**Hamiltonian
Formulation of Nonlinear Water Waves in a Two-Fluid System**
ע⣺ՓڡÔWWӢİ棩1999344331-336.l
ʹՈעՓĳ̎
*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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