A modal method for finite amplitude, nonlinear sloshing

A modal method is used to calculate the two-dimensional sloshing motion of an inviscid liquid in a rectangular container. The full nonlinear problem is reduced to the solution of a system of nonlinear ordinary differential equations for the time varying coefficients in the expansions of the interface and the potential. The effects of capillarity are included in the formulation. The simplicity, generality and power of the method are exhibited not only by recovering the earlier results obtained, for example, by Penney and Price [1], Tadjbakhsh and Keller [2] and Faltinsen et al [3], but also by obtaining new and interesting results of the effects of capillarity and shallow depth, which would be difficult to obtain otherwise. For example, it is found that for the initial interface profile considered here, parasitic capillary waves, borne by the higher number wave modes, are generated for moderate capillarity but disappear for larger values of the parameter. The method can be extended to other simple geometries.