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Three-Dimensional Steady Capillary-Gravity Waves

In: Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems

Author

Listed:
  • Mariana Hărăguş-Courcelle

    (Universität Stuttgart, Mathematisches Institut A)

  • Klaus Kirchgässner

    (Universität Stuttgart, Mathematisches Institut A)

Abstract

Three-dimensional steady capillary-gravity water-waves are studied in this paper. Potential flow of an ideal fluid in a layer with finite depth and upper free surface is considered. The existence of these waves is derived through bifurcation processes from the state of rest. The waves are assumed to be periodic in the direction of propagation and just bounded in the transverse direction (modulated periodic travelling waves — MPTW). Restricting the analysis to small amplitude waves, one can reduce the problem to a finite-dimensional reversible and reflectionally symmetric dynamical system. Existence and full information about the geometry of the shape of possible crests then follows via normal form analysis and persistence.

Suggested Citation

  • Mariana Hărăguş-Courcelle & Klaus Kirchgässner, 2001. "Three-Dimensional Steady Capillary-Gravity Waves," Springer Books, in: Bernold Fiedler (ed.), Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems, pages 363-397, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-56589-2_16
    DOI: 10.1007/978-3-642-56589-2_16
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