Nonlinear Analysis of a Two-Layer Fluid Sloshing Problem

Two-Dimensional Problem in Rectangular Tanks

Abstract

A nonlinear theory is presented to describe oscillations of two liquid layers formed in a tank. By employing the variational principle, basic equations are derived, which goven interactions of two interfaces, the interface of two liquids and the free surface. The nonlinear ordinary differential equations for two dimensional flows in rectangular tanks are derived by applying Galerkin's method to the basic equations, which represent the nonlinear coupling between linear modes. Wave heights predicted by the analysis are compared with experimental results in previous works. There is reasonable agreement between the analyses and the experiments over the range of low-order mode resonance frequencies. Both the experiment and the analysis show the phenomenon that the interface of two liquids oscillates with the frequency of 1/6-1/7 of the excitation frequency at a particular excitation frequency region. The mechanism of this phenomenon is revealed by observing the time series of nonlinear forces which act on relevant modes.