Solitary Waves in Open Channels with Abrupt Turns and Branching Points
- https://doi.org/10.1142/S1402925112400116How to use a DOI?
- Water waves, solitary waves, tsunami in channels
The dynamics of solitary waves is studied in intricate domains such as open channels with sharp-bends and branching points. Of particular interest, the wave characteristics at sharp-bends is rationalized by using the Jacobian of the Schwarz–Christoffel transformation. It is observed that it acts in a similar fashion as a topography in other wave models previously studied. Previous numerical studies are revisited. A new very efficient algorithm is described, which computationally solves the problem in much more general channel configurations than presented in the literature. Also the conformal mapping naturally leads to a new strategy regarding the geometrical singularity at the sharp-bends. Finally preliminary results illustrate the use of the mapping's Jacobian at a channel's branching point. A future goal of this study regards deducing accurate reduced (one-dimensional) models for the reflection and transmission of solitary waves on graphs/networks.
- © 2012 The Authors. Published by Atlantis Press and Taylor & Francis
- Open Access
- This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).
Cite this article
TY - JOUR AU - André Nachbin AU - Vanessa da Silva Simões PY - 2012 DA - 2012/11 TI - Solitary Waves in Open Channels with Abrupt Turns and Branching Points JO - Journal of Nonlinear Mathematical Physics SP - 116 EP - 136 VL - 19 IS - Supplement 1 SN - 1776-0852 UR - https://doi.org/10.1142/S1402925112400116 DO - https://doi.org/10.1142/S1402925112400116 ID - Nachbin2012 ER -