Numerical Investigation of Two-Dimensional Sloshing: Nonlinear Internal Waves

Abstract

In this paper we examine internal sloshing motions in 2-D numerical wave tanks subjected to horizontal excitation. In all of the cases studied, the rectangular tank of liquid has a width-to-depth ratio of 2. The results presented are from simulations of internal waves induced by sloshing a density-stratified liquid. Nonlinear, viscous flow equations of a Newtonian, Boussinesq liquid are solved. Some of the features of the evolution of sloshing in nearly two-layer and three-layer fluid systems are described. Initially, the middle of the two layers and the center of the middle layer of the three layers are horizontal and located at the center of the tank. The two-layer cases are forced at resonance. The evolution of sloshing from rest is examined. The maximum amplitude of sloshing occurs during the initial transient. If breaking occurs, it is at the center of the container in the two-layer cases. The subharmonic forcing of a three-layer case induces a resonant response with the middle layer moving in such a way that motion is perpendicular to the isopycnals within this layer. These model problems provide some insights into the relatively complex sloshing that can occur in density-stratified liquids.