| Title | Small-amplitude Stokes and solitary gravity water waves with an arbitrary distribution of vorticity |
| Authors | M. D. Groves, Erik Wahlén |
| Alternative Location | http://dx.doi.org/10.1016/j..., Restricted Access |
| Publication | Physica D: Nonlinear Phenomena |
| Year | 2008 |
| Volume | 237 |
| Issue | 10-12 |
| Pages | 1530 - 1538 |
| Document type | Article |
| Status | Published |
| Quality controlled | Yes |
| Language | eng |
| Publisher | Elsevier Science B.V |
| Abstract 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. |
| Keywords | bifurcation theory, water waves, vorticity, |
| ISBN/ISSN/Other | ISSN: 0167-2789 |
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