Hamiltonian Formulation of the Free Surface and Interface Motions in a Tank

1st Report, Derivation of Canonical Equations and Linear Analysis

Abstract

This paper deals with the internal waves between two bodies of immiscible fluid. In theoretical analysis, we give a formulation for the equations of motion of a system of two incompressible irrotational fluids with a dynamic free surface and interface by a variational formulation. In addition, we derive a Hamiltonian formulation of this problem. This derivation is posed from Hamilton's principle in that the canonical conjugate variables are deduced from the Lagrangian under a Legendre transform. Moreover, we have focused in particular on linearized problems and investigated the character of vibration modes and an amplitude-frequency response of a three-dimensional fluid. On the other hand, the vibration modes and the amplitude-frequency response are obtained experimentally by using a model tank. The theoretical results are shown to be in good agreement with the experimental results.