The motions of barge with partially filled tanks in variable bathymetry are investigated based on linearized potential theory in the frequency domain. The internal sloshing motion is simulated by linearized superposition of natural sloshing modes. The motion of barge is solved by matching eigen-functions expansion in the external fluid domain. Coupling sway and roll motions of floating body with different filling levels are compared. The effects of both inclined bottom with different slopes and hump-shaped bottom with different heights are analyzed. Viewing from the results, coupling sway and roll motions of floating body are significantly affected by the shapes of bottoms.
The need for distribution and consumption of liquefied natural gas (LNG) results in significant research on floating structures used to store, convert and transfer LNG. A specific case is the sea-keeping of LNG floating storage unit in restricted water depth. Wave-induced loads and motions of floating body in variable bathymetry is important for the design of mooring system and insuring that under-keel clearance is sufficient.
The research on wave propagating in variable bathymetry regions is very important for coastal engineering. A nonlinear coupled-mode system is presented in Belibassakis and Athanassoulis (2011) for modelling the evolution of nonlinear water waves in finite depth over a general bottom topography. Fully nonlinear waves interacting with a rapidly varying bathymetry is modeled in Madsen et al (2006) by a Boussinesq-type method. The surface waves interacting with a vertical sheared current is simulated by extended mild-slope equation in Touboul et al (2016). The wave loads on fixed or floating body in coastal engineering is based on these shallow water computational model.
The motions of moored ship is predicted in Bingham (2000) by the hybrid Boussinesq-panel method. The Boussinesq model of Madsen and Sorensen (1992) is used for propagating an irregular wave system from the wave-maker to a moored ship. The local incident wave field is decomposed to be input into a linear sea-keeping software (WAMIT). However there is no feed-back from the diffracted and radiated wave systems by the ship into the Boussinesq model. Nonlinear potential flow equations in an inner domain is coupled with Boussinesq equations of Zou (1997) in an outer domain in Wang et al (2008). The coupling conditions are rendered complicated by the fact that different variables are used in the two domains. A coupling method is proposed in Hamidou et al (2009) between extended Boussinesq equations (Jamois 2006) and integral equation method, under the assumption of potential flow. The fully nonlinear free surface equations are used in both numerical models. Linear Rankine panel method and nonlinear Boussinesq equation are applied for hydrodynamic features of floating body in arbitrary bathymetry in Kim and Kim (2013). In moderate depths, the nonlinear effect can be ignored and linear approach is expected to be reasonable and favorable choice for coastal areas. The hydrodynamic coefficients, exciting forces and motion responses present similar tendencies with results from the problem of constant depth.
