TY - JOUR
T1 - A note on Hamiltonian for long water waves in varying depth
AU - Yoon, Sung B.
AU - Liu, Philip L.F.
N1 - Funding Information:
This researchh as been supportedb y a researchg rant from the National Science Foundation (BCS-8912579), by the Mathematical Sciences Institute at Cornell University, and by a researchg rant from the Army Research Office (DAAL 03-92-G-01 16).
PY - 1994/12
Y1 - 1994/12
N2 - 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.
AB - 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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U2 - 10.1016/0165-2125(94)90019-1
DO - 10.1016/0165-2125(94)90019-1
M3 - Article
AN - SCOPUS:0040057299
SN - 0165-2125
VL - 20
SP - 359
EP - 370
JO - Wave Motion
JF - Wave Motion
IS - 4
ER -