Hamiltonian formulation of nonlinear water waves in a two-fluid system |
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Authors: | Lu Dongqiang Dai Shiqiang Zhang Baoshan |
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Institution: | (1) Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, 200072 Shanghai, P R China |
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Abstract: | In this paper, it
is dealt with that the Hamiltonian formulation of nonlinear water waves in a two_fluid
system,which consists of two layers of constant_density incompressible inviscid fluid with a
horizontal bottom,an interface and a free surface. The velocity potentials are expanded in power
series of the vertical coordinate. By taking the kinetic thickness of lower fluid_layer and the
reduced kinetic thickness of upper fluid_layer as the generalized displacements, choosing the
velocity potentials at the interface and free surface as the generalized momenta and using
Hamilton's principle, the Hamiltonian canonical equations for the system are derived with the
Legendre transformation under the shallow water assumption. Hence the results for
single_layer fluid are extended to the case of stratified fluid. |
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Keywords: | two_fluid system Hamilton's principle nonlinear water waves shallow water assumption Hamiltonian canonical equations |
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