Oscillations of two superposed fluids in an open and flexible container

What is it about?

The interaction of two superposed inviscid liquids with a flexible side wall of a rectangular container is considered. The governing equations describing the behaviour of the system are analyzed using the concept of normal modes, and their solutions presented in the form of infinite series. The expansion coefficients for the velocity potentials are calculated by employing a new inner product which allows orthogonalizing the fluid shape modes. An eigenfrequency equation is then derived from the requirement for a nontrivial solution exists. The influence of the governing parameters on the coupled frequencies is illustrated in the case of water–mercury system.

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Why is it important?

The focus of the present Note is on the extension of these results to hydroelastic systems with two superposed fluids. Once the boundary conditions for the elastic plate are specified, there are, in addition to the parameters involved in a single fluid system, three other crucial factors, namely the interfacial surface tension and the relative thickness and mass density of the two fluids. Various specific physical mechanisms are then expected to contribute to the occurrence of a richer dynamics than that of a one fluid system.

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