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Note on a solitary wave in a slowly varying channel

Published online by Cambridge University Press:  11 April 2006

John W. Miles
John W. Miles
Affiliation:
Institute of Geophysics and Planetary Physics, University of California, La Jolla
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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.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 80 , Issue 1 , 4 April 1977 , pp. 149 - 152
Copyright
© 1977 Cambridge University Press

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References

Johnson, R. S. 1973 On the asymptotic solution of the Korteweg — de Vries equation with slowly varying coefficients. J. Fluid Mech. 60, 813–824.Google Scholar
Lamb, H. 1932 Hydrodynamics. Cambridge University Press.
Madsen, O. S. & Mei, C. C. 1969 The transformation of a solitary wave over an uneven bottom. J. Fluid Mech. 39, 781–791.Google Scholar
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Perroud, P. H. 1957 The solitary wave rofloction along a straight vertical wall at oblique incidenco. Ph.D. thesis, University of California, Berkeley.