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Bibliographic Details
Main Author:	Semenova, Anastassiya
Format:	Preprint
Published:	2024
Subjects:	Pattern Formation and Solitons Mathematical Physics
Online Access:	https://arxiv.org/abs/2411.15184
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author	Semenova, Anastassiya
author_facet	Semenova, Anastassiya
contents	We study two-crested traveling Stokes waves on the surface of an ideal fluid with infinite depth. Following Chen and Saffman (1980), we refer to these waves as class $\mathrm{II}$ Stokes waves. The class $\mathrm{II}$ waves are found from bifurcations from the primary branch of Stokes waves away from the flat surface. These waves are strongly nonlinear, and are disconnected from small-amplitude solutions. Distinct class $\mathrm{II}$ bifurcations are found to occur in the first two oscillations of the velocity versus steepness diagram. The bifurcations in distinct oscillations are not connected via a continuous family of class $\mathrm{II}$ waves. We follow the first two families of class $\mathrm{II}$ waves, which we refer to as the secondary branch (that is primary class $\mathrm{II}$ branch), and the tertiary branch (that is secondary class $\mathrm{II}$ branch). Similar to Stokes waves, the class $\mathrm{II}$ waves follow through a sequence of oscillations in velocity as their steepness rises, and indicate the existence of limiting class $\mathrm{II}$ Stokes waves characterized by a $120$ degree angle at every other wave crest.
format	Preprint
id	arxiv_https___arxiv_org_abs_2411_15184
institution	arXiv
publishDate	2024
record_format	arxiv
spellingShingle	Two-Crested Stokes Waves Semenova, Anastassiya Pattern Formation and Solitons Mathematical Physics We study two-crested traveling Stokes waves on the surface of an ideal fluid with infinite depth. Following Chen and Saffman (1980), we refer to these waves as class $\mathrm{II}$ Stokes waves. The class $\mathrm{II}$ waves are found from bifurcations from the primary branch of Stokes waves away from the flat surface. These waves are strongly nonlinear, and are disconnected from small-amplitude solutions. Distinct class $\mathrm{II}$ bifurcations are found to occur in the first two oscillations of the velocity versus steepness diagram. The bifurcations in distinct oscillations are not connected via a continuous family of class $\mathrm{II}$ waves. We follow the first two families of class $\mathrm{II}$ waves, which we refer to as the secondary branch (that is primary class $\mathrm{II}$ branch), and the tertiary branch (that is secondary class $\mathrm{II}$ branch). Similar to Stokes waves, the class $\mathrm{II}$ waves follow through a sequence of oscillations in velocity as their steepness rises, and indicate the existence of limiting class $\mathrm{II}$ Stokes waves characterized by a $120$ degree angle at every other wave crest.
title	Two-Crested Stokes Waves
topic	Pattern Formation and Solitons Mathematical Physics
url	https://arxiv.org/abs/2411.15184

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