On periodic geophysical water flows with discontinuous vorticity in the equatorial f-plane approximation. (11th December 2017)

• Record Type: Journal Article
• Authors: Martin, Calin Iulian
• Is Part Of: Philosophical transactions. Volume 376:Number 2111(2018)
• Publication Date: 2017-12-11
• Subjects: discontinuous vorticity -- -plane approximation -- Coriolis effects -- dispersion relation; Physical sciences -- Periodicals; Engineering -- Periodicals; Mathematics -- Periodicals; 500
• DOI: 10.1098/rsta.2017.0096
• Languages: English
• ISSNs: 1364-503X

Abstract

Abstract : We are concerned here with geophysical water waves arising as the free surface of water flows governed by the f -plane approximation. Allowing for an arbitrary bounded discontinuous vorticity, we prove the existence of steady periodic two-dimensional waves of small amplitude. We illustrate the local bifurcation result by means of an analysis of the dispersion relation for a two-layered fluid consisting of a layer of constant non-zero vorticity γ 1 adjacent to the surface situated above another layer of constant non-zero vorticity γ 2 ≠ γ 1 adjacent to the bed. For certain vorticities γ 1, γ 2, we also provide estimates for the wave speed c in terms of the speed at the surface of the bifurcation inducing laminar flows. This article is part of the theme issue 'Nonlinear water waves'.