The sloshing of stratified liquid in a two-dimensional rectangular tank

The sloshing of inviscid liquid of stratified density in a rectangular tank is analyzed.As the flow is no longer irrotional,the governing equation is found to be quite different from the Laplace equation used for the liquid of constant density.In particular it contains terms of mixed temporal and spatial derivatives.The problem is solved based on the variable separation method and Laplace transform for the constant Vaisala-Brunt frequency.It is found that the stratification of density may have small effects on those natural frequencies associated with the constant density,but many new natural frequencies have appeared as a result of its effect.