Irrotational two-dimensional free-surface steady water flows over a flat bed with underlying currents. (December 2016)

• Record Type: Journal Article
• Authors: Basu, Biswajit
• Is Part Of: Nonlinear analysis. Volume 147(2016)
• Page Start: 110
• Page End: 124
• Publication Date: 2016-12
• Subjects: 35Q35 -- 35J15; Stokes wave -- Pressure -- Velocity field; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2016.08.016
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We investigate the free boundary non-linear problem for large amplitude smooth Stokes waves in flows of finite depth with underlying currents. The qualitative nature of the flow and pressure fields is investigated using maximum principles. Bounds on the surface profile have been derived. Influence of the relative magnitude of wave and current speed on the flow and pressure fields has been shown. The possible co-existence of propagating surface waves and an underlying uniform current at the wave speed is settled—this can only happen if the surface is flat.