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ON THIN OR SLENDER BODIES

Part of: Fluid mechanics

Published online by Cambridge University Press:  12 October 2012

E. O. TUCK  and
Y. M. STOKES
E. O. TUCK
Affiliation:
School of Mathematical Sciences, The University of Adelaide, South Australia 5005, Australia (email: yvonne.stokes@adelaide.edu.au)
Y. M. STOKES*
Affiliation:
School of Mathematical Sciences, The University of Adelaide, South Australia 5005, Australia (email: yvonne.stokes@adelaide.edu.au)
*
✉For correspondence; e-mail: yvonne.stokes@adelaide.edu.au
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Abstract

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This is a review of thin-body and slender-body theories, with indications of some new applications. Topics discussed include bodies with near-constant surface pressure, subsonic and supersonic aerodynamics, ship hydrodynamics, slender bodies in Stokes flow, slender footings in elastic media, and slender moonpools. Mathematical features of the thin- and slender-body approximations are also discussed, especially nonlocal convolution terms modelling three-dimensionality in the otherwise two-dimensional near field, end effects, and the role of the logarithm of the slenderness ratio. This review was presented by the first author as the IMA Lighthill Memorial Lecture at the British Applied Mathematics Colloquium (BAMC) 2004.

Keywords

slender-body theoryfluid mechanicspotential flow

MSC classification

Secondary: 76-02: Research exposition (monographs, survey articles)
Type
Research Article
Information
The ANZIAM Journal , Volume 53 , Issue 3 , January 2012 , pp. 190 - 212
Copyright
Copyright © Australian Mathematical Society 2012

Footnotes

This is a contribution to the series of invited papers by past ANZIAM medallists (Editorial, issue 52(1)). Ernie Tuck was awarded the 1999 ANZIAM medal and died in 2009.

References

[1]Garabedian, P. R., “Calculation of axially symmetric cavities and jets”, Pacific J. Math. 6 (1956) 611–684; http://projecteuclid.org/euclid.pjm/1103043794.CrossRefGoogle Scholar
[2]Kalker, J. J., “On elastic line contact”, J. Appl. Mech. 39 (1972) 1125–1132; doi:10.1115/1.3422841.CrossRefGoogle Scholar
[3]von Kármán, T. and Moore, N. B., “Resistance of slender bodies moving with supersonic velocities, with special reference to projectiles”, Trans. ASME 54 (1932) 303–310.Google Scholar
[4]Lamb, H., Hydrodynamics, 6th edn (Cambridge University Press, Cambridge, 1932).Google Scholar
[5]Lighthill, M. J., “Supersonic flow past bodies of revolution”, Aeronautical Research Council’s Reports and Memoranda No. 2003 (1945).Google Scholar
[6]Lighthill, M. J., “A technique for rendering approximate solutions to physical problems uniformly valid”, Phil. Mag. Ser. 7 40 (1949) 1179–1201; doi:10.1080/14786444908561410.CrossRefGoogle Scholar
[7]Maruo, H., “Calculation of the wave resistance of ships, the draught of which is as small as the beam”, J. Zosen Kiokai 112 (1962) 21–37; doi:10.2534/jjasnaoe1952.1962.112_21.CrossRefGoogle Scholar
[8]May, A., “Water entry and the cavity-running behavior of missiles”, SEAHAC Technical Report 75-2, NAVSEA Hydroballistics Advisory Committee, Silver Spring, Maryland, 1975.Google Scholar
[9]Michel, J.-M. (ed.) Supercavitating flows, RTO Lecture Series 005, RTO-EN-010 (NATO Research and Technology Organisation, Neuilly-sur-Seine, 2002); http://www.rto.nato.int/Pubs/rdp.asp?RDP=RTO-EN-010.Google Scholar
[10]Michell, J. H., “The wave-resistance of a ship”, Phil. Mag. Ser. 5 45 (1898) 106–123; doi:10.1080/14786449808621111.CrossRefGoogle Scholar
[11]Molin, B., “On the piston and sloshing modes in moonpools”, J. Fluid Mech. 430 (2001) 27–50; doi:10.1017/S0022112000002871.Google Scholar
[12]Panek, C. and Kalker, J. J., “A solution for the narrow rectangular punch”, J. Elasticity 7 (1977) 213–218; doi:10.1007/BF00041093.CrossRefGoogle Scholar
[13]Reichardt, H., The laws of cavitation bubbles at axially symmetrical bodies in a flow, Volume 766 of Reports and Translations (Ministry of Aircraft Production, Moscow, 1946).Google Scholar
[14]Savchenko, Yu. N., “Experimental investigation of supercavitating motion of bodies”, in: Supercavitating flows, RTO Lecture Series 005, RTO-EN-010 (ed. J.-M. Michel), (NATO Research and Technology Organisation, Neuilly-sur-Seine, 2002); 4-1–4-24; http://www.rto.nato.int/Pubs/rdp.asp?RDP=RTO-EN-010.Google Scholar
[15]Tuck, E. O., “The steady motion of a slender ship”, Ph.D. Thesis, Cambridge University, 1963.Google Scholar
[16]Tuck, E. O., “Some methods for flows past blunt slender bodies”, J. Fluid Mech. 18 (1964) 619–635; doi:10.1017/S0022112064000453.CrossRefGoogle Scholar
[17]Tuck, E. O., “Toward the calculation and minimization of Stokes drag on bodies of arbitrary shape”, 3rd Australasian Conference on Hydraulics and Fluid Mechanics (Institute of Engineers, Australia, 1970) 29–32.Google Scholar
[18]Tuck, E. O. and Mei, C. C., “Contact of one or more slender bodies with an elastic half space”, Internat. J. Solids Structures 19 (1983) 1–23; doi:10.1016/0020-7683(83)90034-3.CrossRefGoogle Scholar
[19]Tuck, E. O. and Newman, J. N., “Longitudinal waves in slender moonpools”, in: 17th International Workshop on Water Waves and Floating Bodies (ed. Rainey, R.), (Royal Institution of Naval Architects, London, 2002).Google Scholar
[20]Tuck, E. O., Scullen, D. C. and Lazauskas, L., “Wave patterns and minimum wave resistance for high-speed vessels”, in: 24th Symposium on Naval Hydrodynamics (Office of Naval Research, Washington, DC, 2002).Google Scholar
[21]Tulin, M. P., “Steady two-dimensional cavity flows about slender bodies”, Report No. 834, Navy Department, David W. Taylor Model Basin, 1953.Google Scholar
[22]Tulin, M. P., “On the shape and dimensions of three-dimensional cavities in supercavitating flows”, Appl. Sci. Res. 58 (1998) 51–61; doi:10.1023/A:1000707013033.CrossRefGoogle Scholar
[23]Vossers, G., “Some applications of the slender body theory in ship hydrodynamics”, Ph.D. Thesis, Delft University, 1962.Google Scholar
[24]Ward, G. N., Linearised theory of steady high-speed flow (Cambridge University Press, Cambridge, 1955).Google Scholar
[25]Wehausen, J. V. and Laitone, E. V., Surface waves, Volume IX of Encyclopedia of Physics (ed. Flügge, S.), (Springer, Berlin, 1960) 446–778; http://coe.berkeley.edu/SurfaceWaves/.Google Scholar