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Nonlinear three-dimensional interfacial flows with a free surface

Published online by Cambridge University Press:  30 October 2007

E. I. PĂRĂU,
J.-M. VANDEN-BROECK and
M. J. COOKER
E. I. PĂRĂU
Affiliation:
School of Mathematics, University of East Anglia, Norwich, NR4 7TJ, UK
J.-M. VANDEN-BROECK
Affiliation:
School of Mathematics, University of East Anglia, Norwich, NR4 7TJ, UK
M. J. COOKER
Affiliation:
School of Mathematics, University of East Anglia, Norwich, NR4 7TJ, UK
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Abstract

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A configuration consisting of two superposed fluids bounded above by a free surface is considered. Steady three-dimensional potential solutions generated by a moving pressure distribution are computed. The pressure can be applied either on the interface or on the free surface. Solutions of the fully nonlinear equations are calculated by boundary-integral equation methods. The results generalize previous linear and weakly nonlinear results. Fully localized gravity–capillary interfacial solitary waves are also computed, when the free surface is replaced by a rigid lid.

Information

Type
Papers
Information
Journal of Fluid Mechanics , Volume 591 , 25 November 2007, pp. 481 - 494
Copyright
Copyright © Cambridge University Press 2007

References

REFERENCES

Avital, E. & Miloh, T. 1998 On an inverse problem of ship-induced internal waves. Ocean Engng 26, 99–110.CrossRefGoogle Scholar
Benjamin, T. B. 1992 A new kind of solitary wave. J. Fluid Mech. 245, 401–411.CrossRefGoogle Scholar
Calvo, D. C. & Akylas, T. R. 2003 On interfacial gravity–capillary solitary waves of the Benjamin type and their stability. Phys. Fluids 15, 1261–1270.CrossRefGoogle Scholar
Crapper, G. D. 1967 Ship waves in a stratified ocean. J. Fluid Mech. 29, 667–672.CrossRefGoogle Scholar
Dias, F. & Iooss, G. 1996 Capillary–gravity interfacial waves in infinite depth. Eur. J. Mech. B/Fluids 15, 367–393.Google Scholar
Ekman, V. W. 1904 On dead water. Norwegian North Polar Expedition, 1893–1896, Scientific Results vol. 5, pp. 1–150.Google Scholar
Forbes, L. K. 1989 An algorithm for 3-dimensional free-surface problems in hydrodynamics. J. Comput. Phys. 82, 330–347.CrossRefGoogle Scholar
Hudimac, A. A. 1961 Ship waves in a stratified ocean. J. Fluid Mech. 10, 229–243.CrossRefGoogle Scholar
Hughes, B. A. 1986 Surface wave wakes and internal waves wakes produced by surface ships. Proc. 16th Symp. Naval Hydrodyn. Berkeley, CA, pp. 1–17.Google Scholar
Keller, J. B. & Munk, W. H. 1970 Internal wave wakes of a body moving in a stratified fluid. Phys. Fluids 13, 1425–1431.Google Scholar
Kim, B. & Akylas, T. R. 2005 On gravity–capillary lumps. J. Fluid Mech. 540, 337–351.Google Scholar
Kim, B. & Akylas, T. R. 2006 On gravity–capillary lumps. Part 2. Two-dimensional Benjamin equation. J. Fluid Mech. 557, 237–256.Google Scholar
Laget, O. & Dias, F. 1997 Numerical computation of capillary–gravity interfacial solitary waves. J. Fluid Mech. 349, 221–251.CrossRefGoogle Scholar
Lamb, H. 1932 Hydrodynamics, 6th edn. Cambridge University Press.Google Scholar
Landweber, L. & Macagno, M. 1969 Irrotational flow about ship forms. Iowa Institute of Hydraulic Research Rep. IIHR 123, 1–33.Google Scholar
Părău, E. I. & Vanden-Broeck, J.-M. 2002 Nonlinear two and three dimensional free surface flows due to moving disturbances. Eur. J. Mech. B/Fluids 21, 643–656.CrossRefGoogle Scholar
Părău, E. I., Vanden-Broeck, J.-M. & Cooker, M. J. 2005 a Nonlinear three-dimensional gravity–capillary solitary waves. J. Fluid Mech. 536, 99–105.Google Scholar
Părău, E. I., Vanden-Broeck, J.-M. & Cooker, M. J. 2005 b Three-dimensional gravity–capillary solitary waves in water of finite depth and related problems. Phys. Fluids 17 (12), 122101.Google Scholar
Părău, E. I., Vanden-Broeck, J.-M. & Cooker, M. J. 2007 Three-dimensional gravity and gravity–capillary interfacial flows. Math. Comput. Simulation 74, 105–112.Google Scholar
Thompson, W. 1887 On ship waves. Proc. I Mech. E Reprint 1891. In Popular Lectures and Addresses vol. 3, pp. 450–500.Google Scholar
Tulin. M. P. & Miloh, T. 1991 Ship internal waves in a shallow thermocline: the supersonic case. Proc. 18th Symp. Naval Hydrodyn., pp. 567–581, National Academy Press.Google Scholar
Tulin, M. P., Wang, P. & Yao, Y. 1994 Numerical prediction of ship generated internal waves in a stratified ocean at supercritical Froude numbers. Proc. 6th Intl Conf. Numerical Ship Hydrodyn. pp. 289–309, National Academy Press.Google Scholar
Wey, G., Lu, D. & Dai, S. 2005 Waves induced by a submerged moving dipole in a two-layer fluid of finite depth. Acta Mec. Sin. 21, 24–31.CrossRefGoogle Scholar
Yeung, R. W. & Nguyen, T. C. 1999 Waves generated by a moving source in a two-layer ocean of finite depth. J. Engng Maths 35, 85–107.CrossRefGoogle Scholar
Yih, C. S & Zhu, S. 1989 Patterns of ship waves. Q. Appl. Maths 47, 17–33.Google Scholar