On stratified water waves with critical layers and Coriolis forces

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Abstract

We consider nonlinear traveling waves in a two-dimensional fluid subject to the effects of vorticity, stratification, and in-plane Coriolis forces. We first observe that the terms representing the Coriolis forces can be completely eliminated by a change of variables. This does not appear to be well-known, and helps to organize some of the existing literature. Second we give a rigorous existence result for periodic waves in a two-layer system with a free surface and constant densities and vorticities in each layer, allowing for the presence of critical layers. We augment the problem with four physically-motivated constraints, and phrase our hypotheses directly in terms of the explicit dispersion relation for the problem. This approach smooths the way for further generalizations, some of which we briefly outline at the end of the paper.

Original languageEnglish
Pages (from-to)4747-4770
Number of pages24
JournalDiscrete and Continuous Dynamical Systems- Series A
Volume39
Issue number8
DOIs
Publication statusPublished - 1 Aug 2019

Keywords

  • Bifurcation
  • Free boundary problems
  • Stratified water waves
  • Vorticity
  • Water waves

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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