Reflectionless wave dynamics in channels of variable depth and width
Abstract
In this work we discuss long wave dynamics in rectangular channels of variable depth and width. Demonstrated, that for conditions of "self-consistent channel" when Bc = const (B is a channel width, and c is a celerity), the wave propagates without inner reflection from the channel bottom and walls even if the function c(x) is arbitrary. It is shown, in the framework of the linear shallow-water theory, that the temporal shape of the travelling wave does not change with the distance; its amplitude and duration are constant. However, the spatial shape of the wave varies due to the change in celerity along the channel. In the framework of the nonlinear shallow-water theory, it is shown that the travelling wave deforms while the inner reflection from the channel bottom and walls is still absent. In this case dispersive effects lead to a disintegration of the initial wave into solitons. This process is studied in detail. Such unusual waves may propagate over long distances without loss of energy.
- Publication:
-
EGU General Assembly Conference Abstracts
- Pub Date:
- April 2017
- Bibcode:
- 2017EGUGA..19.2977P