# Hydrodynamic effects on fast monohulls or catamarans travelling through the critical speed in shallow water

## DOI:

https://doi.org/10.21914/anziamj.v51i0.2635## Keywords:

ship, hydrodynamics, transcritical## Abstract

The speed of linear waves in shallow water approaches a constant value as the wavelength becomes large relative to the water depth. For ships travelling in shallow water, this speed is known as the `critical speed' and acts as a barrier, similar to the speed of sound for aeroplanes. The possibility of travelling at transcritical and supercritical speeds is discussed for existing monohull and catamaran ships. We explore the predicted linearised flow around a ship as it approaches the critical speed, and the singularities that result. Experimental results show the actual flow patterns that occur at ship speeds close to the critical speed, for monohulls or catamarans, in open water or confined channels.**References**

- Ang, W. T. 1993
*Nonlinear sinkage and trim for a slender ship in shallow water of finite width*. Internal report, University of Adelaide. - Chen, X. N. 1999
*Hydrodynamics of wave-making in shallow water*. Ph.D. thesis, University of Stuttgart. - Chen, X. N., Sharma, S. D. and Stuntz, N. 2003 Wave reduction by S-Catamaran at supercritical speeds.
*Journal of Ship Research***47**, No. 1, pp. 1--10. - Constantine, T. 1960 On the movement of ships in restricted waterways.
*Journal of Fluid Mechanics***9**, pp. 247--256. doi:10.1017/S0022112060001080 - Dand, I. W., Dinham-Peren, T. A. and King, L. 1999 Hydrodynamic aspects of a fast catamaran operating in shallow water.
*Proceedings, Hydrodynamics of High Speed Craft*, London, November 1999. - Gourlay, T. P. 2000
*Mathematical and Computational Techniques for Predicting the Squat of Ships*. Ph.D. thesis, University of Adelaide. - Gourlay, T. P. 2001 The supercritical bore produced by a high-speed ship in a channel.
*Journal of Fluid Mechanics***434**, pp. 399--409. doi:10.1017/S002211200100372X - Gourlay, T. P. and Tuck, E. O. 2001 The maximum sinkage of a ship.
*Journal of Ship Research***45**, No. 1, pp. 50--58. - Gourlay, T. P., Duffy, J. T. and Forbes, A. 2005 The bore produced between the hulls of a high-speed catamaran in shallow water.
*International Journal of Maritime Engineering***147**, Part A3, pp. 1--8. - Gourlay, T. P. 2006 A simple method for predicting the maximum squat of a high-speed displacement ship.
*Marine Technology***43**, No. 3, pp. 146--151. - Gourlay, T. P. 2008 Sinkage and trim of a fast displacement catamaran in shallow water.
*Journal of Ship Research***52**, No. 3, pp. 175--183. - Graff, W., Kracht, A. and Weinblum, G. 1964 Some extensions of D. W. Taylor's standard series.
*Trans. SNAME***72**, 374--401. - Huang, D. B., Sibul, O. J., Webster, W. C., Wehausen, J. V., Wu, D. M. and Wu, T. Y. 1982 Ships moving in the transcritical speed range.
*Proceedings, Conference on Behaviour of Ships in Restricted Waters, Varna*, Vol. II, pp. 1--10. - Insel, M. 1990
*An investigation into the resistance components of high speed catamarans.*Ph.D. thesis, Department of Ship Science, University of Southampton. - Lea, G. K. and Feldman, J. P. 1972 Transcritical flow past slender ships.
*Proceedings, 9th Symposium on Naval Hydrodynamics*, ONR, Washington D.C., p1527. - Mei, C. C. 1976 Flow around a thin body moving in shallow water.
*Journal of Fluid Mechanics***77**, pp. 737--751. doi:10.1017/S0022112076002863 - Michell, J. H. 1898 The wave resistance of a ship.
*Philosophical Magazine***45**, pp. 106--123. - Mueller-Graf, B. 1995 General resistance aspects of advanced fast marine vehicles.
*Proceedings, Design of Advanced Fast Marine Vehicles*, September, Glasgow. - Newman, J. N. 1977
*Marine Hydrodynamics*, MIT Press. - Stoker, J. J. 1957
*Water Waves*. Interscience. - Tuck, E. O. Shallow water flows past slender bodies.
*Journal of Fluid Mechanics***26**, pp. 81--95. doi:10.1017/S0022112066001101 - Tuck, E. O. 1974 One-dimensional flows as slender-body problems, with applications to ships moving in channels.
*Proceedings, Workshop on Slender Body Theory*, Ann Arbor. University of Michigan Report NAME 164, pp. 27--35.

## Published

2010-04-27

## Issue

## Section

Proceedings Engineering Mathematics and Applications Conference