Wave induced motions of two ships advancing on parallel course
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- Institutt for marin teknikk 
Under way replenishment between two ships is a critical operation, and accidents have been reported. Hydrodynamic interaction between the hulls may influence the forces and the motions of the vessels, and both manoeuvring and seakeeping performance may be affected. The steady loads on ships travelling in the vicinity of each other in calm water have been investigated in several previous studies. This thesis focuses on seakeeping of two ships advancing on paralles course in waves. The far field wave pattern of an oscillating ship with forward speed is studied in order to evaluate the effect of the generated waves on the other ship. The wave pattern is a function of the frequency of oscillation and the forward speed of the ship. Some of the wave systems generated by the ship will have enough energy to induce motions on the other ship. It is demonstrated that for τ = wU/g>~0.4 a 2D wave pattern with forward speed effect is a good representation of the ship generated wave pattern. A linear frequency domain solution for wave induced forces and motions of two slender ships with equal speed on parallel course is devoloped. The procedures is a generalization of Newman's unified theory for one hull and Kashiwagi's theory for catamarans. The ships are assumed to be other's hydrodynamic far field i.e. the transverse distance is formally assumed to be fo the order of the ship length, O(L). The full 3D problem is simplified by dividing it into an inner region for each ship and a common outer region where not all the boundary conditions need to be fulfilled. The solutions from the inner and outer domains are matched in an overlap region for each ship forming the complete solution near each ship. The two-ship numerical method can also be used for catamarans at moderate forward speed including wave interaction between the hulls. Model tests with two ships advancing at forward speed in regular head waves are sonducted as a part of the validation of the presented theory. Experimental bias due to the set-up is thoroughly discussed. An interesting wave phenomenon was discovered in the experiments. For a τ value slightly above 1/4, large amplitude 2D wavespropagating in the forward direction developed between the hulls. Possible mechanisms of the phenomenon are described. The seakeeping theory calculations are compared with published experiments for monohulls and catamarans and with new experiments for the two ship case. The overall agreement for hydrodynamic forces and motions is good.