Journal article
Gravity perturbed Crapper waves
Proceedings of the Royal Society. A, Mathematical, physical, and engineering sciences, v 470(2161), 20130526
08 Jan 2014
Featured in Collection : UN Sustainable Development Goals @ Drexel
Abstract
Crapper waves are a family of exact periodic travelling wave solutions of the free-surface irrotational incompressible Euler equations; these are pure capillary waves, meaning that surface tension is accounted for, but gravity is neglected. For certain parameter values, Crapper waves are known to have multi-valued height. Using the implicit function theorem, we prove that any of the Crapper waves can be perturbed by the effect of gravity, yielding the existence of gravity-capillary waves nearby to the Crapper waves. This result implies the existence of travelling gravity-capillary waves with multi-valued height. The solutions we prove to exist include waves with both positive and negative values of the gravity coefficient. We also compute these gravity perturbed Crapper waves by means of a quasi-Newton iterative scheme (again, using both positive and negative values of the gravity coefficient). A phase diagram is generated, which depicts the existence of single-valued and multi-valued travelling waves in the gravity-amplitude plane. A new largest water wave is computed, which is composed of a string of bubbles at the interface.
Metrics
Details
- Title
- Gravity perturbed Crapper waves
- Creators
- Benjamin F. Akers - United States Air ForceDavid M. Ambrose (Corresponding Author) - Drexel UniversityJ. Douglas Wright - Drexel University
- Publication Details
- Proceedings of the Royal Society. A, Mathematical, physical, and engineering sciences, v 470(2161), 20130526
- Publisher
- The Royal Society
- Number of pages
- 14
- Grant note
- DMS-1008387; DMS-1016267; DMS-0908299; DMS-1105635 / National Science Foundation; National Science Foundation (NSF) 1105635 / Division Of Mathematical Sciences; National Science Foundation (NSF); NSF - Directorate for Mathematical & Physical Sciences (MPS)
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000332392800010
- Scopus ID
- 2-s2.0-84890107513
- Other Identifier
- 991019169415904721
UN Sustainable Development Goals (SDGs)
This publication has contributed to the advancement of the following goals:
InCites Highlights
Data related to this publication, from InCites Benchmarking & Analytics tool:
- Collaboration types
- Domestic collaboration
- Web of Science research areas
- Mechanics