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Global bifurcation of capillary–gravity-stratified water waves

Published online by Cambridge University Press:  24 July 2014

David Henry
Affiliation:
School of Mathematical Sciences, University College Cork, Western Road, Cork, Ireland, [email protected]
Anca-Vocihita Matioc
Affiliation:
Institut für Mathematik, Universität Wien, Nordbergstraße 15, 1090 Vienna, Austria, [email protected]

Abstract

We study steady periodic water waves with variable vorticity and density, where we allow for stagnation points in the flow, and where we admit the capillarity effects of surface tension. Using global bifurcation theory, we extend a local curve of non-trivial solutions of the governing equations to a global continuum of solutions. Furthermore, we obtain a description of the behaviour of the solutions along this continuum.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 2014 

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