Hamiltonian Long Wave Expansions for Internal Waves Over a Periodically Varying Bottom

ZHOU Hong-yan; PIAO Da-xiong

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Article Navigation > Applied Mathematics and Mechanics > 2008 > 29(6): 676-686

ZHOU Hong-yan, PIAO Da-xiong. Hamiltonian Long Wave Expansions for Internal Waves Over a Periodically Varying Bottom[J]. Applied Mathematics and Mechanics, 2008, 29(6): 676-686.

Citation:

ZHOU Hong-yan, PIAO Da-xiong. Hamiltonian Long Wave Expansions for Internal Waves Over a Periodically Varying Bottom[J]. Applied Mathematics and Mechanics, 2008, 29(6): 676-686.

Citation:

ZHOU Hong-yan, PIAO Da-xiong. Hamiltonian Long Wave Expansions for Internal Waves Over a Periodically Varying Bottom[J]. Applied Mathematics and Mechanics, 2008, 29(6): 676-686.

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Hamiltonian Long Wave Expansions for Internal Waves Over a Periodically Varying Bottom

Research Center for Applied Mathematics, Ocean University of China, Qingdao, Shandong 266071, P. R. China

Received Date: 2007-11-27
Rev Recd Date: 2008-04-14
Publish Date: 2008-06-15

Abstract

Abstract

A Hamiltonian formulation for two-dimensional nonlinear long waves between two bodies of immiscible fluid with a periodic bottom was derived. From the formulation, using the Hamiltonian perturbation theory, effective Boussinesq equations that describe the motion of bidirectional long waves and unidirectional equations that are similar to the KdV equation for the case in which the bottom possesses short length scale were obtained. The computations for these results are performed in the framework of an asymptotic analysis of multiple scale operators.
- internal waves,
- Hamiltonian perturbation theory,
- potential function,
- Dirichlet Neumann operator,
- Boussinesq equation,
- KdV equation

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References(13)

References

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