Journal of Nonlinear Mathematical Physics

Volume 19, Issue Supplement 1, March 2013, Pages 34 - 42

On Constant Vorticity Flows Beneath Two-Dimensional Surface Solitary Waves

Authors
Raphael Stuhlmeier
Faculty of Mathematics, University of Vienna, Nordbergstraße 15, 1090 Vienna, Austria, raphael.stuhlmeier@univie.ac.at
Received 25 March 2012, Accepted 20 April 2012, Available Online 28 November 2012.
DOI
https://doi.org/10.1142/S1402925112400049How to use a DOI?
Keywords
Euler equations, free boundary, solitary waves, vorticity
Abstract

We demonstrate that, for a two-dimensional, steady, solitary wave profile, a flow of constant vorticity beneath the wave must likewise be steady and two-dimensional, and the vorticity will point in the direction orthogonal to that of wave propagation. Constant vorticity is the hallmark of a harmonic velocity field, and the simplified vorticity equation is used along with maximum principles to derive the results.

Copyright
© 2012 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
19 - Supplement 1
Pages
34 - 42
Publication Date
2012/11
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.1142/S1402925112400049How to use a DOI?
Copyright
© 2012 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

TY  - JOUR
AU  - Raphael Stuhlmeier
PY  - 2012
DA  - 2012/11
TI  - On Constant Vorticity Flows Beneath Two-Dimensional Surface Solitary Waves
JO  - Journal of Nonlinear Mathematical Physics
SP  - 34
EP  - 42
VL  - 19
IS  - Supplement 1
SN  - 1776-0852
UR  - https://doi.org/10.1142/S1402925112400049
DO  - https://doi.org/10.1142/S1402925112400049
ID  - Stuhlmeier2012
ER  -