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Journal article
Periodic traveling interfacial hydroelastic waves with or without mass
Zeitschrift für angewandte Mathematik und Physik, v 68(6), pp 1-27
01 Dec 2017
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Abstract
We study the motion of an interface between two irrotational, incompressible fluids, with elastic bending forces present; this is the hydroelastic wave problem. We prove a global bifurcation theorem for the existence of families of spatially periodic traveling waves on infinite depth. Our traveling wave formulation uses a parameterized curve, in which the waves are able to have multivalued height. This formulation and the presence of the elastic bending terms allow for the application of an abstract global bifurcation theorem of "identity plus compact" type. We furthermore perform numerical computations of these families of traveling waves, finding that, depending on the choice of parameters, the curves of traveling waves can either be unbounded, reconnect to trivial solutions, or end with a wave which has a self-intersection. Our analytical and computational methods are able to treat in a unified way the cases of positive or zero mass density along the sheet, the cases of single-valued or multivalued height, and the cases of single-fluid or interfacial waves.
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Details
- Title
- Periodic traveling interfacial hydroelastic waves with or without mass
- Creators
- Benjamin F. Akers - U.S. Air Force Institute of TechnologyDavid M. Ambrose - Drexel University, MathematicsDavia W Sulon - Drexel University, Mathematics
- Publication Details
- Zeitschrift für angewandte Mathematik und Physik, v 68(6), pp 1-27
- Publisher
- Springer Nature
- Number of pages
- 27
- Grant note
- DMS-1515849 / NSF; National Science Foundation (NSF) Office of Naval Research (ONR grant APSHEL)
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000417753500005
- Scopus ID
- 2-s2.0-85035092170
- Other Identifier
- 991019169519204721
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- Collaboration types
- Domestic collaboration
- Web of Science research areas
- Mathematics, Applied