Document Type

Article

Disciplines

1.1 MATHEMATICS

Publication Details

https://www.sciencedirect.com/science/article/pii/S002203962300387X

Delia Ionescu-Kruse, Rossen Ivanov, Nonlinear two-dimensional water waves with arbitrary vorticity, Journal of Differential Equations, Volume 368, 2023, Pages 317-349.

https://doi.org/10.1016/j.jde.2023.05.047

Abstract

We consider the two-dimensional water-wave problem with a general non-zero vorticity field in a fluid volume with a flat bed and a free surface. The nonlinear equations of motion for the chosen surface and volume variables are expressed with the aid of the Dirichlet-Neumann operator and the Green function of the Laplace operator in the fluid domain. Moreover, we provide new explicit expressions for both objects. The field of a point vortex and its interaction with the free surface is studied as an example. In the small-amplitude long-wave Boussinesq and KdV regimes, we obtain appropriate systems of coupled equations for the dynamics of the point vortex and the time evolution of the free surface variables.

DOI

https://doi.org/10.1016/j.jde.2023.05.047

Funder

Science Foundation Ireland

Creative Commons License

Creative Commons Attribution-Share Alike 4.0 International License
This work is licensed under a Creative Commons Attribution-Share Alike 4.0 International License.

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