Dispersion relations for fixed mean-depth flows with two discontinuities in vorticity. (April 2019)

• Record Type: Journal Article
• Authors: Kluczek, Mateusz; Martin, Calin Iulian
• Is Part Of: Nonlinear analysis. Volume 181(2019)
• Page Start: 62
• Page End: 86
• Publication Date: 2019-04
• Subjects: 35D30 -- 70K50 -- 74J15 -- 74J30 -- 76B15 -- 76E05; Steady water waves -- Dispersion relation -- Discontinuous vorticity -- Stability of laminar solutions -- Fixed mean-depth formulation; 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.2018.11.007
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We derive here the dispersion relation for small-amplitude steady two-dimensional periodic water waves that propagate over a flat bed with a specified and fixed mean-depth. The water flow has a discontinuous vorticity distribution reflecting an isolated rotational layer of fluid. We then use the dispersion relation to obtain necessary and sufficient conditions for local bifurcation to occur. Moreover, a stability analysis of the laminar flows is presented.