Reflections from solitary waves in channels of decreasing depth
- 20 April 1985
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Fluid Mechanics
- Vol. 153 (-1) , 1-16
- https://doi.org/10.1017/s0022112085001112
Abstract
We have found that the reflected wave that is created by a right-going solitary wave as it travels in a region of slowly changing depth does not satisfy Green's law. The amplitude of the reflected wave is constant along left-going characteristics rather than proportional to the negative fourth root of depth. This new finding allows us to satisfy the mass-flux conservation laws to leading order and establishes that the perturbed Korteweg–de Vries equation is a consistent approximation for the right-going profile.Keywords
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