Small-amplitude Stokes and solitary gravity water waves with an arbitrary distribution of vorticity
Författare
Summary, in English
This paper presents an existence theory for small-amplitude Stokes and solitary-wave solutions to the classical water-wave problem in the absence of surface tension and with an arbitrary distribution of vorticity. The hydrodynamic problem is formulated as an infinite-dimensional Hamiltonian system in which the horizontal spatial coordinate is the time-like variable. A centre-manifold technique is used to reduce the system to a locally equivalent Hamiltonian system with one degree of freedom for values of a dimensionless parameter a near its critical value alpha*. The phase portrait of the reduced system contains a homoclinic orbit for alpha < alpha* and a family of periodic orbits for alpha > alpha*; the corresponding solutions of the water-wave problem are respectively a solitary wave of elevation and a family of Stokes waves. (c) 2008 Elsevier B.V. All rights reserved.
Avdelning/ar
- Matematik (naturvetenskapliga fakulteten)
- Partial differential equations
Publiceringsår
2008
Språk
Engelska
Sidor
1530-1538
Publikation/Tidskrift/Serie
Physica D: Nonlinear Phenomena
Volym
237
Issue
10-12
Dokumenttyp
Artikel i tidskrift
Förlag
Elsevier
Ämne
- Mathematics
Nyckelord
- bifurcation theory
- water waves
- vorticity
Status
Published
Forskningsgrupp
- Partial differential equations
ISBN/ISSN/Övrigt
- ISSN: 0167-2789