal Name:
 Journal of Fluid Mechanics
 Volume:
 860
 ISSN:
 00221120
 Page Range / eLocation ID:
 408 to 418
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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Abstract 
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