Traveling Gravity Water Waves with Critical Layers

Traveling Gravity Water Waves with Critical Layers We establish the existence of small-amplitude uni- and bimodal steady periodic gravity waves with an affine vorticity distribution, using a bifurcation argument that differs slightly from earlier theory. The solutions describe waves with critical layers and an arbitrary number of crests and troughs in each minimal period. An important part of the analysis is a fairly complete description of the local geometry of the so-called kernel equation, and of the small-amplitude solutions. Finally, we investigate the asymptotic behavior of the bifurcating solutions. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Mathematical Fluid Mechanics Springer Journals

Traveling Gravity Water Waves with Critical Layers

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Publisher
Springer International Publishing
Copyright
Copyright © 2017 by Springer International Publishing
Subject
Physics; Fluid- and Aerodynamics; Mathematical Methods in Physics; Classical and Continuum Physics
ISSN
1422-6928
eISSN
1422-6952
D.O.I.
10.1007/s00021-017-0316-7
Publisher site
See Article on Publisher Site

Abstract

We establish the existence of small-amplitude uni- and bimodal steady periodic gravity waves with an affine vorticity distribution, using a bifurcation argument that differs slightly from earlier theory. The solutions describe waves with critical layers and an arbitrary number of crests and troughs in each minimal period. An important part of the analysis is a fairly complete description of the local geometry of the so-called kernel equation, and of the small-amplitude solutions. Finally, we investigate the asymptotic behavior of the bifurcating solutions.

Journal

Journal of Mathematical Fluid MechanicsSpringer Journals

Published: Feb 6, 2017

References

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