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Title: Traveling capillary waves on the boundary of a fluid disc
Abstract

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.

 
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Award ID(s):
2039071 1716822
NSF-PAR ID:
10361297
Author(s) / Creator(s):
 
Publisher / Repository:
Wiley-Blackwell
Date Published:
Journal Name:
Studies in Applied Mathematics
Volume:
148
Issue:
1
ISSN:
0022-2526
Page Range / eLocation ID:
p. 125-140
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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