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Hamiltonian Formulation of Nonlinear Water Waves in a Two-Fluid System

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Applied Mathematics and Mechanics - English Edition, Vol. 20, No. 4, pp. 343-349, Apr 1999.

Lu Dongqiang,Dai Shiqiang,Zhang Baoshan

(Shanghai Institute of Applied Mathematics and Mechanics,Shanghai University, Shanghai 200072,P R China)

 

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.
Key words: two-fluid system; Hamilton's principle; nonlinear water waves; shallow water assumption; Hamiltonian canonical equations

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