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arXiv · 1904.00401

Solitary waves on rotational flows with an interior stagnation point

Vladimir Kozlov·Nikolai G. Kuznetsov·Evgeniy Lokharu
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Abstract

The two-dimensional free-boundary problem describing steady gravity waves with vorticity on water of finite depth is considered. Under the assumption that the vorticity is a negative constant whose absolute value is sufficiently large, we construct a solution with the following properties. The corresponding flow is unidirectional at infinity and has a solitary wave of elevation as its upper boundary; under this unidirectional flow, there is a bounded domain adjacent to the bottom, which surrounds an interior stagnation point and is divided into two subdomains with opposite directions of flow by a critical level curve connecting two stagnation points on the bottom.

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Vladimir Kozlov, Nikolai G. Kuznetsov, Evgeniy Lokharu. 2020-01-10. Solitary waves on rotational flows with an interior stagnation point. https://doi.org/10.1017/jfm.2020.647

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