A new formulation of the water wave problem for Stokes waves of constant vorticity

  • Ehrnström M
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Abstract

We consider steady symmetric gravity water waves on finite depth with constant vorticity and a monotone surface profile between crests and troughs. The problem is transformed into one concerning the vertical velocity. A representation formula for the stream function in terms of the surface and the vorticity is presented, and we show that the surface can be determined from the vertical velocity. © 2007 Elsevier Inc. All rights reserved.

Author-supplied keywords

  • Formulation
  • Nonlinear partial differential equation
  • Steady water waves
  • Surface
  • Uniqueness
  • Vorticity

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Authors

  • Mats Ehrnström

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