Figure 1. Schematic configuration of two- dimensional wave sloshing
Sloshing has been very important for many years and widely studied in many of the engineering areas. Wave sloshing can be described as motion of the wave in a subjected area. More specifically, wave sloshing is the change of wave height and its frequency with time.
Wave sloshing could be very dangerous for ship containers during navigation because sloshing may cause serious damages on container walls and sometimes even hull structures, eventually affecting vessel's motion, especially for offshore supply vessels which transport natural gas (LNG carriers). For those kind of vessels the behavior of the liquid may be even more dangerous if the excitation frequency increases too much. It might damage the ship and effect the environment because of the high hydrodynamic forces acting on the container (Coupling Effect). For those reasons, wave amplitude and wave frequency are two very important parameters which people have researched for years.
For this paper, I have reviewed the articles published about wave sloshing and related problems (mostly coupling effects) over a fifteen-year period and have selected the most cited ones. In the paper I present these articles in order of their published dates. Also, I shortly describe what researchers have studied related to this topic and what the current popular problem is.
Armenio and Rocca (1996)  analyzed two different governing equations to simulate the equation of motion in the fluid. First one is Reynolds averaged Navier-Stokes equation and the second one is the shallow water equation.
Studies which include the interaction between sloshing fluid and tank motion started to be published after 2000's. Some of these studies are: B.F.Chen and H.W. Chiang (2000)  explained the concepts of the complete two-dimensional analysis actions of surge, heave, and pitch motions. In that study they showed that the motion of sloshing fluid inside the tank is travelling with the dynamic motion of the tank. Their research was based on random excitations. Researchers used finite element method to analyze liquid sloshing based on the fully non-linear wave potential theory. S.J.Lee and M.H.Kim (2007)  conducted a research on the effects of tank sloshing on LNG vessel and floating terminal responses. In that study, they used a new computer program based on Navier-stokes equation solver to analyze the effects between ship motion and inner-tank liquid sloshing.
Moreover, in the last decade researchers have started to focus on coupling effects because there has been a growing demand from the ship manufacturers due to the significant size increase of LNG carriers.
Y.Kim, B.W.Nam (2007) focused on coupling effects of ship motion and sloshing in their research. S.J.Lee and M.H.Kim (2007)  also worked on this topic by emphasizing the growing concern about the LNG FPSO/FSRU operation in the production site...