Identifying linear and nonlinear coupling between fluid sloshing in tanks, roll of a barge and external free-surface waves

Wave-induced roll motions of liquefied natural gas carriers with partially filled spherical tanks are of practical concern. The fluid within the tanks may be excited into resonance and thus strong sloshing motion may occur at certain frequencies. However, the nature of the coupling between internal sloshing and global roll motions, possibly via higher harmonics, is uncertain. A NewWave-type approach, based on the average shape of large waves, is used to examine nonlinearity of the roll response with and without liquid cargo motion. A phase-combination method based on weakly nonlinear theory is adopted to extract the components of the high frequency signals coupled to the low frequency signals. A significant contribution is observed from the higher harmonics of the main roll response, which are coupled to the liquid cargo sloshing motion. This coupling between higher harmonics of the main roll resonance and internal sloshing appears to be linear, despite the internal sloshing being coupled nonlinearly to the low frequency roll.