Premium
Exact steady periodic water waves with vorticity
Author(s) -
Constantin Adrian,
Strauss Walter
Publication year - 2004
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.3046
Subject(s) - inviscid flow , monotone polygon , mathematics , euler equations , vorticity , mathematical analysis , gravity wave , stratification (seeds) , potential vorticity , bifurcation , crest , euler's formula , vortex , gravitational wave , classical mechanics , geometry , mechanics , nonlinear system , physics , seed dormancy , germination , botany , quantum mechanics , dormancy , biology , astrophysics
We consider the classical water wave problem described by the Euler equations with a free surface under the influence of gravity over a flat bottom. We construct two‐dimensional inviscid periodic traveling waves with vorticity. They are symmetric waves whose profiles are monotone between each crest and trough. We use bifurcation and degree theory to construct a global connected set of such solutions. © 2003 Wiley Periodicals, Inc.