Solitary waves on constant vorticity flows with an interior stagnation point. (10th December 2020)

• Record Type: Journal Article
• Authors: Kozlov, V.; Kuznetsov, N.; Lokharu, E.
• Is Part Of: Journal of fluid mechanics. Volume 904(2020)
• Publication Date: 2020-12-10
• Subjects: solitary waves, -- critical layers, -- surface gravity waves; Fluid mechanics -- Periodicals; 532.005
• DOI: 10.1017/jfm.2020.647
• Languages: English
• ISSNs: 0022-1120

Abstract

Abstract: 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.