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Traveling gravity water waves with critical layers

Varholm, Kristoffer; Aasen, Ailo
Journal article, Peer reviewed
Accepted version
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URI
http://hdl.handle.net/11250/2467397
Date
2017
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  • Institutt for matematiske fag [1769]
  • Publikasjoner fra CRIStin - NTNU [26648]
Original version
Journal of Mathematical Fluid Mechanics. 2017, .   10.1007/s00021-017-0316-7
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.
Publisher
Springer Verlag
Journal
Journal of Mathematical Fluid Mechanics

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