Existence and qualitative theory for stratified solitary water waves

Robin Ming Chen, Samuel Walsh, Miles H. Wheeler

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)

Abstract

This paper considers two-dimensional gravity solitary waves moving through a body of density stratified water lying below vacuum. The fluid domain is assumed to lie above an impenetrable flat ocean bed, while the interface between the water and vacuum is a free boundary where the pressure is constant. We prove that, for any smooth choice of upstream velocity field and density function, there exists a continuous curve of such solutions that includes large-amplitude surface waves. Furthermore, following this solution curve, one encounters waves that come arbitrarily close to possessing points of horizontal stagnation. We also provide a number of results characterizing the qualitative features of solitary stratified waves. In part, these include bounds on the wave speed from above and below, some of which are new even for constant density flow; an a priori bound on the velocity field and lower bound on the pressure; a proof of the nonexistence of monotone bores in this physical regime; and a theorem ensuring that all supercritical solitary waves of elevation have an axis of even symmetry.

Original languageEnglish
Pages (from-to)517-576
Number of pages60
JournalAnnales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Volume35
Issue number2
Early online date1 Jul 2017
DOIs
Publication statusPublished - 1 Apr 2018

Keywords

  • Free boundary problems
  • Global bifurcation
  • Stratified solitary waves
  • Water waves

ASJC Scopus subject areas

  • Analysis
  • Mathematical Physics
  • Applied Mathematics

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