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A NOTE ON HAMILTONIAN FOR LONG WATER-WAVES IN VARYING DEPTH
- Authors
- Yoon, Sung B; Liu, Philip L.-F.
- Issue Date
- Dec-1994
- Publisher
- ELSEVIER SCIENCE BV
- Citation
- WAVE MOTION, v.20, no.4, pp.359 - 370
- Indexed
- SCIE
SCOPUS
- Journal Title
- WAVE MOTION
- Volume
- 20
- Number
- 4
- Start Page
- 359
- End Page
- 370
- ISSN
- 0165-2125
- Abstract
- The Hamiltonian for two-dimensional long waves over a slowly varying depth is derived. The vertical variation of the velocity field is obtained by using a perturbation method in terms of velocity potential. Employing the canonical theorem, the conventional Boussinesq equations are recovered. The Hamiltonian becomes negative when the wavelength becomes short. A modified Hamiltonian is constructed so that it remains positive and finite for short waves. The corresponding Boussinesq-type equations are then given.
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