Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9690621 | European Journal of Mechanics - B/Fluids | 2005 | 12 Pages |
Abstract
In this paper, we prove the existence of a large family of nontrivial bifurcating standing waves for a model system which describes two-way propagation of water waves in a channel of finite depth or in the near shore zone. In particular, it is shown that, contrary to the classical standing gravity wave problem on a fluid layer of finite depth, the Lyapunov-Schmidt method applies to find the bifurcation equation. The bifurcation set is formed with the discrete union of Whitney's umbrellas in the three-dimensional space formed with 3 parameters representing the time-period and the wave length, and the average of wave amplitude.
Related Topics
Physical Sciences and Engineering
Chemical Engineering
Fluid Flow and Transfer Processes
Authors
Min Chen, GĂ©rard Iooss,