Nonlinear Free-Surface and Viscous-Internal Sloshing in 2-D Numerical Wave Tanks

This paper examines free-surface and internal-pycnocline sloshing motions in 2-D numerical wave tanks subjected to horizontal base excitation. In all of the cases studied, the rectangular tank of liquid has a width-to-depth ratio of 2. The first set of results are based on an inviscid, fully nonlinear finite difference free-surface model. The model equations are mapped from the physical domain onto a rectangular domain. Case studies at and off resonance are presented illustrating when linear theory is inadequate. The next set of results are concerned with analyzing internal waves induced by sloshing a density-stratified liquid. Nonlinear, viscous flow equations are solved. The influence of the side-wall boundary layers on sloshing motions as well as the onset of internal breaking of the primary sloshing mode are discussed. The frequencies that characterize the motion of internal waves are also reported.