Document Type
Article
Publication Date
4-7-2017
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 multi-valued height. This formulation and the presence of the elastic bending terms allows 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 multi-valued height, and the cases of single-fluid or interfacial waves.
Source Publication
Zeitschrift Für Angewandte Mathematik Und Physik (ISSN 0044-2275 | e-ISSN 1420-9039)
Recommended Citation
Akers, B. F., Ambrose, D. M., & Sulon, D. W. (2017). Periodic traveling interfacial hydroelastic waves with or without mass. Zeitschrift Für Angewandte Mathematik Und Physik, 68(6), 141. https://doi.org/10.1007/s00033-017-0884-7
Comments
Sourced from the e-print version at arXiv:1704.02387 [math.AP]. Date of arXiv submission: 7 Apr 2017.
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