Steady periodic water waves under nonlinear elastic membranes

P Baldi, John F Toland

Research output: Contribution to journalArticle

15 Citations (Scopus)

Abstract

This is a study of two-dimensional steady periodic travelling waves on the surface of an infinitely deep irrotational ocean, when the top streamline is in contact with a membrane which has a nonlinear response to stretching and bending, and the pressure in the air above is constant. It is not supposed that the waves have small amplitude. The problem of existence of such waves is addressed using methods from the calculus of variations. The analysis involves the Hilbert transform and a Riemann-Hilbert formulation.
Original languageEnglish
Pages (from-to)67-112
Number of pages46
JournalJournal Fur Die Reine Und Angewandte Mathematik
Volume652
DOIs
Publication statusPublished - Mar 2011

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Periodic Wave
Water waves
Water Waves
Membrane
Periodic Traveling Waves
Membranes
Hilbert Transform
Nonlinear Response
Calculus of variations
Streamlines
Ocean
Hilbert
Contact
Stretching
Formulation
Air

Cite this

Steady periodic water waves under nonlinear elastic membranes. / Baldi, P; Toland, John F.

In: Journal Fur Die Reine Und Angewandte Mathematik, Vol. 652, 03.2011, p. 67-112.

Research output: Contribution to journalArticle

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