Clamond D. New exact relations for steady irrotational two-dimensional gravity and capillary surface waves.
PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2018;
376:rsta.2017.0220. [PMID:
29229804 DOI:
10.1098/rsta.2017.0220]
[Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 08/01/2017] [Indexed: 06/07/2023]
Abstract
Steady two-dimensional surface capillary-gravity waves in irrotational motion are considered on constant depth. By exploiting the holomorphic properties in the physical plane and introducing some transformations of the boundary conditions at the free surface, new exact relations and equations for the free surface only are derived. In particular, a physical plane counterpart of the Babenko equation is obtained.This article is part of the theme issue 'Nonlinear water waves'.
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