Three-dimensional gravity waves in a channel of variable depth |
| |
Authors: | Ranis N. Ibragimov Dmitry E. Pelinovsky |
| |
Affiliation: | aDepartment of Mathematics, McMaster University, Hamilton, Ontario, Canada L8S 4K1 |
| |
Abstract: | We consider existence of three-dimensional gravity waves traveling along a channel of variable depth. It is well known that the long-wave small-amplitude expansion for such waves results in the stationary Korteweg–de Vries equation, coefficients of which depend on the transverse topography of the channel. This equation has a single-humped solitary wave localized in the direction of the wave propagation. We show, however, that there exists an infinite set of resonant Fourier modes that travel at the same speed as the solitary wave does. This fact suggests that the solitary wave confined in a channel of variable depth is always surrounded by small-amplitude oscillatory disturbances in the far-field profile. |
| |
Keywords: | Three-dimensional gravity waves Euler’ s equations Spatial dynamics Hamiltonian functions Linearized equations |
本文献已被 ScienceDirect 等数据库收录! |