Journal article
Traveling waves from the arclength parameterization: Vortex sheets with surface tension
Interfaces and free boundaries, v 15(3), pp 359-380
01 Jan 2013
Featured in Collection : UN Sustainable Development Goals @ Drexel
Abstract
We study traveling waves for the vortex sheet with surface tension. We use the angle-arclength description of the interface rather than Cartesian coordinates, and we utilize an arclength parameterization as well. In this setting, we make a new formulation of the traveling wave ansatz. For this problem, it should be possible for traveling waves to overturn, and notably, our formulation does allow for waves with multi-valued height. We prove that there exist traveling vortex sheets with surface tension bifurcating from equilibrium. We compute these waves by means of a quasi-Newton iteration in Fourier space; we find continua of traveling waves bifurcating from equilibrium and extending to include overturning waves, for a variety of values of the mean vortex sheet strength.
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Details
- Title
- Traveling waves from the arclength parameterization: Vortex sheets with surface tension
- Creators
- Benjamin Akers - Air Force Institute of TechnologyDavid M. Ambrose - Drexel UniversityJ. Douglas Wright - Drexel University
- Publication Details
- Interfaces and free boundaries, v 15(3), pp 359-380
- Publisher
- European Mathematical Soc
- Number of pages
- 22
- 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:000329994600004
- Scopus ID
- 2-s2.0-84890057293
- Other Identifier
- 991019169529204721
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- Collaboration types
- Domestic collaboration
- Web of Science research areas
- Mathematics
- Mathematics, Applied