Analytical study of a generalised Dirichlet–Neumann operator and application to three-dimensional water waves on Beltrami flows
Year: 2024
Type: article
Abstract: We consider three-dimensional doubly periodic steady water waves with vorticity, under the action of gravity and surface tension; in particular we consider so-called Beltrami flows, for which the velocity field and the vorticity are collinear. We adapt a recent formulation of the corresponding problem for localised waves which involves a generalisation of the classical Dirichlet–Neumann operator. We study this operator in detail, extending some well-known results for the classical Dirichlet–Neumann operator, such as the Taylor expansion in homogeneous powers of the wave profile, the computation of its differential and the asymptotic expansion of its associated symbol. A new formulation of the problem as a single equation for the wave profile is also presented and discussed in a similar vein. As an application of these results we prove existence of doubly periodic gravity-capillary steady waves and construct approximate doubly periodic gravity steady waves.
Authors: M.D. Groves, D. Nilsson, S. Pasquali, E. Wahlén
Language: English
Topic: Nonlinear Waves and Solitons
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,050
Funders: Swedish Foundation for MS Research, Knut och Alice Wallenbergs Stiftelse, Vetenskapsrådet, Cambridge-MIT Institute, European Research Council, H2020 Marie Skłodowska-Curie Actions, HORIZON EUROPE Marie Sklodowska-Curie Actions, HORIZON EUROPE Reforming and enhancing the European Research and Innovation system
OpenAlex ID: W4402120091