Boussinesq Models with Moving Boundaries and Their Applicability to Waves Generated by Lateral Oscillation and Bottom Deformation

Abstract

This paper presents analytical solutions based on Boussinesq models with moving boundaries and their applicability to the phenomena of water waves: sloshing in a rectangular tank on an oscillation table generated by lateral moving boundaries and tsunami generation by a moving bottom. In the application to sloshing, the linear solutions in Boussinesq and hydrostatic models were derived, and their characteristics were examined by comparing them with experimental results. It was shown that the result for the Boussinesq models was in close agreement with measurements for high wave numbers. In the application to tsunami generation, linear solutions were compared with numerical simulation results. The linear solutions with the effect of vertical acceleration on the bottom and across the depth improved the reproducibility of the wave profiles. The reproducibility of the linear solutions was confirmed to be good, except for the case of faster bottom motion with linear temporal change. These analytical solutions will be useful to engineers in understanding the phenomena considered.