A Hamiltonian approach to fairly low and fairly long gravity waves

✍ Scribed by W. A. Veen; F. W. Wubs

• Publisher: Springer
• Year: 1995
• Tongue: English
• Weight: 794 KB
• Volume: 29
• Category: Article
• ISSN: 0022-0833
• DOI: 10.1007/bf00042760

✦ Synopsis

The propagation of nonlinear dispersive gravity waves in an inviscid irrotational fluid can be described by a Hamiltonian system. The canonical equations contain a boundary integral which is computationally expensive. However, for fairly low and fairly long waves an approximation can be made that gives rise to the solution of computationally mort attractive Helmholtz-type equations. In an earlier attempt by Broer et al. [4,6] canonical equations were derived that are stable for all wavenumbers. However, two Helmholtz-type equations need to be solved per right-hand side evaluation. In this paper, canonical equations are presented with the same qualities, but now only once per right-hand side evaluation a Helmholz-type equation needs to be solved, which is optimal.