Note on a solitary wave in a slowly varying channel
- 4 April 1977
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Fluid Mechanics
- Vol. 80 (1), 149-152
- https://doi.org/10.1017/s0022112077001578
Abstract
Johnson's (1973) description of a solitary wave in water of slowly varying depth is extended to a channel of slowly varying breadth and depth b and d on the assumption that the scale for the variation of b and d is large compared with d5/2a3/2. It is inferred from conservation of energy that the amplitude of the wave is proportional to $b^{-\frac{2}{3}}d^{-1}$ (cf. Green's law $a\propto b^{-\frac{1}{2}}d^{-\frac{1}{4}}$ for long waves of small amplitude). Comparison with experiment (Perroud 1957) yields fairly satisfactory agreement for a linearly converging channel of constant depth. The agreement for a linearly diverging channel is not satisfactory, but the experimental data are inadequate to support any firm conclusion.
Keywords
This publication has 4 references indexed in Scilit:
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- Obliquely interacting solitary wavesJournal of Fluid Mechanics, 1977
- On an asymptotic solution of the Korteweg–de Vries equation with slowly varying coefficientsJournal of Fluid Mechanics, 1973
- The transformation of a solitary wave over an uneven bottomJournal of Fluid Mechanics, 1969