Journal of Mathematical Fluid Mechanics

, Volume 14, Issue 3, pp 407–419 | Cite as

Steady Water Waves with Multiple Critical Layers: Interior Dynamics

  • Mats EhrnströmEmail author
  • Joachim Escher
  • Gabriele Villari


We study small-amplitude steady water waves with multiple critical layers. Those are rotational two-dimensional gravity-waves propagating over a perfect fluid of finite depth. It is found that arbitrarily many critical layers with cat’s-eye vortices are possible, with different structure at different levels within the fluid. The corresponding vorticity depends linearly on the stream function.

Mathematics Subject Classification (2010)

Primary 76B15 Secondary 35Q35 


Steady water waves Small-amplitude waves Critical layers Vorticity 


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Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  • Mats Ehrnström
    • 1
    Email author
  • Joachim Escher
    • 1
  • Gabriele Villari
    • 2
  1. 1.Institut für Angewandte MathematikLeibniz Universität HannoverHannoverGermany
  2. 2.Dipartimento di MatematicaFirenzeItaly

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