A computer program BEShiWa, based on Boussinesq's equations for the far-field flow and on a slender-body theory for the near-ship flow, is a applied to predict the squat, sinkage and trim of ships in shallow-water of varying depth with and without lateral restriction. It covers geometrical, dynamic and environmental effects, yields a good agreement with model experiments, and can be, therefore, used in many practical cases. Due to the strong interaction between the ship's squat and the water-bottom a special attention has to be paid for ships operating over a varying topography.

　

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[2] Chen, X.-N. and Sharma, S.D.: "A Slender Ship Moving at a Near-Critical Speed in a Shallow Channel," Journal of Fluid Mechanics 291 (1995, pp. 263-285) Presented at the 18^th Int. Congress of Theoretical and Applied Mech., Haifa, Israel, 1992.

[3] Constantine, T.: "On the Movement of Ships in Restricted Waterways", Journal of Fluid Mechanics, Vol. 9, 1961.

[4] Courlay. T.P.: "Ship Squat in Water of Varying Depth", RlNA Transaction, 2002.

[5] Fluegge, C. and Uliczka. K: "Dynamisches Fahrverhalten und Wechselwirkungen mit 'der Fahrrinnensohle von sehr grossen Containerschiffen unter extremen Falchwasserbedingungen", HANSA, 2001 (in German)

[6] Henn, R., Sharma, S. D. and Jiang, T. "Influence of Canal Topography on Ship Waves in Shallow Water," Proceedings of the 16^th Int. Workshop on Water Waves and Floating Bodies, Hiroshima, Japan, 2001.

[7] Horn, F.: "Theorie des Schiffes", Handbuch der Physik und Technischen Mechanik, Leipzig, 1929, pp 552-719 (in German).

[8] Jiang, T.: "Investigation of Waves generated by Ships in Shallow Water", Proceedings of the 22^nd Symposium on Naval Hydrodynamics, Washington, 1998.

[9] Jiang, T.: "Ship Waves in Shallow Water," Fortschritt-Berichte VDI, Series 12, No. 466 with ISBN 3-18-346612-0, 2001 .

[10]Jiang, T.; Henn R. and Sharma, S.D.: "Wash Waves of Ships on Fairways of Varying Topography", Proceedings of the 24^th Symposium on Naval Hydrodynamics, Fukuoka, Japan, 2002.

[11] Mei, C.C. and Choi, H.S.: "Forces on a Slender Ship Advancing Near the Critical Speed in a Wide Canal", Journal of Fluid Mechanics, 1987, pp.59-76.

[12] Peregrine, D.H.: "Long Waves on a Beach," Journal of Fluid Mechanics, Vol. 27, 1967, pp. 815-827.

[13]Roemisch, K.: "Squat - der hydrodynamisch bestimmte Anteil der Underkeel Claerance", Schiff & Hafen, No. 4, 2003, pp. 90-94 (in German).

[14] Schmiechen, M.: "Squat Formulae", Proceedings of the 18th Duisburg Colloquium Ship and Offshore Technology, 1997 (in German).

[15]Tuck, E.O.: "Shallow-Water Flows past Slender Bodies", Journal of Fluid Mechanics, Vol. 27, 1966, pp. 81-95.

[16] Tuck, E.O.: "Sinkage and Trim in Shallow Water of Finite Width", Schiffstechnik Bd. 14, 1967, 92-94.

　

 The authors are grateful to cand. arch. nav. B. Friedhoff and cand. arch. nav. J. Hundemer for their assistance in computation and post-processing.

 Dr. Tao Jiang has obtained the Bachelor of Science in Naval Architecture at the Dalian University of Technology, the Diplom and Doctor Degree at the Institute of Shipbuilding of the University Hamburg, and the Habilitation Degree at the University Duisburg. Currently he is a Member of the Board and Manager Ship Hydrodynamics of the VBD. His main research fields are shallow-water hydrodynamics and nonlinear ship hydrodynamics.

　

 Rupert Henn has obtained the Diplom Degree in the Institute of Ship Technology at the Mercator University of Duisburg. Since 1999 he works as a research associate at the Institute of Ship Technology and Transport Systems at the University Duisburg-Essen. His main research interest is numerical ship hydrodynamics, particularly the application of shallow-water hydrodynamics.