Waves Generated by a Moving Source in a Two-Layer Ocean of Finite Depth
Rent the article at a discountRent now
* Final gross prices may vary according to local VAT.Get Access
The velocity potentials of a point source moving at a constant velocity in the upper layer of a two-layer fluid are obtained in a form amenable to numerical integration. Each fluid layer is of finite depth, and the density difference between the two layers is not necessarily small. The far-field asymptotic behavior of the surface waves and internal waves are also derived using the method of stationary phase. They show that the wave system at the free surface or at the interface each contains contributions from two different modes: a surface-wave mode and an internal-wave mode. When the density difference between the two layers is small or the depth of the upper layer is large, the surface-wave mode mainly affects the surface waves while the internal-wave mode mainly affects the internal waves. However, for large density difference, both modes contribute to the surface wave or internal wave system. For each mode, both divergent and transverse waves are present if the total depth Froude number is less than a certain critical Froude number which is mode-dependent. For depth Froude number greater than the critical Froude number, only divergent waves exist for that mode. This classification is similar to that of a uniform fluid of finite depth, where the critical Froude number is simply unity. The surface waves and internal waves are also calculated using the full expressions of the source potentials. They further confirm and illustrate the features observed in the asymptotic analysis.
- V. W. Ekman, On dead water. Norwegian North Polar Expedition, 1893–1896, Scientific Results 5 (1904) 1–150.
- T. Miloh and M. P. Tulin, A theory of dead water phenomena. Proc. 17th Symp. Naval Hydrodyn., The Hague (1988) 127–142.
- T. Miloh, M. P. Tulin and G. Zilman, Dead-water effects of a ship moving in stratified seas. J. Offshore Mech. Arctic Eng. 115 (1993) 105–110.
- B. A. Hughes, Surface wave wakes and internal wave wakes produced by surface ships. Proc. 16th Symp. Naval Hydrodyn., Berkeley, CA (1986), 1–17.
- M. P. Tulin and T. Miloh, Ship internal waves in a shallow thermocline: the supersonic case. Proc. 18th Symp. Naval Hydrodyn., Ann Arbor, MI (1991) 567–581.
- J. B. Keller and W. H. Munk, Internal wave wakes of a body moving in a stratified fluid. Phys. Fluids 13 (1970) 1425–1431.
- C. S. Yih and S. Zhu, Patterns of ship waves. Q. Appl. Math. 47 (1989) 17–33.
- M. P. Tulin, P. Wang and Y. Yao, Numerical prediction of ship generated internal waves in a stratified ocean at supercritical Froude numbers. Proc. 6th Int. Conf. Num. Ship Hydrodyn. Iowa City (1993) 519–539.
- H. L. Wong and S. M. Çalişal, Numerical algorithms for slender bodies with vortex shedding and density stratification. J. Ship Res. 40 (1996) 11–21.
- R. W. Yeung and S. H. Kim, A new development in the theory of oscillating and translating slender ships. Proc. 15th Symp. Naval Hydrodyn. Hamburg, W. Germany (1984) 195–212.
- A. A. Hudimac, Ship waves in a stratified ocean. J. Fluid Mech. 11 (1961) 229–243.
- G. D. Crapper, Ship waves in a stratified ocean. J. Fluid Mech. 29 (1967) 667–672.
- L. N. Sretenskii, On the wave resistance of ships in the presence of internal waves. Izv. Akad. Nauk C. C. C. R., Otdelenie Tekhnicheskikh 1 (1959) 56–63.
- P. N. Uspenskii, On the wave resistance of a ship in the presence of internal waves under conditions of finite depth. Akad. Nauk USSR Tr. Morskogo Gidrophizicheskogo Instituta 18 (1959) 68–84.
- T. Sabunçu, The theoretical wave resistance of a ship travelling under interfacial wave conditions. Trondheim: Norwegian Ship Model Exp. Tank (1961) 124 pp.
- J. H. Michell, Wave resistance of a ship. Phil. Mag. 5,45 (1898) 106–123.
- H. Lamb, Hydrodynamics. New York: Dover Publication Inc. (1932) 738 pp.
- I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products. Orlando: Academic Press (1980) 1160 pp.
- H. L. Pond, The theoretical pressure signature of bodies represented by source distributions. Maryland: DTMB Rep. No. C-743 (1957) 38 pp.
- E. T. Copson, Asymptotic Expansions. Cambridge: Cambridge U. Press (1967) 119 pp.
- J. V. Wehausen and E. V. Laitone, Surface waves. Handbuch der Physik 9 (1960) 446–778.
- Y. K. Chung and J. S. Lim, A review of the Kelvin ship wave pattern. J. Ship Res. 35 (1991) 191–197.
- S. D. Conte and C. Boor, Elementary Numerical Analysis. New York: McGraw-Hill (1980).
- T. Nguyen and R. W. Yeung, Steady-wave sytems in a two-layer fluid of finite depth. Proc. 12th Int. Workshop Water Waves and Floating Bodies. Marseilles, France (1997) 115–119.
- Waves Generated by a Moving Source in a Two-Layer Ocean of Finite Depth
Journal of Engineering Mathematics
Volume 35, Issue 1-2 , pp 85-107
- Cover Date
- Print ISSN
- Online ISSN
- Kluwer Academic Publishers
- Additional Links
- gravity waves
- internal waves
- satisfied flow
- Green's function
- shallow-water effects
- Founde number
- wave patterns
- Industry Sectors