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Archive for Rational Mechanics and Analysis

, Volume 216, Issue 2, pp 449–471 | Cite as

Trimodal Steady Water Waves

  • Mats EhrnströmEmail author
  • Erik Wahlén
Article

Abstract

We construct three-dimensional families of small-amplitude gravity-driven rotational steady water waves of finite depth. The solutions contain counter-currents and multiple crests in each minimal period. Each such wave is, generically, a combination of three different Fourier modes, giving rise to a rich and complex variety of wave patterns. The bifurcation argument is based on a blow-up technique, taking advantage of three parameters associated with the vorticity distribution, the strength of the background stream, and the period of the wave.

Keywords

Vorticity Water Wave Implicit Function Theorem Critical Layer Vorticity Distribution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Department of Mathematical SciencesNorwegian University of Science and TechnologyTrondheimNorway
  2. 2.Centre for Mathematical SciencesLund UniversityLundSweden

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