First in case of Fig. 10 indicating the deep water, slight difference is noted, but relatively good agreement is seen. However in case of H/d = 1.5 where the water depth is relatively shallow, the tendency is quite different from the one in case of the deep water. Especially in case that S < 3.0, disagreement is noted. That is to say, it is almost impossible to align the lateral force by means of exclusively the lateral moving distance.
As a method to express the transitional lateral force quantitatively, modeling of the transitional lateral force coefficient is attempted by introducing the concept of "circulation" as a variable closely related with the magnitude and development of the vortex surrounding the hull. From the fact that the velocity of the separated vortex is in proportion to the lateral moving velocity Uo of the hull, a circulation shown below is hereby considered by substituting as a the lateral moving velocity for the velocity of the separated vortex and by substituting the distance from the hull surface to the vortex for the lateral moving distance of the hull^{11)}.
Γ = ∫uds ∝∫U^{2}0dt (3)
The transitional lateral force coefficient obtained by taking the equation shown above is shown in Fig. 12 and 13. They comply with the lateral coefficient in case that H/d is 7.0 and 1.5, respectively. Comparing the above figures with Fig. 10 and 11 obtained taking up the lateral moving distance, it is known that it is possible to use circulation in case of both the deep water and the shallow water. However in case of the shallow water (Fig. 13), the one exclusively with NDA 0.5 becomes smaller than the other ones in the vicinity of Γ≒0.5. By using the circulation obtained by multiplying the lateral moving velocity of the hull with its moving distance, it is considered that modeling of the lateral force coefficient ranging from a resting state to uniform movement has become possible. Investigation for modeling to describe the transitional lateral force coefficient of real ship except Wigley is required using an idea of the circulation in future.
Fig.12 
Lateral drag coefficient according to the circulation(H/d 7.0). 
Fig. 13 
Lateral drag coefficient according to the circulation(H/d 1.5). 
4. CONCLUSION
By applying the 3dimensional CFD method to the Wigley hull, unsteady hydrodynamic force has been obtained. A summary of the results obtained in this study is as follows:
1) The CFD computation result is finely in agreement with the experimental result, and it is ensured that the unsteady hydrodynamic force under the lateral berthing maneuver can be estimated with sufficient accuracy by CFD technique .
2) It is ensured that water depth is an important factor to exercise influence on the inertia force and transitional lateral force acting on ship hull.
3) The added mass in case of acceleration and deceleration was almost of the same magnitude despite the difference of the fluid field surrounding the hull.
4) An attempt has been obtained that modeling of the transitional lateral force ranging from rest to acceleration movement and uniform movement is possible using a circulation obtained by multiplying the lateral moving distance with moving velocity.
These results in the research are useful information for safe ship operation, and are applicable to shiphandling simulators, structure strengthening of berths, design of fenders, rational assessment of required horse power of tugboats, etc.
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[8] Patel, V.C, Chen, H.C. and Ju, S. "Ship Stern and Wake Flows : Solutions of the FullyElliptic ReynoldsAveraged NavierStokes Equations and Comparisons with Experiments", Journal of Computational Physics, Vol. 88, N0.2, pp. 305336, 1990.
[9] Tahara,VY. "Computation of Viscous Flow around Series 60 Model and Comparison with Experiments", Journal of The Kansai Society of Naval Architects, N0.220, pp. 2947, 1993.
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[11] Lee, Y.VS. "A Study on the Maneuvering Hydrodynamic Forces for Berthing Using CFD Technique", Ph. D. Thesis, Dept. Maritime Science, Kobe University of Mercantile Marine, 2003 .
AUTHOR'S BIOGRAPHY
YunSok LEE
1993: Bachelor of Dept of Maritime Transportation Science, Korea Maritime University
19931995: Korea Navy Officer
19951997: Instructor of Training Ship HANNARA
2000: Master of Mercantile Marine Science, Kobe University of Mercantile Marine (KUMM)
2003: Doctor of Engineering, KUMM
2003: Foreign Researcher in KUMM Researcher in Korea Maritime University, Aids to Navigation Research Center
Yasuyuki TODA
1984 : Doctor of Engineering (Osaka University)
19841992: Dept. of Engineering, Osaka University
19921999: Dept. of Mercantile Marine Science,
Kobe University of Mercantile Marine
1999: Dept. of Global Architecture,Osaka University
Hiroyuki SADAKANE
19671986: Dept.of Engineering, University of Osaka Prefecture (UOP)
1987: Doctor of Engineering, UOP
1986: Dept. of Maritime Studies, Kobe University of Mercantile Marine
